DE1547523B2 - planetarium - Google Patents

Description

The invention relates to a planetarium with a star field projector, sun, moon, earth and planet projectors as well as drive devices for the projectors with an electrical computing device and a coordinate converter with resolvers to control the star field projector, the planetary projectors are arranged separately from the star field projector

Such a planetarium is known from US Pat. No. 3,074,183 Hereafter and the rest In the prior art, there was no planetarium on the priority day, in which the planetary projectors as well as one sun, one earth and one moon projector, spatially and temporally completely independent of the star field pro- ' jektor are adjustable and controllable. It has already become extraordinarily complex mechanical and electronic Facilities run just looking at the stars and planets from wants to imitate an observation place on earth or between earth and moon. In the case of the mentioned Publication is the representation of a second planet, e.g. B. Mercury, through a projection device made, namely like this second planet for an observer on earth appears opposite the fixed star sky. The earth-centric location is essential here, see above that the earth is understood as a fixed center and the sun is assumed to revolve around the earth will. Another planet (Venus) revolves around the sun on a circular orbit. One is with this one known planetarium tied to the observation of the ecliptic plane of the body. There are Observations from the earth or possibly positions of one body relative to the other in the solar system shown from the in said publication; indicated angles and arrows for the direction of travel one recognizes that - as with all other previous devices in planetarium technology - it is a kind of clockwork acts The essence of the clockwork is counting. It will be in the well-known planetariums Movements are provided that take place in a certain mechanical relationship and coupling to one another, because otherwise obvious problems with the coupling of the individual celestial bodies to one another would arise. In all known devices, analogs (mechanical-optical display device for the celestial bodies) arranged on the same frame or stand The problem persists in the known case in the representation of bodies running in the ecliptic plane. A departure from this was out of the question because otherwise obvious mechanical and computational difficulties would arise would be. That is why one has so far always limited oneself to earth-related observations and representations.

As far as the imitation of planetary orbits is concerned, according to older German patents 14 97 739 and 14 97 740 the time-controlled coupling of the

Planet projectors eliminated with the star field projector older proposal can optionally be set to any desired part of its orbit. The those However, representations that imitate planets are still aimed at mimicking orbits limited as seen from or near the earth.

The invention is therefore based on the object of creating a planetarium of the known type, which is in complete independence of the planetary projectors from the star field projector a perfect projection of all planets, including the sun, moon and earth, in the star field, viewed by each Any point within the solar system is permitted, even if the observation location changes quickly

This object is achieved according to the invention in that the sun, moon, earth or planet projectors are controllable by means of coordinate converters with electromechanical resolvers depending on the observer position or the observed point and a so-called line of sight Planet projectors - separated from each other and driven so that Cartesian coordinates (xp, Yp, z _p ) are formed from the parameters (ξ, i, Ω, r) of the respective planetary orbit, which are converted into the control signals for the servomotors of the respective Planet projector are transformed, and that each sun, moon, earth or planet projector has at least two separate drive devices, each with a radiation deflecting device

The new planetarium system can be controlled by computers to a greater extent than known systems, so that it is more adaptable; this in particular insofar as it is an observer somewhere in the solar system can imitate. The new plant can equally to a greater extent than before those effects and Mimic effects that occur in cislunar space, areas of the Solar system, to be seen. The new invention is not just about getting rid of the temporal Restrictions, but also the exemption from restrictions on position in space to such a degree enables any position in the space of the solar system to be imitated.

In contrast to the well-known systems in which the planetary projectors are based on the imitation of Orbits seen from or near-earth are now restricted to Planet projectors as well as one sun, one earth and one moon projector are completely independent in terms of space and time adjustable and controllable by star field projector. These possibilities are now according to the invention created, although these possibilities for observation go beyond the earth or near-earth space from places outside the ecliptic plane and, what is even more difficult, outside space between earth and moon, d. H. somewhere in the entire solar system, given the obvious at first sight Difficulties were not envisaged.

According to the invention, the usual mechanical coupling between Abandoned star field projector and planetary projectors, rather these are now all according to the invention arranged and driven separately from each other. The anticipated major complication was due Creation of a connecting computer system compensates which signals for the drive devices generated by all projectors. According to the invention, so-called line-of-sight vectors are created by a further trick generated, with the help of which a much simpler coupling with the star field projector is made possible.

The subject matter of the invention is not just about simulating space flight outside the plane of the ecliptic, but rather it is more general about the observation of a any starfield planetary constellation from anywhere in the solar system in one any point in time including past and future periods in which, for example, the The celestial pole does not coincide with today's Pole Star.

The new and special thing about the planetarium according to the invention is the fact that you can use the Can simulate movement through space. This means first of all that one can observe any planet in the solar system, or any place between or outside of the planets the planetary plane can simulate. Outside the plane, the observer looks at the planetary orbits down like full ellipses instead of line segments, all generally at the stick to the ecliptic plane.

The movement through the solar system outside the ecliptic plane is simulated to date to bring about an unimagined effect. This one is especially noteworthy and important when you think about this Relative visibility and the rapid change in position of a planet is simulated as soon as it comes on one passes more or less closely in space

The detachment from the clockwork system also has the advantage that the movement motors only from Need to be moved position to position, d. H. only briefly until the correct position is reached of the projector are turned on.

By the mutually independent radiation deflecting devices, which in an expedient embodiment Are mirrors, setting options in in a simple and low-maintenance manner. It is also advantageous if every mirror is closed its axis of rotation is attached at an angle and the axes of rotation in different directions to each other lie. For example, one axis of rotation can be in the horizontal and the other in the vertical of the Electric motor can be driven. In this way, one adjustment is sufficient for faster adjustability by a few degrees in order to move the projected object to another desired location on the dome.

In an advantageous further development of the invention, the parameters of the respective planetary orbit the Cartesian coordinates formed by means of coordinate converters by adding circuits for generating the component signals of the line-of-sight vectors between the observer position and the observed Point the coordinate signals corresponding to the coordinates assigned to one another Add coordinate converters to each other. It is also useful here if as a position computer trained further coordinate converters provided

which are the components of the line of sight vectors corresponding signals in the coordinates of a Cartesian one related to the star field projector Convert corresponding signals to the coordinate system and the motion motors only from position to Move position.

Another embodiment of the invention is characterized in that the coordinate converter has three resolvers, the first resolver has a fixed, the radius of a certain planet from Sun zero point or the observer distance from the sun representing signal input and that the Outputs of this resolver are each placed on one of two inputs of the other two resolvers are.

It is also beneficial if a simplified coordinate converter has only two resolvers while eliminating the angular variable Ω , and it is also useful if the position computer has five resolvers and a parallax correction signal is applied to one input of the last two of the resolvers in series . By attaching resolvers to the motor shafts to indicate the position, operation is simplified. In one embodiment, the beam direction of the light source is expediently aligned vertically, the computer system is expediently arranged at a distance from the respective projector and the only connection between the projector and the computer system are electrical lines. Such a system is very suitable for teaching purposes and makes the simulation more realistic, so that the effects caused are not disturbed by the lecturer or the technician operating the computer system. For example, the star field projector can be equipped with at least three axes of rotation, and at least one position sensing device is coupled to the computer system.

The representations described above and achieved by the planetarium according to the invention are made possible by using coordinate converters for converting into rectangular coordinates. The device used takes the difference between the corresponding rectangular coordinates and generates the components of line of sight vectors from an observer position to an observed point in celestial coordinates. (The input signal to these coordinate converters or computer systems is information about the position of a line of sight vector.) This information is then converted into spatial coordinates by position computers in order to generate the signals that are necessary for setting the projector, which imitates the point under consideration. Said information is preferably generated by using a reference system, e.g. B. a system with the zero point in the center of the sun, with axes extending to the North Star, the vernal equinox and in a direction perpendicular to these two axes. Positions described on the dome representing the celestial sphere in width units, length and the like are then converted into right-angled coordinates (e.g. x, y and z) which are perpendicular to one another, with the pole in the Z-axis and the Spring point lie in the X-axis. The line-of-sight vectors are then obtained from the rectangular coordinates.

The invention also enables the use of an earth-centered reference system when the cislunar or space on this side of the moon is considered. This frame of reference can in turn be within of the sun-centered reference system for other parts of the solar system by imitating the earth in this System coordinated. The cislunar space is defined here in such a way that it is twofold Moon distance from earth extends. The mutual positions of the earth, the moon and an observer ίο at any chosen location in cislunar space can be determined by procedures which determine the procedures used for planets and general observers in solar system space are similar. The invention also enables a realistic imitation of the phases of the moon and the Earth from any observation position. It also enables the viewing of the Moon and earth in and near the orbit of the moon. It also enables the correction of the lunar and earth position when the position of an observer in cislunar space changes.

