DE3636081A1 - Electronic celestial globe - Google Patents

Abstract

The electronic celestial globe is a three-dimensional rotatable precision instrument having real-time progression with advancing date and time display, daily rising and setting of the stars and moon phases with realistic inclination angle with respect to the earth. Familiarisation is facilitated by clicking-on the stars, planets, nebula, star clusters and galaxies. The items of information which can be called up give name, scientific designation, brightness, distance in light years, etc. 30,000 years, from 1.1.15,000 BC to 31.12.15,000 AD, can thus be astronomically retraced and predicted for the past, present and future. The colour diagram gives information on physical parameters such as colour, spectral type, luminosity, diameter, temperature and mass of the stars. The planetarium circuit, likewise with advancing date and time display (a rate of 1 day for every 3 seconds), shows the orbital paths of the planetary movements with their standstills, return movements and loop formations. Enlargements, networks of parallels and meridians, meteor showers, connection lines of the stars appear as required. Illustration and use of the coordinate systems are contained in the accompanying brochure, as are historical dates and descriptions of particular star and planet constellations, retraceable by data regarding date, time and geographical location.

Description

The electronic celestial globe is a three-dimensional, rotatable precision instrument, which for 30 000 years, from 1. 1. 15 000 BC A.D. to Dec. 31, 15,000 AD, all astronomical Reproduces phenomena. The globe contains the 88 constellations the southern and northern hemisphere with 820 stars, 121 star clusters, Galaxies and nebulae.

The real-time process with continuous date and time information gives the daily rise and set of stars and planets with theirs Own movements again, including the phases of the moon.

The planetarium circuit - also with a continuous date - and time display - shows the planetary movements with their Downtimes, returns and loops. The movement sequence here is 3 seconds, 1 day.

Magnifications, graticules, meteor streams, connecting lines to appear a constellation of your choice. information about Stars, planets, open and spherical star clusters, galaxies, planetary and other nebulae available by clicking. The precessional movement of the earth's axis and the resulting Changes in the position of the stars are over millennia comprehensible.

The Herzsprung-Russel diagram provides information about state variables like spectral class, diameter, mass, brightness and Luminosity.

Explanation and application of the 3 coordinate systems in this Booklet, as well as historical data and descriptions special star and planet constellations - through geographical Location, date and time entry traceable and much more  

Date, time and geographical location example

Date: 23. 3rd 2000 Latitude: 51 Longitude: 7 Time: 12 Grid network horizon / equator / ecliptic: 0.0.0 Azimuth: 0.0 Height: 30.0

Complete each entry with the return or enter key. Longitude and latitude lines are a world map or earth globe.

Times always in world time. The world time results from Deduction of one hour from the time in Germany (2 hours in summer).

If you enter 0.0.90, the ecliptic appears, if you enter 90.0.0, the Cardinal directions zenith nadir, at 0.90.0 the celestial equator. Degree networks when entering 1, 5, 10, 15, 30 or 60 degrees.

The azimuth indication turns the globe into any desired one Direction and view. The cardinal points have following values:

0 degrees = south;
90 degrees = west;
180 degrees = north;
270 degrees = east.

If you enter a zero after the comma (, 0) none, 1 (, 1) double, 2 (, 2) maximum magnification.

By specifying the elevation angle, the globe becomes corresponding inclined. Entry up to 90 degrees.

Negative height entry for the process below the horizon in the form: -30.1.

If you enter a zero (, 0) after the decimal point, the Stars with alignments (constellations), 1 (, 1) without lines.  

The Greek astronomer Hipparch (190-125 BC) shared the Stars visible to the naked eye in six size classes. The brightest received size 1.

They appear on the celestial globe in the following form:

Key functions

Key "G" - call up information by directing the arrow. Key "O" - local sidereal time. Key "P" - planetarium circuit. Key "S" - restart. "U" key - real-time sequence. Key "W" - select sight. "M" key - Meteor streams.