In the following, the invention is explained in more detail with reference to the figures, for example. It shows

F i g. 1 shows a schematic section through the planetarium including the planetarium device, des domed auditorium and the control table,

F i g. 2 shows a side view of the planetetarium device with separate planetary and star field projectors,
F i g. 3 shows a section along the line 3-3 in FIG. 2,
F i g. 4 shows a section along the line 4-4 in FIG. 3,
F i g. 5 shows a section along the line 5-5 in FIG. 2,
F i g. 6 one of the F i g. 2 similar view, in which another embodiment of a celestial sphere projector is shown,

F i g. 7 is a top plan view taken along line 7-7 in FIG. 2 on one of the planetary projectors,

F i g. 8 is a partially broken away and sectioned side view of the FIG. 7 planetary projector shown,

F i g. 9 is a schematic representation of a preferred coordinate system which, according to the invention is advantageously used for the axes of the planetarium device,

Fig. 10 is a graph showing the orbit and position of a planet in its

Overlay shown with the preferred rectangular coordinate system according to the invention are,

11 shows a circuit diagram of a coordinate converter for the planetary position,

FIG. 12 is a graph similar to FIG. 10 Representation, which, however, relates in particular to the orbit and position of the earth,

F i g. 13 a circuit diagram of a coordinate converter for the earth position,

Fi g. 14 a coordinate converter for a generalized Observer position in the space of the solar system,

F i g. 15 is a schematic representation of a system that includes planetary and earth coordinate converters Line-of-sight computing systems in an earth mode, with the planet and the sun be observed as if observed from the surface of the earth, expressed in the celestial Reference system,

F i g. 16 is a schematic representation of a system in which a general observer transducer with Earth and planet converters to line-of-sight computing

genes can be summarized in a general observer mode, with the earth being another Planet and the sun are observed as if they were from a selected point in the space of the solar system would be observed from

17 shows a schematic representation of a system for a number of observation computer systems in one Planet mode, whereby the earth and another planet and the sun are observed as if they were observed from a third planet,

F i g. 18 a circuit diagram of a planetary position computer system,

19 is a circuit diagram in which a general Observer is combined with a lunar coordinate converter to form a line-of-sight computer, observing the moon as if it were being observed from a selected point in cislunar space would,

F i g. 20 is a circuit diagram of a coupling system for coupling components, whereby the coordinate conversion an earth-centered observation is made possible in a sun-centered one,

Fig. 21 is a schematic representation of earth, Sun and moon, in which the geometry of the moon phases is shown,

F i g. 22 a circuit diagram of a system for calculating the phases of the moon in the planetarium,

F i g. 23 is a schematic diagram showing an apparatus for solving the problem is, which occurs with the moon position control,

Fig. 24 is a circuit diagram of the computer system for controlling the moon position,

F i g. 25 is a schematic diagram showing the geometry of the lunar view control;

F i g. 26 is a circuit diagram of the moon view control computer;

Fig. 27 a summarizing circuit diagram of a Embodiment of the complete planetarium system according to the invention,

F i g. 28a a schematic representation of the spherical triangle, which is solved by the computing system must be to the in F i g. 2 correctly set the star field projector shown,

F i g. FIG. 28b is a schematic representation of the modified spherical triangle which is used by the computing system must be solved to the in F i g. 6 correctly set the star field projector shown,

F i g. 29 is a block diagram in which components of computing systems are shown that are used in the Planetarium according to the invention can be used,

F i g. 30 a circuit diagram of a computer system for the general daily rotation in a star field projector,

F i g. 31 is a circuit diagram of a computer system showing a shift from vertical to non-vertical compensates vertical axis in a star field projector,

F i g. 32 a circuit diagram of a computer system which fao a shift of a polar axis of a star field projector from a position passing through the polar star balances, and

F i g. 33 is a circuit diagram of a computer system that includes a selected amount of movement by longitudinal, The transverse and vertical axes of the setting or movement of a star field projector are superimposed.

The plant in FIG. 1 consists of a planetarium device 1, a hemispherical ball 2, the device being approximately in the middle of the enclosed space. Suitable seats are preferably arranged within the room along a floor which is stepped, but they can also be arranged in a conventional manner in a circle on a flat floor. A control table 3 is arranged at any point in the room, preferably behind the auditorium seating arrangement. The planetarium show is set and programmed from this control desk, and the operating mode of the planetarium can be controlled from there. The control table includes machine controls, meters, input selector switches, and other devices.
As shown in FIG. 2 is the star field projector

4 of the planetarium device 1 separated from the projectors 5, which planets, the sun, the moon and the Project earth and natural and artificial satellites of all kinds. By separating the planetary and Auxiliary projector from the star field projector is a substantial reduction in mass and possibly the volume of the star field projector allows. The low inertia achieved in this way enables the Use of auxiliary effects, such as the imitation of movements around the longitudinal, transverse and vertical axes. the separate projectors for each planet also have low inertia and are different in their operation very adaptable. Because they are separate, these projectors require a sequential, through a Computer controlled coordination with the star field. The planetary movements don't just have to the daily movement and others beforehand with the change of an observer position on the earth's surface connected movements, but each movement are superimposed, which changes the Imitates observer position and orientation in space. Separate projectors with a universal Adjustment options also enable projections of planets, sun, moon and earth against each part of the star field, not just on the general area of the ecliptic, creating the mimicking of an observation their orbits from any possible starting point. This additional Adaptation is therefore important when imitating spaceship flights or the like, and mimicking the effects of roll, pitch, and yaw can make such mimicked flights make it even closer to reality.

In the following, the star field projector 4 in FIG. 2 and the associated F i g. 3,4 and

5 referred to. First of all, the separation of the star field projector 4 from the planetary projectors 5 can be clearly seen, so that the star field projector can be designed as a spherical unit as a hollow spherical housing 10. The housing 10 contains a suitable light source in conjunction with a suitable dimming device forming the horizon and is provided with known, suitable lenses and holes to display the brighter stars and Milky Way on the sky dome. However, only approximately one hemisphere is projected onto the planetarium dome at the same time. In order to allow this star field projector mimics the sky, as seen from any place on earth or from any point in space of the solar system, the ball 10 must all possible rotational adjustments around its center with respect to the planetarium dome 2 in the in F i g . 1 can perform the arrangement. Around

809 525/7

To effect such an adjustment or orientation, the ball must have at least three axes of rotation (I, II or III) provided. In a three-axis system, the axis I is preferably a polar axis, which is so is arranged to coincide with the polar axis of the earth to make terrestrial effects easier to be able to imitate, like the daily rotation of the earth, which takes place around its axis. The axis III is preferably a vertical axis about which the sphere

10 is rotated to change the direction of movement or flight with respect to the planetarium dome. The axis

11 is perpendicular to axes I and III and is at of the preferred embodiment used to mimic declination differences. The axes I and III can of course also be oriented in a different way.

As can be seen from Fig.2, the axis III is through the fork 11 is formed, soft on bearings between their vertically arranged drive shaft 12 and a suitable rigid base 13 rotates, which in turn on the Common base 14 can be attached to which the planetary projectors 5 are also attached. A Motor 15, which is fixed to the base, is used to rotate the drive shaft 12 with respect to the base 13 the generally vertical axis III due to the meshing of the gear 16 fixed to the motor shaft and the Wave 12 used. A similar gear connection couples a function resolver 17 or one similar position sensor with the shaft 12, relative to the angular position of the shaft 12 about the axis III a predetermined reference position to be scanned. The arms 18 of the fork 11 form the bearings for peg-like Projections 19 from the Rint 20, which coincide with the axis II. A drive motor 21 is on one of the Fork arms 18 attached (see Fig. 5). A gear 22 On the shaft of the motor 21, a gear 23 drives one of the trunnions 19 and thereby the ring 20 to which the pivot pins are attached, with respect to the fork arms 18 about the horizontal axis II. As shown in FIG F i g. 5 shows a function resolver 24 for scanning the rotary position of the star field projector the axis II according to the German patent 13 03 505 is used.

The resolver 24 is held by the fork 18 so that its shaft rotates with the pivot 19.

The ball 10 is on the other hand on the ring 20 in suitable bearings by aligned, rod-like projections 27 rotatably mounted, which define the axis I and one of which is the shaft of the ball 10 fixed function resolver 28 forms. In the illustrated embodiment, a movement of the Ball 10 with respect to the ring 20 around the axis I, preferably the polar axis, through the equatorial Ring flange 29 caused on the ball 10. As shown in FIGS. 3 and 4, the flange 29 of gripped a pair of rollers 30 with their beveled edges against the beveled edge of the perimeter of the Annular flange 29 are printed so that a frictional contact is generated, and if one of the Rollers 30 is set in rotation, the flange 29 is moved by means of the rollers by friction and thereby the ball 10 is driven about its axis I formed by the projections 27. The roles are within parallel flanges of a holder 32, which in turn is held by the ring 20, as best from Fig. 3 can be seen. The rollers are provided with shafts 33 lying in a line, which in the parallel Flanges 34 of the holder 32 are rotatably mounted, and they are supported by spring elements 35 along their shaft pressed together. The annular flange 29 is held between the rollers 30. One of the roller shafts 33 ends in a bevel gear 38, which in turn meshes with a bevel gear 39 on a shaft 40, which in FIG a part of the same holder 32 is rotatably mounted, the motor 42 also being attached to this holder. The shaft 40 is preferably the shaft of the motor 42, so that the drive by the motor via the ίο the conical edge 40 is transferred to the bevel gear 38 and from there to the roller 30 on the shaft 33. As a result of the Frictional contact with the annular flange 29 generating spring force move both rollers 30 with the same speed and thereby drive the flange 29 and the ball 10.

Due to various difficulties that arise with a cardanic bearing, the star field projector, to give him greater mobility or adaptability, with a fourth axis be equipped, as shown in the embodiment shown in Fig.6. With this arrangement the polar axis can go through zenith positions without a shift of 180 ° by one or more of the Axes must be done and response difficulties occur, which are often associated with a three-axis Arrangement occur.

In Fig. 6, corresponding parts are provided with the same reference numerals, but with a prime is added. Instead of the vertical shaft 50 serving as the shaft of the fork 11 'in this case, the shaft 50 is here rather attached to a base segment-shaped carrier 52, which in turn supports the shaft 12 'of the fork 11' rotatably supported in a suitable bearing, whereby a rotation about the axis of the shaft 12 '

-'5 is possible. A drive motor 54, which is held by the base 13 ′, drives the shaft 50 and thereby the segment part 52 via gear wheels 55 in order to set the direction of the axis III defined by the shaft 12. The segment part 52 itself is rotated with respect to the base 13 ′ about the axis of its vertically arranged shaft 50. A scanner 56 in the manner of a resolver scans the position of the shaft 50 and the segment 52. The shaft 12 'can also be viewed here as the axis III, which is inclined at an angle T. the

Fork 11 'is driven by motor 15' via shaft 12 'by means of ( Driven gears 16 '. The resolver 17 'scans the shaft setting about the axis III. The gear 17 'is mounted coaxially on the shaft 50. It can be seen that the shaft 50 has a new fourth axis

so results and that a relative rotation around all four axes is possible.

With the exception of the differences explained, it can be assumed that the one shown in FIGS. 2 to 5 The star field projector 4 shown and the one shown in FIG. 6 are identical in all essential parts. Several planetary projectors are assigned to the star field projector, the number of which corresponds to the desired representation can be changed. As a schematic representation of a possible arrangement is in Fig. 1 shows a number of planetary projectors which have different heights so that they do not stand in each other's way and that the light switch-off of the star field projector is as small as possible and that The star field projector does not shade any light from the same. Various other arrangements can be used be chosen for this purpose, the planetary projectors even at a great distance from each other be arranged at the ends of the room

can. If the star field projector is in the middle, corrections have to be made for those that have moved out of the middle Positions of the planetary projectors are attached to the correct orbits of the respective Preserve planets. Such corrections can be made in the given to the motors of the planetary projectors Signal can be made. The individual planetary projectors stand with their frames on the Base 14. The frames 60 can also have any inclined shape. With every planetary projector a light source 61 is connected, which is used to represent the respectively projected celestial objects Size, color, features and orientation is provided. The light source is arranged so that you Light beam is projected upward through the upper end of the frame 60 and onto a mirror 63 hits. The mirror 63 has a fixed angle on the order of 45 ° with respect to the vertical on the light beam, whereby the light is deflected from a vertical to a horizontal direction. The light beam is again deflected from the horizontal by a second mirror 65, which the Light beam reflected in the desired direction so that it is on the planetarium dome 2 at a selected point.

The mirror system of the planetary projectors is based on the F i g. 7 and 8 explained in more detail. From Fig. 7 and 8 it can be seen that the mirrors 63 and 65 are mounted on a turntable 67 at the upper end of the frame 60 are. The turntable has a vertically arranged axis and is with suitable bearings between the upper one The end of the frame and the turntable. A rotation of the turntable with respect to the frame is Caused by means of the motor 68, which is attached to the frame and whose shaft the turntable 67 and also drives the resolver 70 via gears 69. Attached to the turntable and with this itself rotating is the holder 72, which the mirror 63 in its selected position at about 45 ° against the holds vertical light beam. The turntable is hollow so that the light beam from the light source 6t can be unobstructed can impinge through the same on the mirror 63. The mirror 63 is on the holder part 74 of the Turntable mounted rotatably by a shaft 75, the axis of rotation with that of the mirror 63 reflected light bundle coincides.

The shaft 75 is rotatably mounted in the holder 74 and can rotate about its longitudinal axis, and the mirror 65 is rigidly attached to the end of the shaft 75, preferably so that the plane of the mirror 65 a selected angle here in the order of 45 ° with the shaft. The angles are like that chosen that by the combination of the rotation of the turntable 67 and the shaft 75 of the mirror 65 the Can project light bundles on the zenith and on any other place of the planetarium dome 2. If those Condition is met, then by a combination of the rotation of the turntable 67 and the rotation the shaft 75 the light beam successively on all successively selected points in the planetary orbit on the planetarium dome 2. The rotation of the shaft 75 is controlled by the resolver 77 is scanned, which is driven by gears 78 which also connect the motor 79 to the shaft 75. The motor 79 and the resolver 77 are also attached to the holder 74 in a three-axis star field projector system it is preferred that the axis of the planetary projector, which is fixed in space, is parallel runs to the axis III of the star field projector.

Because the star field from the solar system or from the range of the visible with the naked eye The planets are essentially unchanged, are star projectors showing the positions of the Stars do not change in relation to each other, quite useful because the star field as a whole is movable. However, the same is not true of the planets. The planets are in the planetarium through projectors simulated, which can be mechanically simpler than known planetary projectors.

According to the invention it is necessary to choose a universal frame of reference which is applicable to the whole Space of the solar system is usable. Appropriately, such a reference system is sun-centered, since the sun is the center of the solar system and the planets revolve around it. It is possible that To choose reference system axes for the star field in any way, since our earthbound Observation point will still occupy a large part of the planetarium's useful life, a suitable reference system is obtained if the direction to the celestial pole is chosen as the z-axis. The direction to the vernal equinox is then at right angles to this axis and therefore results in an expedient one X axis. The third or y-axis can then be chosen perpendicular to these two axes. These axes are shown in FIG. 9 combined with the axes of the planetarium system. When Polarstern and The vernal equinox is chosen as a pair of mutually perpendicular axes, the third lies beyond that Axis in the equatorial plane.

In a terrestrial mode of operation of the planetarium, this reference system rotates with respect to the Space around the polar axis to mimic the daily movement of the earth. At every point in the imitated In the space of the solar system, the reference coordinates are always identifiable and lie in relation to the star field fixed. F i g. 9 also shows the plane of the ecliptic, as this is of great importance for the geometry of the planetarium owns.

The in Fig. The coordinate system shown in FIG. 9 is used in FIG. 10 to describe the orbit of a planet. It can be seen from Figure 10 that the orbit of each planet spans a plane which intersects the equatorial plane at an angle Ω with the vernal equinox, which angle is constant for a given planet. The angle / between the planes is also constant. The position of the planet naturally changes within its orbital plane. If the planet's orbit is not circular, the quantity r _p -j representing its radius or distance from the sun cannot be constant. The angular velocity

German

the planet can also be considered variable with negligible error for the purposes of this Planetarium facility to be considered. The angular position from a reference point, such as the intersection of the Orbital plane, with the equatorial plane, then becomes the only variable, measured at the sun's zero point. The variable can be generated in an analogous manner, for example by using a common one Variable speed motor which is geared to the correct relative Generate periods which are associated with the rotation of shafts and other, analog, the

Planets including bodies representing the earth are characteristic of the sun. The angular position of the shaft of each, the planet The analog device representing the variable then becomes the planet representation.

It can be seen from Fig. 10 that from coordinates which correspond to the right ascension and declination in the star field, if the radius r _p - _{s is} added, the planetary position in right-angled coordinates of the planets Xp, y _p and z at a given point in the orbit _p can be expressed as shown in FIG. The position with respect to the star field is therefore determined along with the use of the radius in order to perfect the spherical coordinates. Using the information corresponding to the position in the \ 5 star field and the radius, right-angled coordinates are generated by coordinate converters.

The planetary position in right-angled coordinates in the sun-centered reference system according to FIG. 10 is determined by the in FIG. 11 generated system shown. Three resolvers 80, 82 and 84 are used in this system. In this embodiment, the resolver 80 has a signal input which, for. B. is a signal related to a normal and stored in a control computer system for use at this input to represent the radius of a selected planet from the sun's zero point. The input can also be set at a fixed height relative to the inputs for other planets to represent the constant mean radius of a particular planet in the solar system from the sun. This signal input r _p _ _s to the resolver 80 induces a voltage in each of its mutually perpendicular coils, which are mounted on its shaft and rotatable with it. In the resolver 80, the shaft setting is changed as a function of the changes in the angle ζ which, as can be seen from FIG. 10, changes when the planetary position changes in the course of its revolution around the sun. The outputs of the resolver 80 are then r _p ~ _s · sin , which variable is given to the input of the resolver 82, and r _P s · cos ζ, which variable is given to one of two inputs of the resolver 84. The shaft of the resolver 82, which carries mutually perpendicular coils, is fixed in position to represent the constant angle / between the plane of the planet's orbit and the equatorial plane. As a result, the outputs of this resolver 82 are r _p - _s · sin ζ · cos i, which quantity is given to the second input of the resolver 84, and Γρ-s · sin ζ · sin i, which quantity by trigonometric conversion is equal to the right-angled coordinate Zp is. The shaft of the resolver 84 adjusts its mutually perpendicular coils so that the angle Ω is shown, which according to FIG. 10 is the displacement angle of the intersection of the plane of rotation of the planet in the equatorial plane from the vernal point. The resolver 84 generates output signals Γρ-s · sin ξ cos / sin Ω and r _p _ _s sin ζ cos / cos Ω, which each correspond to the rectangular coordinates x _p and y _p. As mentioned above, when setting the angle ζ, the information normally available is ζ + Ω. This is the information normally obtainable from observation data and thus contains small f> 5 errors, so that it can serve as an input variable instead of ξ.
Fig. 12 represents the orbit of the planet constitutes a particularly simple case the display 10. In particular, according to FIG. In this case, the angle Ω by definition zero, the vernal equinox is the intersection of the equatorial plane with the plane of the ecliptic, and by definition, the plane of the ecliptic is the plane of the earth's orbit around the sun for our epoch. The distance of the earth from the sun r _e - _s is an astronomical unit and serves as a reference value for the relative distances of other planets from the sun and / in this case is a fixed angle of 23 - '/ 2 ⁰ .