If the entered date coincides with the activity times of one of the meteor streams together, the name and appears Duration of activity - "M" key.  

Constellations

The names of many constellations come from the Greek Mythology, e.g. B. Hercules, Perseus, Andromeda, whale u. a. The names of the zodiac constellations Scorpio, Cancer, Leo etc. belong to the prehistory of mankind. Some constellations the southern sky have only recently been given names like air pump (lat. Antlia), chemical furnace (lat. Fornax), Pendulum clock (Latin horologium).

47 of the 88 constellations are south of the sky equator, 32 north, 9 enclose it.

Many stars have proper names like Antares, Castor and Pollux von the Greeks, Benetnasch, Ras Alhague, Alamak by the Arabs.

The German astronomer Johannes Bayer (1572-1625), who combined many stars in the southern sky into new constellations, introduced a system according to which the brighter stars are identified. This division also represents an approximate sequence of brightness. The brightest star received the first Greek letter, the second brightest the following, etc. Some differ from the rule. In the constellation Ursa Maior (Big Bear), ε (epsilon) Ursae Maioris is the brightest star. The small Greek letter is always followed by the Latin name in the genitive, e.g. B. Bear Keeper, Latin Bootes, genitive Bootis, constellation Cancer, Latin Cancer, genitive Cancri.

Greek alphabet:

Milky Way

The founder of the atomic term Democritus from Abdera in Thrace (460-370) suspected that the Milky Way consists of the shine of countless stars. The Milky Way is a lenticular concentration of around 100 billion stars - it forms the galactic plane of symmetry. Our solar system lies within this level 30,000 light years from its center, which is roughly in the direction of the Sagittarius lies - there is the concentration of the Most dense stars. The division of the Milky Way in the constellation Swan, eagle and snake bearer is made by interstellar Dust matter causes the starlight behind it absorbed. This interstellar matter forms the starless zones within the Milky Way (popular Called "coal sacks").

Historical examples

In the 6th century BC A battle raged between Medes and Lydiern, one predicted by Thales from Miletus Solar eclipse that ended the fighting - it was the darkness of May 28, 585 BC BC

Date: 28 5. -584 (subtract year information before Christ 1 year and enter negative). Latitude: 37 Longitude: 27 (longitude and latitude of the ruins of Milet) Time: 3 p.m. (world time 3 p.m. = 4 p.m. Central European time) Degree networks: 90.0.90 (ecliptic with cardinal points) Azimuth: 45.0 (direction south 45 ° west,, 0 = without magnification) Height: 30.1 (elevation above the horizon 30 degrees, 1 = without guidelines)

Information about stars and planets by clicking (button "G").

According to the ancient Chinese Chung K'ang script, there was a solar eclipse at noon 4100 years ago, which triggered a great panic. In ancient China, the people believed that in a darkness, a dragon devoured the sun, which could only be chased away by loud noises such as bangs, howls and trumpets. The court astronomers Hi and Ho were responsible for the warnings, who, according to the Chronik report, neglected their positions. Hi and Ho were publicly executed.
Date of solar eclipse: October 22, 2137 BC BC

Date: 22. 10. -2136 Geogr. Latitude: 39 Longitude: 126 (longitude and latitude Beijing) Time: 4 (4 a.m. world time = 5 a.m. Central European time) Degree networks: 10.0.0 (degree network 10 to 10 degrees for determining altitude and compass direction) Azimuth: 0.1 (direction south, 1 = double magnification) Height: 40.1 (center of the globe 40 degrees above the horizon)

Sun and moon height above the horizon 47 degrees, Azimuth (compass direction) south 11 degrees west.

For the 17th January 272 BC The astronomer Claudius Ptolemy (100-180 AD) reported a close approximation of Mars to the star β (beta) Scorpii.

Date: 17th 1. -271 Geogr. Latitude: 31.11 Longitude: 29.54 (29 degrees 54 arc minutes east longitude, 31 degrees 11 arc minutes after br.) Time: 3 Degree networks: 1,0,0 (degree network 1 to 1 degree for height and azimuth determination Azimuth: 330.2 (cardinal direction 330 degrees, 2 = maximum magnification) Height: 40.1 (center of the globe 40 degrees above the horizon)

The yellow cross marks the entered altitude and compass direction. Mars is 2 ° from Jupiter and 0.3 ° from Acrab ( β Skorpii, brightness 2.9 mag., Distance 544 light years, altitude 42.5 °, azimuth 328.5 °).

The brightness information of the stars is on zenith brightness based. The weakening of light (extinction) by the The lower the altitude of the, the greater the earth 's atmosphere Stars over the horizon. It is a good approximation Attenuation of light proportional to the cosecans of height. From 15 ° height, this approximation can therefore be used:

m = 0.28 (1 / sin h-1).
Zenith brightness Mars on 17th January -271:
0.9 likes + 2.8 * (1 / sin 42.2-1) = 1.0 mag. (Brightness of Mars at 42.2 degrees).

Antares is one of the supergiants. The surface temperature is around 3000 degrees C - hence its red color (flashing point near the dotted temperature line leading downwards). The radius exceeds that of our sun by 300 times (flashing point above the dashed line for radius (R) = 100 (sun = 1). Markings for mass in blue color on the main row of the diagram [mass M = ¼ solar mass, M = ½ , M = 1 (solar mass), M = 2 and M = 5]. Antares has approximately 10 times the mass. The brightness value on the right edge of the diagram shows that this star has a luminosity that is around 10,000 times greater (sun = 1). Our sun is one yellow dwarf star with spectral class G2, surface temperature 6000 degrees C, radius 696 000 km.

Astronomy in ancient times

In our latitudes, the starry sky is far from being as impressive as in the Orient, where celestial science already exists was a flourishing art millennia ago.

The Babylonians calculated veritable ephemeris of the Planet positions from day to day. The calculated ecliptical Lengths corresponded almost exactly to the actual errors 1 degree rarely occurred.

The Babylonians were already familiar with the medium length of the Lunar month, the solar year, the synodic orbital periods the planet and the Saros cycle of darkness. The Kidinnu's moon tables (380 BC) allowed them to do so Predicting the first appearance of the crescent moon after new moon. They have been watching planetary movements for centuries, were able to make the synodic from their records Derive round-trip times, with the help of which they make approximate forecasts about future positions. Of the true sequence of movements they didn't know anything. The Greeks were interested in that first, who took over and developed the astronomical knowledge of the Babylonians.

In the 6th century BC The Pythagoreans recognized the spherical shape the earth. Meton determined around 440 using the Gnomon (shadow stick) the solstices. Around 400 BC BC made Philolaus from Croton the first attempt to interpret planetary movements by entering a Central fire assumed to be around the sun, earth and planets concentrated circles moved. Democritus taught that the Milky Way consists of countless stars. Watched around 384-322 Aristotle that the shadow of the earth always with darkness is circular - he saw it as proof of the spherical shape the earth.  

256 BC Aristarch of Samos tried the first Determine distances of the sun and moon from Earth. He dropped the theory of the central fire and set it Sun at the center of our system. Eratosthenes (276-194) measured the circumference of the earth Determination of the latitude difference between Alexandria and Syene. Hipparch of Nicaea (190-125 BC), determined the length of the year with the accuracy of the Babylonians, put star catalogs and founded scientific astronomy. After comparing Hipparch discovered precession with older star catalogs (western movement of the spring point under the stars).

With Ptolemy, née 100 AD in Egypt, reached the Astronomy of antiquity their culmination point. The "Almagest" of Claudius Ptolemy [by Abul Wefa (959-989) published under this title] contained a summary and improvement of the astronomical systems of that time. Be The book remained the "Bible" of the book for 1½ millennia Astronomy. His writing was considered the irrefutable truth viewed. Because of his professional authority, he is considered the founder of the geocentric world system with the earth in focus which are Mercury, Venus, Sun, Mars, Jupiter, Saturn and in the end should move the sphere of the fixed stars.