The simplified coordinate converter for the earth is shown in FIG. Only two resolvers are required due to the elimination of Ω. A stationary input to resolver 80 'corresponding to an astronomical unit and a wave setting corresponding to ξ produces outputs a sin ζ and a cos ζ, the latter value being the rectangular coordinate x _e . The resolver 82 'receives an input corresponding to / = 23 -V2 ⁰ and the output of the resolver 82' corresponds to a sin ξ cos 23 - '/ 2 ° and a sin ξ sin 23 -' / 2 °, which values are the rectangular coordinates y _e and z _e correspond to the earth. Ecliptic coordinates with a sun zero point, where the x ^E and j ^ axes are in the ecliptic plane and the z ^£ axis are perpendicular to these two axes, can be generated even more easily for the earth. The y _f ^£ coordinate is equal to a sin ξ, which value, as can be seen, is the output of the resolver 80 '. The ^ / coordinate remains a cos ξ, and for the earth z _e ^E is of course zero. Ecliptic coordinates for planets with orbits outside the plane of the ecliptic naturally have a z ^£ coordinate which can be generated using the plane of the ecliptic instead of the equatorial plane as a reference.

A generalized observer position can be obtained by the observer coordinate converter shown in FIG. It should be noted that in the space of the solar system an astronomical measurement can be made either in ecliptic coordinates or in equatorial coordinates. It is assumed that the observer indicates his position in ecliptic coordinates with χ and that the observer width ψ _ο the observer length Φ _ο and the observer distance from the sun r _o - _s , then the input to the resolver 86 is an input signal which is proportional to r _o - _z is. The shaft setting of the resolver 86 represents the width of the observer. Therefore, the resolver 86 generates an output Γο-s sin ψ, which is given as an input signal to the resolver 86. The resolver 86 also generates an output / · <, - * cos ψ which reproduces z _o ^E. The shaft setting of the resolver 88, so that its outputs reflect the observer length Φ _ο , results in r _o - _s sinysm <I> or Γο-s sin φ cos Φ corresponding to y ₀ ^E or x _o ^E. Signals corresponding to the coordinates y _o ^E or z _o ^E are therefore sent to the resolver 90, the shaft setting of which corresponds to the ecliptic angle of 23 '/ 2 °. The outputs of resolver 90 are equatorial rectangular coordinates and correspond to Zo and yo, the equatorial coordinates of the observer. The z _o ^£ output of resolver 86 is also by definition z _o without further modification.

F i g. 15, 16 and 17 are schematic representations in FIG soft summaries of the in Figs. 11,13 and 14 shown coordinate converter for line-of-sight re-

systems for calculating the direction of are shown from a selected observation point.

Either the observer position or the observed point, or both, can change its position as it does through the variable inputs in the coordinate converter according to FIG. 11, 13 and 14 is reproduced. The examples according to FIGS. 15, 16 and 17 serve the purpose of explanation and are intended to other possible combinations do not exclude.

Fig. 15 shows an apparatus for calculating line-of-sight vectors from the earth to an exemplary planet. The information obtained can be used to guide the projector for this planet through its successive orbital positions with respect to the star field, viewed from earth. It is noted that in a practical planetarium system, each planetary coordinate converter can be tied to the earth coordinate converter in the same way in order to obtain a line of sight direction of the associated planetary projector for mimicking the view from the earth. In this system, the planetary coordinate converter 92, which is shown in FIG. 11 is shown, combined with the earth coordinate converter 94 which is shown in FIG. 13 is shown. In particular, the respective coordinate output signals of each transducer are combined. By selectively connecting the output terminals of each earth coordinate converter, the output _{signals x ft} y _e and z _e can be selected as either positive or negative signals. Negative signals - x _a -JK or —Ze are equal to the sun coordinates + Xs, + Ys and + z _s, which defines a line of sight vector from the earth to the sun. The x signals from the planetary coordinate converter 92 and from the earth coordinate converter 94 are summed in the summing amplifier 98x. The corresponding y and z signal outputs are summed in summing amplifiers 98j / and 98z. Since the outputs from transducer 94 are negative, summing amplifiers 98x, 98j / and 98z produce differential output signals which together define the line of sight direction from earth to the point of interest. When these signals are fed into a suitable planetary position computer, they generate suitable directional signals for setting the planetary projector, as shown in FIGS. 2, 7 and 8 are shown. The negative earth coordinate signals from the earth coordinate converter represent, without any further change, sun coordinate signals in a sun-centered coordinate system in which the sun is at the zero point from which the planetary position coordinates are measured. Since the distances are the same but the direction is reversed, the negative values of the planetary coordinates indicate the direction to the sun. These negative earth coordinates are therefore used to adjust the sun projector. A mean solar coordinate position can be generated in a similar way by the coordinate converter 94 by using negative ecliptic coordinate outputs - x _e ^E or - ye ^k '. It is noted that in this, as in all other modes of operation, different planetary coordinate converters are provided for each of the mimicked planets. A single earth coordinate converter for observer position is used with each planetary coordinate converter in exactly the same way to define the vector direction from earth to that planet for each of them.

In the general observer mode, the earth becomes just another planet. Therefore, the general observer line-of-sight calculator of FIG corresponding to corresponding parts denoting corresponding parts in the earth observer line-of-sight calculator of Fig. 15, in the general observer line-of-sight calculator of Fig. 16, the corresponding primed reference numerals are given, indicating the similarity of their functions. The observer coordinate converter 94 'is analogous in its function to the earth coordinate converter 94 in FIG. 15 and its negative output signals are used in the same way. The negative signals obtained in this way are components of the line-of-sight vector to the sun, viewed from the observer's position. These signals are combined in summers 98 * ', 98y' and 98z 'with signals representing the respective components from the planetary coordinate converters to obtain the component signals which correspond to the line-of-sight vector from the observer position to the observed point in perpendicular coordinates. The Earth coordinate converter 92 _e is constructed the same as those for other planets and the Earth line of sight components are obtained by summing 102x 102Je and 102z. The mean sun position coordinates are obtained by choosing the negative output of the ecliptic coordinates generated at the coordinate converter 94 '. In this example, three ecliptic coordinate signals are required since the observer position can theoretically be anywhere in space.

A planetary mode of operation is shown in FIG. 17, where the observer position is chosen on some planet other than earth and the planetary and earth coordinate converters 92 "and 92 _e 'perform the same functions as in the general observer mode of FIG 16. Instead of a general observer's point of view, the observer's place of observation is another planet, the changing coordinates of which are generated by the coordinate converter 94 ″. Negative signals are selected in the same way by the observer coordinate converter 94 "and added in the same way by summing devices 98x", 98y "and 98z" or tO2y ', 102a' and 102z '

In Fig. 18 a typical position computing system is shown schematically. These position computers can be used to guide the projector to project the image of the planets, the earth, the moon, the sun, or any natural or artificial satellite. It is noted that this same computer can be used as a sun position calculator, earth position calculator, and the like, its function being to receive the various signals corresponding to the rectangular coordinates of the line of sight vector of the observed point in each case in the celestial frame of reference and by appropriate calculation Line of sight azimuth and elevation angle signals in the spatial reference system, which are used to move a suitable planetary projector. In the case of the in Fi g. 18, a general planetary position is obtained and the signals x _p -x ₀ and

809 625/7

47 523

y _P -y _o (where the index "ρ" refers to the planet and the index "o" refers to the observer) are given to the resolver 110, the shaft position of which corresponds to the angular position Φ \ of the polar axis (axis I) of the planetarium device . The output of this resolver is y 'and x', the respective components of the line of sight along the normal to the horizontal axis (axis II) in an equatorial plane. The signals y ' and Zp-Z ₀ are given to the second resolver 112, the shaft position of which corresponds to 90 ° -Φ \\ (the complementary width of the planetarium device). The output of resolver 112 is y " and z", respectively, which are the components of the line of sight vector normal to and in the direction of the A 'axis along the planetarium horizon plane and along the zenith, respectively. The / "signal and the *" signal are applied to the resolver 114, the shaft position of which is the azimuth of the planetarium set by the vertical axis III. The output of resolver 114 is * '"and y'", respectively, the components of the line of sight vector along the polar and horizontal axes of the planetarium device.

In the preferred embodiment, in which the axis III is vertical, the outputs of the Resolver 114 given both as inputs to the resolver 116, the shaft position of which corresponds to the height of the Set planets. The outputs of resolver 116 close an output through a signal amplifier 118 to a motor 180 which drives the height adjustment shaft in the event that the height adjustment is not right. This signal continues and the motor drives until there is no more signal at the output of resolver 116 is received. The other output of resolver 116 is used as an input for a resolver 122 is used, the other input of which is the output z "of the resolver 112. One the outputs of the resolver 122 in turn feeds a signal amplifier 124, which the azimuth position motor 126 drives whose modified shaft setting changes the coil positions in resolver 122 certainly. The signal is generated by the signal amplifier 124 until the detector is in the correct position to adjust each signal to determine at what point the correct azimuth is achieved. In the event that the Axis III is not vertical, the setting of the planet is still made by the above calculation set correctly, provided that the fixed axis of the planetary projector is parallel to axis III, but in in this case the exits do not correspond to the azimuth and altitude of the planet.

When working near the earth or the moon, one has to consider some of the flaws, which otherwise can be neglected in the case of sun-centered working methods. Besides, it is close when working of the earth for the purpose of simplifying the calculation, in an earth-centered mode of operation and not to work with another cislunar center. This earth-centered operating mode can, if necessary to be coupled with a sun-centered operating mode for the rest of the planetary system.