Why the Ptolemaic World System Has Lasted 14 Centuries was also due to the fact that in Almagest a mature theory satisfactorily explained the zigzag movements of the planets and also allowed to predict their positions. Ptolemy assumed that the planets were in small circles (epicycles) move around the earth in a larger circle (deferent). Hipparch pointed out 300 years before Ptolemy, that the planetary course can be described by a circle, progressing to a bigger one.  

Copernicus was born on February 19, 1473 in the Polish city of Thorn. Basically, he did not deliver a much better planetary theory. Like Ptolemy, he worked with epicycles ( Fig. 14) and also wanted to trace the actually elliptical, uneven-speed planetary movements to circular orbits and uniform movements. In his book "De revolutionibus Coelesticum" (on the orbits of the celestial bodies) Copernicus tried to prove that the earth rotates around its axis, that it orbits the sun in one year and that the planets orbit the sun.

Aristarch of Samos already said 18 centuries before Copernicus, that the sun could be the center and the earth the general Movement must participate. A follower of Phythagoras by name Philolaus also taught a progressive earth movement. The Syracuse Higetas assumed a rotation of the earth around its axis. Nicholas of Cusa was also close, a heliocentric Shaping worldview, around 1440 he said that with oval tracks the planet must be counted.  

In Ptolemy’s day, the planetary movements were still possible can be calculated with sufficient accuracy, but occurred in the course of Time larger and larger deviations on - Mars already deviated 2 degrees from its predicted position. Commissioned in the 13th century the Castillian King Alfonso X (1223-1284) Arab, Christian and Jewish astronomers, the errors revealed to fix the Ptolemaic Tables. The "Alfonsine Panels "were also unsatisfactory. The theory of" Copernicus was able to better determine the celestial mechanics do not contribute. It was reserved for Johannes Kepler correct movements based on accurate sky observations Discover Tycho Brahes.

Tycho Brahe was an avid sky watcher. In 1576 he built his observatory "Uranienburg" on the island of Hven. It contained large angle measuring instruments designed by him (wall quadrants, Sextans and armillary spheres), which is a measurement of the star and Planetary positions on around 1 arc minute enabled. His very precise measurements and work earned him the reputation of the greatest astronomer before the invention of the telescope. In 1599 he moved to Prague to the Emperor Rudolf II, where he won Kepler as an employee, and Brahe commissioned him with the Editing his observations on Mars.

Johannes Kepler was born on December 27, 1571 in Weil der Stadt (Württ.) born. Through his teacher Michael Mästlin he heard as young astronomy student for the first time from revolutionary teaching of Copernicus, which inspired him. Called him in 1600 Tycho Brahe as an assistant to Prague. Brahe died in 1601. Kepler took over his position as "Imperial Mathematician". Brahe's extensive data, especially the observations of Mars, were the prerequisite for Kepler's work.

Kepler first attempted to use Copernicus' eccentric circular orbits to reconcile what he failed. Only after years of painstaking calculations he found that the planets were on elliptical orbits around the sun move.  

Kepler published the law of the planetary movement 1609 in his work "Astronomia nova" (new astronomy) and 1619 in "Harmonices mundi".

The 3 famous railway laws are:

• I. The planets move on ellipses, in one of them Focal point is the sun.
• II. The radius vector sweeps the same at the same times Surfaces.
• III. The squares of the orbital times of two planets behave like the cubes of its major axis.

Geocentric planetary movement

Date: 29. 5th 1971 Geogr. Latitude: 48.0848 Geogr. Length: 11.36 (Munich) Time: 6 Graticule: 0.0.0 Azimuth: 0.1 Height: 40.1

Key "P" - planetarium circuit.

On July 8, '71 Mars declined ( Fig. 15 and globe).

The inner planets Mercury and Venus recede as they overtake Earth. This is always the case at the time of their lower conjunction (sun, planet and earth in one line). The retrograde of the outer planets Mars, Jupiter, Saturn, Uranus and Neptune always begins a few weeks before their opposition to the sun (positions 1, 2 and 3 - Fig. S.).

On average, Mars turns 37 days before opposition to the sun (Position 1) declining (R = retrogr. Movement), 37 days after lawful (D = direct movement). Return Jupiter 60 days in advance and legally 60 days later. Saturn about 64 days before Opposition receded and legible again 64 days later. From Seen on the respective planet, the Earth performs similar loops.

The loops result from the inclination angle of the path planes against the ecliptic (earth orbit level). The geocentric ekl. The width of Mercury is max. 6 degrees, Venus can be up to 10 degrees deviate from the ecliptic, Mars 7, Jupiter 1.5, Saturn 2.5, Uranus 0.5 and Neptune 2 degrees.

If the planetary orbits were in the ecliptic plane, a loop would be formed not possible - the planet could only oscillate back and forth.

The movements of the sun and moon are always to the east directed; as well as that of the planets - except e.g. At the moment of their decline. We then observe for perspective reasons Downtimes, returns and loops. Since the Earth's Sun is closer, it is faster on its path. To the During the opposition, the earth overtakes the slower one seemingly moving planet. You experience the same effect when overtaking two railways, compared to the faster one Zug seems to slow down.  

Herzsprung-Russel diagram

The position of the selected star in the diagram is shown by Flashing and two guidance lines set.

The Danish astronomer Ejnar Herzsprung (1873-1967) was the first to establish a relationship between brightness, diameter and spectral type, which was taken up and further developed by the American astronomer Henry Russel ( Fig. 3).

Brightness, temperature and color are interdependent Sizes, as well as a piece of metal that teaches with increasing Heating red-hot, yellowish-white, then bluish-white Emits light.

According to the property mentioned above, the space of the Diagram are not evenly filled with star points. Most legally follows a main series, so are radiant hot stars with the greatest absolute brightness arranged on the left in the blue spectral range of the diagram (Spectral class O-A); the cool red stars with small abs. Brightness on the right in the yellow-red area (spectral class G-M).

There are also a number of red giant stars with large ones absolute brightness like Arctur and Capella. Lies above the area of supergiants, Antares, Betelgeuse, Rigel etc. Two stars with the same spectral class and temperature can have very different luminosity and dimensions.

Antares ( α Scorpii) in the Herzsprung-Russel diagram: spectral class M1, abs. Brightness -5M. The intersection of the two lines shows the position of the star in the upper right corner of the diagram (flashing point).

Starry sky z. Zyt. Des Odysseus

"The hero joyfully hoisted the swelling sails in the wind,
And now he sat down at the helm and steered artfully over the flood.
No sleep closed his watchful eyes,
Aimed at the Pleiades, and at Bootes, slowly
Sets, and the bear, which others name the carriage,
Who turns in a circle, looks at Orion,
And that of all of them never bathes in the ocean.
Because when divorced the noble goddess Kalypso ordered him
That he would always keep him on the left during his journey. "
(After a translation by H. Voß).

According to ancient information, the Trojan War lasted from 1194 to 1184. Odysseus is - according to the Homeric epic - the land of the Phaeacians almost at the end of his ten-year odyssey, around 1174 have reached in autumn (sinking of the constellation boat). Odysseus steered his raft eastward toward the stars.

"Because when divorced the noble goddess Kalypso ordered him That on his journey he (the constellation of the Great Bear) always on the left. "

After seventeen days, Odysseus reached the land of the Phaeacians (Schliemann thought Corfu to be).

Date: 23. 9-1173 Geogr. Latitude: 39 Geogr. Length: 20 (Corfu) Time: 8:00 p.m. (8:00 p.m. World Time = 9:00 p.m. Central European Time [CET]) Grade networks: 10.90.90 (10 to 10 degree horizon system, equator and ecliptic) Azimuth: 180.1 (direction north, 1 = double size) Height: 40.1

That still had the circumpolar constellation of the Great Bear 3100 years ago its lowest northern level (lower Culmination) at 20 degrees ("And never alone bathes in the ocean. ").