The problems present with the earth and the moon generally occur within a radius of the earth from about twice the distance from the earth to the moon. In this part of the solar system space it is in addition to the problems of setting the moon and earth in the planetarium it is necessary that both celestial bodies are in the right phase to each other, the right position in the celestial ice sphere and be viewed from the right side and of the right size. The output voltage of the earth and moon position calculator is proportional to the distance between the observer and the celestial object and can be used to control the size of the projected image on the dome be used. Each of the other problems is related and yet requires a separate one Solution and separate computing systems. Since in the

ίο most cases those with looking at the earth related problems are analogous to those related to viewing the moon, a viewing can the problem with the moon can easily be traced back to the analogous problem with the earth be transmitted. Therefore the problems with the moon are given special consideration and apply equally also for the corresponding problem regarding the earth.

As mentioned above, the position of the moon must be in

Solar system when observed near the earth for the purpose of accuracy in the representation of the mutual Relationships between the moon and earth are taken into account. Hence is an earth-centered coordinate system when considering the position of the moon within the cislunar space it is essential. When looking at the The diagram according to FIG. 10 is analogous to the problem in earth-centered instead of sun-centered coordinates a diagram that can be drawn for the earth-centered coordinates. Therefore, it is obviously that the coordinate converter for the

JO Moon position in an earth-centered system, which is shown in FIG. 19 is shown, the one in FIG. 11 for a planet in a sun-centered system is entirely analogous. One difference that must be taken into account in the earth-centered system is that the orbit does not occupy a fixed position in relation to the reference system, but rather the ascending node of the moon shifts. This means that the angle Ω is variable, since the length of the moon's rise or the ascending knot of the lunar cycle is variable. Also, the lunar data are usually obtained in expressions related to the ecliptic plane and not to the equatorial plane, and in order to be able to use the tabulated data expediently, the reference values should be in

the plane of the ecliptic rather than the equatorial plane. Around a line of sight vector with accuracy It is therefore necessary to get the observer's longitude and latitude in ecliptic coordinates obtain. This is done with respect to the earth and not with respect to the sun for the reason stated above carried out.

As can be seen from Fig. 19, the lunar coordinate converters and an observer coordinate converter are combined into a line-of-sight calculator in order to generate the coordinates of the line-of-sight vector when required. The lunar coordinate converter consists of the resolvers 140, 142 and 144 with inputs and outputs and suitable connections in the manner shown: An input signal proportional to the radius from the center of the earth to the center of the moon is given to the resolver 140, the shaft of which is set at such an angle is that it represents the moon position angle, which ζ in FIG. 10, but here as a crescent moon ([is shown.

Since tabulated data is not usually available in this form, the input is usually ([ --Ω, which value can be expressed as ω . Since the length of the ascending

Node shifts, Ω is no longer fixed as with planets, but variable and mechanically suitable differential devices must be provided, which accept (J and Ω inputs in order to obtain an exact (J - Ω input on the shaft. The output r _e - _m sin ((J - Ω) is given as an input to the resolver 142. The wave setting of the resolver 142 is the angle i, approximately 5 ¹ At ", between the orbital plane of the moon and the plane of the ecliptic. The cos -Output of this resolver is x _m ^E. ι ο The sin component r _e - _m sin / sin (((—Ω) of the resolver 142 results in an input for the resolver 144. A second input for the resolver 144 is the output signal r _e -, n cos ((J-Ω) of the resolver 140. The wave setting of the resolver 144 corresponds to Ω, the angle between the vernal equinox and the ascending node of the lunar cycle. Since Ω is variable in this example, a suitable device for generating the changeable signa Is intended for adjusting the shaft. The output of the resolver 144 at the sin output is z _m ^E and at the cos output is y _m ^E. Since the exits from the moon -. Coordinate converter as quantities of the moon position,

7 $, viewed from an earth-centered system, are present, the observer's position in the same coordinate system must be known in order to obtain the direction of the observer's line of sight. Furthermore, rectangular coordinates must be obtained and this is achieved by means of resolvers 146 and 148 . A signal proportional to the observer radius from the center of the earth r _e - _u is the only signal input of the resolver 146 _{whose shaft setting} corresponds to the observer width (P oe. The cos output of the resolver 146 corresponds directly to the Z coordinate Zoe ^E - the output r _en sin < P _m of resolver 146 is given as the only input to resolver 148. The outputs of resolver 148 correspond to the rectangular coordinates x _oe ^E , which, like output z _oe ^E , can be selected as negative signals by reversing the line , 15Oy amplified and 150z to output differences of the signals Xm ^e -Xoe ^e. ym ^e -y e _O ^e and z _m -z ^e _oe ^e to give, respectively the moon vector coordinates in the ecliptic

Λ system, viewed from the earth, x _O m ^E , y _O m ^E and z _om ^E correspond. The shaft setting of the resolver 154 corresponds to the ecliptic angle / = 23 - '/ 2 °. The coordinates are converted from the obtained ecliptic right-angled line-of-sight coordinates into those coordinates which are related to the equatorial planes y and ζ by giving signals to the resolver 154 . The coordinate x _om ^E is by definition equal to the coordinate x _om .

The lunar coordinate converter and line of sight calculator, with appropriate various inputs to resolvers 140 and 144 , can be used to mimic any earth satellite. This can be done by using the same computer of FIG. 19 for the moon, or by using additional computing system components if artificial earth satellites are sufficiently important in a particular planetarium shape.

In many planetariums it is not necessary to have a coupling between the earth-centered observer reference system and the sun-centered reference system. In this case it is clear that the moon position calculator exactly to the one shown in FIG. 17 corresponds to the planetary position calculator shown. A coupling of the earth-centered and sun-centered systems can, however, be effected in the manner shown in Fig. 20 if this is necessary or desirable.

F i g. 20 shows the device for transferring the earth-centered observer reference system to the sun-centered reference system or for coupling the two reference systems. Since the earth has no altitude, only its azimuth with respect to the sun has to be fed into the resolver 160 as a wave setting. The resolver 160 receives an input signal corresponding to a, that is an astronomical unit (the distance between the earth and sun). The output of resolver 160 is the earth position, expressed in ecliptic x ^E and yZ coordinates. In contrast, a general observer position in cislunar space requires more input information. The observer width ϊΌβ is fed to the resolver 162 as a shaft setting to produce a signal proportional to the radius between the earth and the observer. The output r _oe sin Φ _{οβ of} the resolver 162 is given to the resolver 164 and the cos coordinate directly represents the component z _oe ^E. The shaft setting of the resolver 164 represents the observer length <P _oe in relation to earth, so that the outputs of the resolver 164 are the observer's x and / coordinates in the earth-centered system and still in an ecliptic frame of reference. The x and y coordinates of the observer with respect to the earth are chosen negative and combined with the earth position coordinates with respect to the sun in the summing amplifiers 166 * and I667, respectively. The output signals x _is ^e - x and y _eo ^e _it ^e -yeo ^E are applied to the resolver 168 as input signals. The shaft of this resolver represents the observer length in a sun-centered system and its sin output winding generates a signal which is amplified in signal amplifier 170 and fed to motor 172 , which drives the shaft of resolver 168 until that of the sin coil of the The resolver generated signal is adjusted. This shaft setting then represents the correct position of the observer length in a sun-centered system. Since the resolver 174 in an observer solar computer has a common shaft with the resolver 168 and the motor 172 , the shaft of the resolver 174 also represents an observer length. The cos The output of the resolver 168 is then given to the resolver 176 , which also receives the cos-S'-signal output of the resolver 162 , which represents z _oe ^E. These two signals are combined by resolver 176 , the shaft setting of which represents the observer latitude Ψ Ό with respect to the sun. The sin component of the signal is used to couple the shaft position of resolver 176 , which represents the observer's solar latitude. The sin signal output of resolver 176 is applied to amplifier 178 . If the shaft position of the resolver 174, which represents the observer width <P _O , is incorrect, a signal is generated which drives the motor 180 to adjust the shaft until no signal output is obtained, at which point that of the shaft width shown is correct. The same shaft setting determines the position of the shaft of the resolver 182 in the observer solar system. The other output of the resolver 176, the cos component, is a signal corresponding to the radial distance of the observer from the sun and can therefore be given directly as an input signal to the resolver 182

will. The sin output of resolver 182 gives an input for resolver 174 and the cos signal gives a ^ coordinate of the observer. The y and z coordinates of the observer are generated from the output of the resolver 174 , the shaft setting of which is determined by the motor 174 and represents the length of the observer's position in the solar system. This observer exit is the same as the general observer exit in FIG. 14th

The problem of the phases of the moon is shown schematically in Fig. 21. This becomes a problem of planar geometry in the sense that the earth, moon and sun can be assumed to be essentially in a common plane. If the vernal equinox is taken as the reference direction from the earth, the angle of the sun Φ ₅ with respect to the vernal equinox, viewed from the earth, is an important value. The angle (J, i.e. the angle between the moon and the vernal equinox, viewed from the earth, is another important value. Φ ₅ - (J is the information required to operate a known type of moon phase control The basic idea is that if Φ * - <1 is equal to zero, the moon cannot be seen from the earth, since only the far side of the moon is illuminated. If Φ ₅ - (J equals Π arc units, the side of the moon facing the earth is fully illuminated and it is full moon. Intermediate phases of the moon can then be calibrated as different positions between these two output signals of the earth representation, which the coordinates x _s ^E and y _s ^E in the ecliptic system and in the plane of the As shown in Fig. 22, these signals are applied to the moon phase resolver 184 , the shaft of which is set to represent the angle (f at the resolver 184. The sin and cos signal outputs of the resolver are given as inputs to resolver 186 . The shaft of resolver 186 is set to represent Φ ₅ - (J. The sin output of resolver 186 is amplified by signal amplifier 188 and fed to motor 190 which drives the shaft until it reaches the position in which no signal is generated, and this is therefore the correct position in which Φ ₅ - (J is represented. This wave, on the other hand, is coupled to the phase mechanism for the moon.