The constellation Bootes sets in the north-west. The celestial north pole is always at a height that corresponds to the value of the latitude - here 39 degrees. Today's Polarstern ( α Ursae Minoris) stood z. Currently Odysseus is still far from the North Pole (key "P" and "K"). How do sailors view the constellation today?

Date: 23. 9. 2000 Geogr. Latitude: 39 Geogr. Length: 20 Time: 22 Gradual network: 10.90.90 Azimuth: 180.1 Height: 10.1

Is the Big Bear still visible over Corfu in 2000 years?

Date: 23. 9. 4000 Geogr. Latitude: 39 Geogr. Length: 20 Time: 0 Gradual network: 10.90.90 Azimuth: 180.1 Height: 10.1  

Precession

Precession (Latin: precedere = 'going ahead') denotes the slow shifting of the equinox points (spring and autumn point). The equinox point for the beginning of spring is also the zero point for counting the length, which is continuously increasing due to this shift to the east. As a result, the coordinates (ecliptical longitude, recascension and declination) are only strictly valid for a certain point in time. This constant shift of the equinox and solstice points from the stars is caused by the gyroscopic movement of the earth's axis around the pole of the ecliptic ( Fig. 17).

Those visible today at midnight in the south at the beginning of summer Constellations will become winter constellations in 12,000 years. The sky equator is also slowly shifting and runs in several millennia through completely different constellations.  

To stabilize the earth's rotation, a so-called equatorial bulge was formed, on which mainly the sun and moon exert their attraction. These forces endeavor to straighten the axis of rotation inclined by 23.5 degrees. As a result of the counteracting centrifugal force, the earth's axis cannot follow the attractive forces and deviates by precessing against the direction of rotation ( Fig. 18).

A gyroscopic movement around the pole of the ecliptic spans 26,000 years (Platonic year). The starry sky is perfect during this period one turn around the pole of the ecliptic. As a result of Precession therefore increases the ecliptical length of a star, while the ecliptical latitude remains the same (the ecliptical latitude changes only through the star's own motion.  

Orion is a winter constellation. The star Mintaka ( δ Orionis) is on December 21, 2000 (beginning of winter) at 11:29 p.m. World time in London's north-south circle (longitude 0 degrees).

Date: 21. 12. 2000 Geogr. Latitude: 51 Geogr. Length: 0 Time: 23.29 Degree network: 90, 15.90 [cardinal points (red arches), 15 to 15 degrees right ascension and declination circles (green lines), ecliptic (yellow arches)] Azimuth: 0.0 Height: 30.1

The yellow arch leading past Orion is the right ascension circle The green runs at 6 o'clock, 15 degrees or 1 hour west Hour circle 5 o'clock. The right ascension is the length of a star along the equator from spring.

The declination (deviation from the equator) of the Mintaka star is 0 degrees (it is currently on the celestial equator). Since the local sidereal time is the time of a right ascension circle in the north South circle corresponds to the displayed local sidereal time - key "O" - the right ascension value. The right ascension of the star Mintaka is the same as the local sidereal time: 5: 32 min the local time is currently 5:32 min., Mintaka says exactly in the north-south district of our village.

When will Mintaka be at 23:29 in 6000 years? London North-South Circle?

Date: 5th 3,8000 Geogr. Latitude: 51 Geogr. Length: 0 Time: 23.29 Graticule: 90.15.90 Azimuth: 0.2 Height: 30.1

In 6000 years, the right ascension of the star takes 5 minutes 6 minutes. and is 10: 38 min. The declination is then -16 degrees south of the sky equator. The yellow one leading past Orion Arc is the 180 degree ecliptical longitude.

The star Mintaka, which is currently culminating in the beginning of winter reaches its world time in 6000 years on March 5th at 11:29 p.m. highest southern level in London's north-south district. The winter constellation Orion became the spring constellation. Culminated on December 21, 8000 Mintaka only at 4:26 min. World time.

brightness

The faintest stars still visible to the naked eye in the dark night sky the size is +6 mag. The brightness of the Stars are generally called "mag." abbreviated or with the superscripted letter "m" (lat. magnitudo = 'Size').

Capella is 0.21 mag. bright, Arcturus 0.24 mag., Altair 0.89 mag. For lighter stars - e.g. B. Sun and Moon - were next to the Brightness 0 mag. negative size classes introduced, similar a temperature scale. The sun's brightness is -26.73 mag., like the full moon -12.55. The brightest after our sun Stern is Sirius with -1.43 mag.

Around 6000 stars up to the 6th size class are visible to the naked eye visible. Half of it is below the horizon. A third goes down in the haze of the horizon, just stay 2000-3000 visible stars on a clear night. With the Binoculars can hold around 1,000,000 stars up to the 11th magnitude can be achieved with larger telescopes up to brightness +15 likes around 30 million.  

The visual perception of brightness corresponds to the logarithm the radiation intensity; we see the same brightness same intensity ratio.

The radiation intensity of a star of brightness 0 mag. is = 1, that of a star of size +5 mag. = 100, which means 100 times is weaker. The intensity changes for each size class of light radiation by a factor of 2,512. A star of greatness -1 likes. is therefore 39.81 × brighter than a star +3 mag.

The decade. Log. of 2,512 is = 0.4. Log 2.512 = 10 ^0.4 .
Computer arithmetic: Print log 10 (2,512) = 0.4. Print 10 ^0.4 = 2,512.
A star of brightness +6 likes. therefore has the intensity 10 ^{0.4 × 6} = 251.188 (Print 10 ^∧ 2.4 = 251.188 - " ^∧ " = potentiation arrow).
The full moon is -12.6 mag. bright, how much brighter is it compared to a star of size +5 mag.?
Size class difference: +5 mag .- (- 12.6 mag.) = 17.6 mag. 10 ^{0.4 × 17.6 mag.} 10 ^7.04 = 10 964 782 brighter.
The full moon is around 11 million times brighter.

Brightness intensity

- 5 mag. 100,000 - 4 mag. 39.810 - 3 mag.15.848 - 2 mag.6.309 - 1 mag. 2.512 0 mag. 1 + 1 mag. 0.398 + 2 mag.0.158 + 3 mag.0.063 + 4 mag.0.025 + 5 mag.0.010 +10 mag.0.0001 +25 mag.0.000001 +20 mag.0.00000001

A +20 likes. The faint star is therefore 100,000,000 × weaker than a star of size 0 mag.
10 ^{0.4 × 20 mag.} = 10⁸ = intensity 1/100 000 000
log 100,000,000 = 10 ^{8 / 0.4} = 20 mag.
Visually, the eye still distinguishes differences in brightness of 1/10 mag.

The difference in brightness between our sun (-26.73 mag.) And that of Sirius (-1.43 mag.) Is: -1.43 - (- 26.73) = 25.3 m.
In intensities 25.3 mag .: 10 ^{0.4 × 25.3 mag.} = 10 ^10.12 = 1.3183 x 10¹⁰;
therefore our sun has 13.181 billion times stronger radiation. Since the distance is not taken into account here, it is only a question of the "apparent brightness".

If the sun and Sirius were at a distance of 32.59 light years, it could the brightnesses are compared; then one speaks of the so-called "Absolute Brightness" that with the capital letter "M" is referred to.

The sun has an absolute brightness of +4.84 M. One light year are 9,463 × 10¹² km. 32.59 light years are therefore 3,084 × 10¹⁴ km (Computer arithmetic: number representation semi-logarithmic 3.084E + 14). The sun is 149 600 000 km away, has -26.73 likes. apparent Brightness, what brightness does it shine in 32.59 light years?