As mentioned above, a similar phasing device intended for the earth. When calculating the phases of the moon, the component is the Lunar orbit, which is not in the plane of the ecliptic, is neglected and results in the effect no significant difference.

The lunar position control must take into account the direction of the lunar pole with respect to the observer. In fact, the polar axis of the moon points approximately to the pole of the ecliptic. In the planetarium, however, it is a reasonable approximation and greatly simplifies the problem if one assumes that the lunar pole points to the pole star instead. This makes it possible for the moon axis to point along its local meridian, ie for the tip to pass through the zenith M or to deviate from it by a simple adjustment of the projector axis. FIG. 23 shows the geometry of the polar direction correction necessary for a moon position control. Ap and E _{9 represent the} azimuth and height of the cushion. A _m and E _n represent the azimuth and height of the moon after the planetary position calculation has been carried out. T represents the desired angle of the moon axis to the local meridian. According to the laws of spherical trigonometry results themselves

cig 7 =

sin (90 - E ₁₁₁ ) cos (90 Z ^ ₁ )

cosjW - Zi ₁₁₁ (siη (90 - Zi ",,) cos (/ I ₁₁₁ - A ₁ ,) ^: - ~ E ,,) s \ niÄ _m - A ₁ ,)

In Fig. 24 the control computer system for the moon position is shown. This consists of a resolver 192 to which a reference signal of standardized size is given. The shaft of the resolver 192 is set against the main star vault at 90 ° -Φ11. The sin output of the resolver 192 can then be sent to the resolver 194 , the shaft setting of which, as derived from the star field, represents the azimuth of the moon reduced by the orientation of the axis III (A _m - Φηι). The sin output of the resolver 194 together with the cos output of the resolver 192 result in input signals for the resolver 196, the shaft setting of which is 90 ° -Em. The sin output of resolver 196 is given as an input to resolver 198, as is the cos output of resolver 194 . These two input signals are combined to produce an output along with the shaft setting, which is the moon position setting. The output on the sin coil is fed to a signal amplifier 200 and operates the motor 202 which adjusts the shaft of the resolver 198 to the correct setting to represent the moon position when it is not in this position. After the wave reaches the setting that represents the correct moon position, no further output is produced. The shaft of the resolver 198 is therefore used to adjust the moon position control device.

The view of the moon or the view of the earth depends on the observer's position in cislunar space. It is conceivable that the rear side or part of the (rear side of the moon could be viewed, for example, from the position shown in Fig. 25. Since there are limitations on the way in which the lunar properties and earth properties can be represented, it is assumed that That the observation is restricted to the plane of the ecliptic. With this simplification the diagram according to Fig. 25, which shows the relative position of the observer, the moon and the earth, can be used. In this diagram the angle between the The vernal equinox and the line earth-moon as ([. The obtuse angle at which the line between the moon and observer intersects the vernal equinox line over the whole earth is marked with Φ , so that the angle between the observer's observation position and the view of the moon, viewed from the earth, Φ _ν - ((becomes. The device for achieving the observer position in ecliptic n coordinates ^ and j ^ are shown in Fig. 19 and these coordinates can be used as input for the in Fig. 26 can be used as the computer system shown in FIG. 19 obtained computer system shown

assuming that the observer is in the plane of the ecliptic, ie z ^{E is} zero. Resolver 206 uses these coordinates as inputs. With a shaft setting representing (J) the output of the resolver % 206 is equal to sin (Φ2- (J) and cos (Φ _ν - ({) · These two signals are then used as inputs of the resolver 208, the shaft setting of _{which represents the angle Φ ν} - Each signal at the sin output of the resolver 208 is passed to the signal amplifier 210, which in turn outputs its signal to the drive motor 212. The motor 212 in turn adjusts the shaft of the resolver 208, if necessary is switched off, the shaft setting remains fixed at the value which has been calculated as Φ _ν - (J, ie the correct setting for the moon position control. If there is no error in the first position, no adjustment of the shaft of the resolver 208 is required.

F i g. 27 shows a very schematic block diagram the overall operation of the computer system controlling the planetarium. In this circuit diagram, the Main star field projector and the individual planetary projectors only shown as blocks. the Associated computing systems are also shown schematically as blocks and only the most general ones Interconnections of the operational components are considered by connecting lines, which are not to show the exact electrical connections. The star field projector 4 is used among ordinary Circumstances controlled by a general rotation calculator 220, preferably of a similar type, as described in DT patent 13 03 505 and which for the imitation of the daily turning movement of the star field around the pole of axis I or any other chosen pole is appropriate. These Computing system enables the imitation of daily movement viewed from the surface of a other planets or a spacecraft, or the imitation of daily movement, viewed from of the earth in another age in which the pole is shifted towards the pole star.

In the event that the axis I does not point to the Pole Star, the general rotation calculator is through Computing system 222 for the correction of axis I is superimposed with a correction. In the event that axis III is not vertical, and especially in the case where axis III is part of the four-axis system according to F i g. 6, if a fourth axis is present, there is yet another computing system 224 for correcting the Position of the third axis required. The computer system described here is intended for the case in which axis III is in the reference meridian, as defined. Of course, given a given Feed the system of computers 224 for the third axis directly into the general rotation computer 220. If if it is desired to mimic tilt and roll, another computing system 226 is to be fed into the general rotation calculator is required, either directly or via a chain, as required of correction computers. The computer system for tilting, rolling and gyrating mimics conditions which can occur in a spacecraft, and the extent of these effects can be chosen depending on b5 according to how the occurring parameters are selected as inputs to the other computer systems.

In addition to the computer system inputs described, manually operated inputs 228 are provided, around the star field projector around the individual axes I, II and HI and other axes, if such are used and define the position of the fixed pole. These inputs can be automatic how to be operated by hand and set according to a predetermined program to the Mimicking the observer's orientation anywhere in the solar system.

The star field projector 4 of the planetarium assumes positions as a function of commands from the computer system and of manual inputs and, in turn, outputs information about the position taken, as required. The star field projector also provides information about the positions of its axes on the position computing systems, as is indicated schematically and has been described in detail above, for example in connection with FIG. 18. The relationship of the planetary position computer to the star field is therefore scanned by each of the computers 230SA 230 /, 230MA 230 V, 230ME, 230 £ and 230SU .

However, as described above, these planetary position computers depend on the information from the coordinate converters 232SA 232 /, 232MA 232 V, 232M £ and 232 £. As detailed in connection with FIGS. 15, 16 and 17, vector sums are obtained by summing amplifiers 234SA, 234 /, 234MA, 234V, 234M £, 234E and 234SU . The special type of connection of the planetary representations to achieve the vector sums requires a selection of the operating mode, which is set by suitable switches, which are shown schematically by the switches 236, 237, 238, 239,240,241,242,243,244 and 245 and are intended to explain the possibility of an operating mode or switch from one observation point to another. Typical modes of operation are shown in FIGS. 15, 16 and 17 for certain limited numbers of celestial bodies, for example. With more computational components, the circuit gets a little more complicated, but the basic idea stays the same. With this vector information and the star field orientation information, the planetary position computers can correctly align their projectors 5SA 5 /, 5MA 5 V, 5ME, 5E and 5SU in order to imitate the correct selected positions of the corresponding planets and the sun on the planetarium dome. The positions of the planets change over time in accordance with the input information from the planetary coordinate converters, which of course have to be programmed with suitable information in relation to one another.

The cislunar system is shown in the dash-dotted box 250 and is provided with its own earth projector 5EA and lunar projector 5MO, which projectors can be equipped with slides showing details of the projected celestial body, and rubber lenses can be provided to measure the size of the celestial body in To imitate the dependence of the distance between observer and celestial body. The system also includes the various computing systems shown in Figs. The general observer coordinate converter 232GE and the lunar or satellite converter 232MO feed into the earth position computer 252 and the moon position computer 254 via the devices which are provided for converting ecliptic to equatorial coordinates

609 525/7

are as shown in FIG. Information from the earth position computer 252 is in turn used to adjust the earth projector 5EA and information from the moon position computer is used to adjust the moon projector 5MO .

In order to convert the cislunar, earth-centered system into a sun-centered system, that of the computer system according to FIG. 20 corresponding converter 258 is used, which acts on the general observer coordinate converter 230GS. A moon phase control computer 260 similar to that shown in FIG. 22 receives input information from the earth coordinate converter 232E and in turn generates an output for setting the phase control flap of the moon projector 5MO. The same or a similar control can be used to imitate the earth phases and is shown here as a separate earth phase control 260 ', which acts on the phase flap of the earth projector 5EA. The moon position controller 262 receives information from the moon position computer 254 in order to calculate the moon position, which is used for setting a slide or otherwise appropriately affects the moon projector 5MO. In the same way, the earth position computer 262 'receives an input from the earth position computer 252 such as the main star field or the star ball and its output is used to set a slide or to otherwise imitate the earth position or earth position in the earth projector 5EA . Finally, a moon view control is effected by the computer system 264 from the coordinate converter input by means of the moon view computer 266. This in turn generates an output which adjusts the moon projector 5MO according to the correct moon view.

Star field projector

F i g. 28a and 28b show two schematic representations showing the spherical geometry illustrate necessary to better understand the problem of adjusting the star field projector and in In this case, the star ball 10 is used. Fig.28a shows the geometry in the case when the Star field projector according to FIG. 2 is applied.

In Fig. 20a, arc A is the angle between the zenith, which in this case coincides with axis III, and the fixed pole, arc C is the angle between axis I on the Pole Star and the fixed pole and angle B is the angle between the arcs A and C in the spherical triangle. The angle B changes constantly in the course of the imitation of the daily movement, but the arcs A and C remain the same. The angles Φι, Φ » and Φηι represent the angle settings of the axes I, II and III, which are obtained by the computer system by solving the spherical triangle with the inputs A, B and C. The direction // is the angle between a reference meridian and a great circle meridian through the fixed pole and in this case, like Φηι, is set by axis III .

F i g. 28b shows the modified geometry when a star ball projector with an inclined axis III according to FIG. 6 is used and / or a further modification of the position of the axis I from the pole star is used. The angles \, Φη and Φμ still represent the angle settings of the axes', II and III de -. The reference meridian is defined by the zenith and the inclined axis III. The direction or course H corresponds to the angle at the zenith between the reference meridian and the zenith and the great circle connecting the fixed pole. This direction is no longer generated directly by the movement of axis III, but is a calculated output, which results from the action of the resolver chains at the loading input.
Arc A ⁺ is the angle between axis III, which

ίο is inclined towards the zenith M and the fixed pole and is calculated from the course and the inclination of axis III. Arc C ⁺ is the angle between the fixed pole and the offset axis I in the same position not going through the Pole Star.

The angle B ⁺ is the angle between the arcs A ⁺ and C ⁺ . The changes in the positions of axes I and III, or one of them, contribute to the change in the calculated triangle. When the triangle in FIG. 28a can be solved, as it is drawn in dash-dotted lines in Fig.28b, then the general solution of each triangle whose points are arranged according to the axes I and III, as shown in solid lines in Fig.28b, by «. Overlay of coordinate converters are obtained, which move the axis III from the zenith M into its chosen inclined position and / or the axis I on the Pole Star in any other chosen position. So shifting axis III results in an input from A together with inputs corresponding to the slope T and the course H an A + output together with a correction value Δ \ B to correct B in B ^+. Likewise, a shift in axis I gives input to C together with the declination of axis I and the difference in

.? 5 right ascensions of the fixed pole and axis I ^{produce a C +} output along with a correction value Δ2Β to correct 3 in B ^+. Correcting B in B ⁺ requires both corrections if both axes are shifted, or only the appropriate correction if one axis is shifted. Once the axes have been shifted, the angles Φ11 and Φνι result from the triangle shown in solid lines in FIG. 28b. Φιπ naturally involves a rotation about the inclined axis III, Φι a rotation, the shifted axis I and Φη a rotation about the \ _ 'axis II, which is shifted with the axis III and advantageously measured from the shifted axis III will.
The block diagram in FIG. 29 is intended to show in somewhat greater detail the manner in which the parameters of FIG. 28a and 28b can be used. It can be seen that the general rotation calculator 220 produces outputs for adjusting the star field projector, star ball 10, about axes I, II, and III (and others if such are used). This adjustment is accomplished with and relative to each axis the manual input 228 coordinated. The inputs to general rotation calculator 220 are parameters A ⁺ , B ⁺ and C ⁺ . These are again obtained from computer 222 for axis I, from computer 224 for axis III and from computer 226 for tilting, rolling and yawing. Each of the calculators 222, 224 and 226 can be omitted and, if all are omitted, the inputs to the general rotation calculator are equal to A, B and C. In the event that the axis I is not a fixed polar axis facing the Pole Star, inputs of the right ascension generate of the fixed PoJ and the arc C in the

Computer 222, assuming that axis 1 is preset to a pole distance Cö \ and to a right ascension ra \ , outputs from C ⁺ and A ₂ B. C ⁺ is then sent directly to the general rotation computer and A ₂ B becomes given the summing differential or amplifier 268 to correct the reading from B to B ^+. If only the calculator 222 were used, the A ⁺ input would be A. Assuming that axis III is at an angle T to the zenith, computer 224 is angecrd-et to receive one input equal to A and one equal to // with the course or direction in that shown in Figure 28b defined way is chosen. The output of calculator 224 is then A ⁺ , which value is fed directly to general rotation calculator 220 , and Δ \ B, which value is fed to summing differential or amplifier 268 together with the B signal. If a <di B signal is present from computer 222 , it would also be passed to summing differential or amplifier 268. Since the B, Δ \ Β, and / ^ B outputs are usually wave adjustments, a differential for summing them is obviously more convenient, but it will be noted that it is possible, using known elements, to convert these mechanical signals to electrical signals therewith they are summed in a suitable summing amplifier.

When pitch, roll, and yaw are mimicked, parameters A and B and heading H are modified and obtained as outputs from computer 226. If the computer 224 is used, the outputs A and H are put on the input of the computer 224 , and if a // input is given manually, the separate // inputs can be combined by a suitable differential 225. Otherwise A can be given directly to the general rotation calculator. Either on input to calculator 224 as shown when using calculator 224 , or in front of general rotation calculator 220, a suitable differential 227 may be used to combine the // signal from calculator 226 with a manually given / 4 input will. B as an output from computer 226 is a variable component of the B value given directly to the summing differential or amplifier 268 and along with the other β inputs to that portion. The tilt, roll and yaw variable voltage inputs to the calculator are first derivatives of time and P, R and Ϋ represent the rates of tilt, roll and yaw. These inputs are voltages each selected by a separate voltage divider which is directly calibrated in units of the speed of tilt, roll or yaw. If the computer 226 is used but no yaw input is available, an electrical B input signal can be manually substituted by suitable switching. In the same way, switching can be provided in order to enable an electrical / manual input on the computer 226. The in F i g. Elements shown as blocks 29 are shown in FIGS. 30, 31, 32 and 3J. FIG. 30 shows the general rotation calculator 220. FIG . 31 shows the computer 222 which is concerned with the modified position of the axis I. F i g. 32 shows the computer 224 dealing with the shifted axis IH. F i g. 33 shows the tilt, roll and yaw calculator 226.

F i g. 30 corresponds to the general rotation calculator of DT patent 13 03 505, the modifications being made to make it useful in the illustrated embodiment of the present invention. The resolvers 270 and 272 are set with their shafts so that they represent the angle A ⁺ . The resolvers 274 and 276 are set with their shafts to represent the angle B ⁺ , and the resolvers 278 and 280 are set with their shafts to represent the angle C ⁺ . The resolvers form two separate chains with the exception of the common shaft setting. The upper chain produces outputs according to the angles Φ \\ and Φ111 and the lower chain produces an output according to the angle Φι. With inputs A ⁺ , B ⁺ and C ⁺ using a fixed reference input signal, the desired output angles are obtained, which are necessary for setting the star field projector. If axis III is not inclined, then A ⁺ equals A and represents the observer latitude, as mentioned above. If the X axis passes through the Pole Star, then C ^{+ represents} the angle between the Pole Star and the chosen fixed pole and corresponds to the value which is normally C. B ⁺ is only equal to B if the III axis is not inclined and the I axis passes through the Pole Star, with the exception of the unique case in which both the Pole Star and the fixed pole are on the reference meridian. In the course of a planetarium show describing the daily rotation of the star field, B ⁺ changes to indicate the daily rotation of the star field around the selected cushions, and the computer according to FIG. 30 calculates and supplies the correct angular position for this process on axes I, II and III. If the axes I or III do not coincide with the Pole Star or the zenith, A ⁺ , B ⁺ and C ^{+ are} no longer the defined expressions, but are modified expressions that are nevertheless used to calculate the required axial setting of axes I, II and III are necessary.

A fixed reference voltage applied to resolver 280 generates outputs sin C and cos C, the former being applied to resolver 276 and the cos C output of resolver 280 being used as an input for resolver 272 , which in turn is the trigonometric shown in the figures Output functions are generated. The output of the resolver 272 which is given to the resolver 17 is equal to ΰοβΦπΐ 5ΪηΦΐι, while the output of the resolver 276 which is given to the resolver 17 is equal to sin Φΐπ sin Φ \\ . A combination of these two inputs in resolver 17 gives an output for servo amplifier 288, which is a function of the angle Φ \\\ to drive motor 15 until its shaft, which is connected to the shaft of resolver 17, the angle Φπι corresponds to the point at which there is no further output on amplifier 288 . The other output of the resolver 17 corresponds to sin Φ \\. This output is sent to the resolver 19 with the output of the resolver 272, which corresponds to cos Φπ, in order to give an output signal proportional to the angle Φ \ ι to the motor 21 via the servo amplifier 292. The motor 21 drives the shaft of the resolver 284 until no further output signal is generated, at which point the shaft assumes a position corresponding to an angle Φ ». One kind of

actual coupling of the drive motors 15 and 21 to their respective axes III and IV is shown in Fig.2 shown.

The same reference input that is given to resolver 280 is given to resolver 270, the outputs of which are therefore sin A ⁺ and cos A ⁺ . The value sin A ⁺ given as the input in the resolver 274 generates the output sin A ⁺ cos 5+ and this output, together with the output cos A ^{+ of} the resolver 270, gives the inputs for the resolver 278. One of the inputs of the resolver 278 is then equal to cos Φ \ sin Φ \\, as shown in the figures, and this output is given as an input to resolver 28. The other input of resolver 28 is the output of resolver 274, which is equal to sin Φ \ sin Φ \\ . An output proportional to the angle Φ \ ι can therefore be taken from the resolver 28 and amplified by the servo amplifier 296 before it is fed into the motor 42. If there is no signal to drive the motor 42, there is the shaft of the resolver 28, which is coupled to the motor 42 via the star ball 10, as shown in FIG. 3 can be seen in the position corresponding to the angle Φι. This shaft can also be used as the output to drive axis I of the star field projector.

If the axis I is not directed towards the Pole Star, the computer 222 (see FIG. 29), which is represented by the resolver chain according to FIG. 31, is required to carry out the necessary corrections in the input of the general rotation computer. In this calculator, the same general reference voltage used for the inputs to resolvers 270 and 280 in Figure 30 is used as the input to resolver 300. The shaft of resolver 300 is set to represent the declination of axis I. The outputs of the resolver 300 are given as inputs to the resolver 302 or 304, the sin output of the resolver 300 being the only voltage input to the resolver 302. The shaft setting of the resolver 302 corresponds to an angle corresponding to the difference in the right ascensions of the fixed pole and the axis I. One of the outputs of the resolver 302 is given together with the second output of the resolver 300 in the resolver 304, the shaft of which is set so that it corresponds to arc C in Fig. 28b. The outputs of the resolver 304 result in inputs for the resolver 306 and 308, respectively. The other input of the resolver 306 is the second output of the resolver 302. One of the output signals received from the resolver 306 is applied to the motor 312 via the servo amplifier 310 in order to generate the coupled Set shafts of this motor and the resolver 306 according to A ₂ B , and when the shaft assumes this position, no further signal is generated at the amplifier 310 to drive the motor. The other output of the resolver 306 is given as a second input to the input 308 . One of the outputs of the resolver 308 is applied to the motor 316 via the servo amplifier 314 in order to adjust the coupled shafts of the motor and the resolver according to the arc C ⁺ . When the shaft setting is C ⁺ , no further output is generated through amplifier 314. As in connection with Fig. 29, the outputs in Fig. 31 are mechanically combined by a suitable differential mechanism or converted into electrical signals and combined by a summing amplifier before being input to the general rotation calculator.

The resolver chain according to Fig. 32 corresponds to that Computer 224 in Fig.29 and compensates for an inclination of the axis III, as in the embodiment according to Fig. 6 occurs. The resolver 320 is supplied with the same standardized reference input voltage like the other resolver chains and is adjusted with its shaft to the angle of inclination, which

ίο is represented by the angle between the vertical on the device and axis III. The outputs of this resolver are given to resolvers 322 and 324, respectively. The resolver 322 is set with its shaft according to the course or the direction H , which corresponds to the angle of a certain selected reference meridian with the plane defined by the vertical and the axis III (see FIG. 6). One output of the resolver 322 provides a second input for the resolver 324 and the other output provides a second input for the resolver 326. The resolver 324 is set with its shaft corresponding to arc A. The outputs of the resolver 324 are each given as a second input, "to the resolver 326 and as an input to the resolver 328". One of the outputs of the resolver 326 is given via the servo amplifier 330 to the motor 332, the shaft of which is coupled to the shaft of the resolver 326. If the motor 332 no longer rotates because it is not driven by a signal via the amplifier 330, its shaft setting and that of the resolver 326 correspond to the correction difference Δ \ B. The other output of the resolver 326 is given as a second input to the resolver 328. One of the outputs of the resolver 328 is amplified by the servo amplifier 332 and sent to the drive motor 334. The shaft of the motor 334 is coupled to the shaft of the resolver 328 and when the signal driving the motor becomes zero, the shaft setting of the motor 334 and the resolver 328 represents the output arc A ⁺ . The outputs Δ \ Β can be converted into an electrical signal can be converted as described above and fed into a summing amplifier 268, the output B ^{+ being} fed into the general rotation calculator together with the output A ⁺ , as shown in ( {Fig. 29. "*"

If tilt, roll, and yaw are to be mimicked, the computer 226 as shown in FIG. 29 is used, which consists of the components shown in Fig. 33. In particular, it consists of the resolver 336 (see FIG. 6), which has signal inputs proportional to the rate of change of rolling or to the rate of change of tilting. The shaft of the resolver 336 is set according to the course H of the observer. One of the outputs of resolver 336 is Λ, the rate of change of angle A, which is one of the inputs to servo amplifier 338. The servo amplifier 338 generates an output which drives the motor 340,

and the rate of change of drive of this motor is measured by a tachometer generator 342 on its shaft. The output of tachometer 342 is fed back to servo amplifier 338 as a second input so that signal A compensates or seeks to compensate for the tachometer output, and after compensation the shaft setting of motor 340 represents angle A. The second output of the resolver 336 is on a

3i

Function amplifier 344 given, the output of which is given to resolver 346 . The other input of the functional amplifier 344 is one of the outputs of the resolver 346, which is fed back to the functional amplifier 344 as an input. With the feedback from resolver 346 to amplifier 344, the output of the functional amplifier is equal to its input times the consicant A (cosec A). This output corresponds to B, the rate of change of angle B. This B signal is used as an input to the servo amplifier 348 which drives the motor 350, the speed of which is measured by the tachometer generator 352. The output of the tachometer generator is fed back as a second input to the servo amplifier 348 against the β signal from the functional amplifier 344 and if the signals are balanced so that there is no output from the amplifier 348 , the shaft setting of the motor 350 corresponds to that Angle B. The second output of resolver 346 is proportional to H, the

Rate of change of heading H. This output is given as an input to servo amplifier 354 which drives motor 356, the shaft of which is coupled to the shaft of resolver 336 and therefore corresponds to heading H. A tachometer generator 358 is also provided on the shaft of the motor 356, the voltage output of which measures the speed of the motor 356 as a signal corresponding to the first derivative of H and contrary to the corresponding signal

ίο The signal from the output of the resolver 346 is fed back. A third input to amplifier 354 is Ϋ, the rate of change of yaw Y, which results in a continuous change in yaw Y , resulting in a continuous change in course. The outputs A and H of this resolver chain are provided as inputs to the resolver 224 and the output B can be connected to an electrical signal and provided to the summing amplifier 268 , as above in connection with FIG. 29 explained.

For this purpose 10 sheets of drawings

809 525/7

Claims (6)

Patent claims: 1. Planetarium with a star field projector, sun, moon, earth and planet projectors and drive devices for the projectors with an electrical computing device and a coordinate converter with resolvers for controlling the star field projector, the planetary projectors being arranged separately from the star field projector, characterized in that the sun, moon, earth or planet projectors (5) each by means of coordinate converters (92, 92 ', 92 ", 92e, 92e', 94, 94 ', 94") with electromechanical resolvers (80, 82, 84; 92 , 94) are controllable depending on the observer position or the observed point and a so-called line of sight that all projectors (4, 5) are arranged and driven separately from one another, that from the parameters (ξ, i, Ω, r) of the respective Planetary orbit Cartesian coordinates (xp, yp, Zp) are formed, which by means of a further coordinate converter (Fig. 18) in the control signals for the servomotors (21) of the respective igen planet projector (4) are transformed, and that each sun, moon, earth or planet projector (5) has at least two separate drive devices (68,79) each with a radiation deflecting device (63,65). 2. Planetarium according to claim 1, characterized in that from the parameters (ξ, i, Ω, r) of the respective planetary orbit Cartesian coordinates (χρ, Υρ, Zp) by means of the coordinate converter (92, 92 ', 92 ", 92e, 92e ', 94,94', 94 ") are formed in that addition circuits (98x, 98y, 98z; 98 *", 98 / '98z'; 98 * ", 98 /", 98z "; 102x, 102j, 102z; 102 * ', 102y', 102z ^ to generate the component signals of the line of sight vectors between the observer position and the observed point, the coordinate signals corresponding to the coordinates assigned to one another (χ _{ρ -χ α} y _P -y'e, z _p -z _e ) of the coordinate converters to one another add. 3. Planetarium according to claim 1 or 2, characterized in that further coordinate converters (110, 112, 114; Fig. 18) designed as position computers are provided, which the signals corresponding to the components of the line of sight vectors in the coordinates (x ", y", z ″) of a Cartesian coordinate system related to the star field projector and convert corresponding signals and move the motion motors (120, 126; FIG. 18) only from position to position. 4. Planetarium according to claims 1-3, characterized in that the coordinate converter (F i g. 11, 14) has three resolvers (80, 82, 84; 86, 88, 90), the first resolver (80; 86) has a fixed signal input (r _p - _s or r _o -s) representing the radius of a certain planet from the sun's zero point or the observer distance from the sun and that the outputs (r ■ sin ξ, r · cos ξ; r - sin ψ, r ■ cos ψ) of this resolver (80; 86) are each placed on one of two inputs of the other two resolvers (82.84; 88.90). 5. Planetarium according to claims 1-3, characterized in that a simplified coordinate converter (Fig. 13) has only two resolvers (80 ', 82') while eliminating the angular size Ω. 6. Planetarium as claimed in claims 1-5, characterized in that the position computer (Fig. 18) five resolver (110-116, 122), one input of the last two of the resolvers in series (116,122) having a parallax Correction signal is applied