3.084E + 14 km / 1.496E + 8 km = 2 061 497 (= around 2 100 000 times the sun-earth distance). The brightness decreases with the square of the distance: 2 061 497² = 4.2498E + 12; this sum is the intensity ratio to be converted into size classes:
Log 4.2498 × 10¹² = 10 ^12.628 / 10 ^0.4 = 31.57 size classes.
Apparent solar brightness in 1 496 000 000 km = -26.73 mag. +31.57 mag. = Absolute brightness in 32.59 light years apart: +4.84 mag.

According to astronomical measurements, the annual parallax of the Sirius is 0.375 ″ (arc seconds), so Sirius is 3.26 / 0.375 = 8.69 light years away (1 pc - parsec - parallax second = 3.26 light years). 32.59 Lj./8.69 Lj. = 3.7503 times further away (0.375 ″ × 10). Brightness decreases with the distance square:
3.7503² = 14.06475 (intensity ratio): Log ^{14.06475 = 10 1,148 / 10 0.4 =} 2.87 mag. = -1.43 M + 2.87 mag. = Abs. Brightness in 32.59 ly. = + 1.44 M.
Size class difference: +4.84 M-1.44 M = 10 ^{3.4 × 0.4 mag.} = 10 ^1.36 = 22.9 mag.
Sirius exceeds the luminosity of our sun by 23 times.

A star with parallax 0.015 ″ of apparent brightness +2.97 has the abs. Brightness -1.14 mag. This is larger because the brightness increases with the square of the decreasing distance. Deneb - brightest star in the constellation Swan (Cygnus) - has the abs. Brightness -6.2 mag. (with interstellar absorption), in 32 light years it would be 3 × brighter than Venus. However, Deneb is 930 light years away, so its apparent brightness only likes +1.3. is. With the abs. Comparing the brightness of the sun, it is around 4.84 M - (- 6.2 mag.) = 11.04 mag. (10 ^{0.4 × 11.04} = 10 ^4.416 ) = 26 061 × brighter.

Aldebaran - brightest star in Taurus (Taurus) - is about 40 × larger and has 4 × more mass, but its average density is 200,000 times less. Antares - by the Greeks because of its Red color of Mars comparable to the planet Mars Called (Ant-Ares) - surpasses our 1.4 million km sun 300 times, the red supergiant Betelgeuse even that 400-500 times.

A Hefner candle at a distance of one meter corresponds to the apparent visual brightness: -14.2 mag. (= 1 lux). Venus is an average of -4 mag. bright. difference: -4 - (- 14.2) = 10.2 mag.
Intensity ratio: 10 ^{0.4 × 10.2 amg.} = 10 ^4.08 = 12 022.6.
A candle at a distance of one meter is 12 023 × brighter. -4 likes corresponding to the brightness of a candle in √ = 109.6 meters.

Mercury is between +4 mag. and -2 likes. bright, Venus -3.5 mag. to -4.5 mag., Mars +2 and -2.6 mag., Jupiter -1.5 to -2.5 mag., Saturn's brightness varies between +1.2 and -0.5 mag., Uranus max. +5 mag., Neptune is with max. +7.5 likes no longer with the naked eye to see. The most distant planet Pluto (Hell. +15 mag.) Is only visible with large telescopes. Venus is that after the sun and moon brightest star - its light is brilliant white.

The planets are particularly noticeable in that they face the flickering stars (scintillation) shine much more calmly.  

Sidereal time

The sidereal time is the orbit of the earth around the sun certainly; as opposed to the mean solar time that comes from derived from the rotation of the earth around its axis.

The sun reaches the middle point of spring (equinox point for the beginning of spring) after 365.2422 days (1 tropical Year). Due to the precession, this point migrates annually 50.26 arcseconds (= 0.0139611 degrees) to the west of the sun opposite. Therefore, she does not complete 360, but only 360-0.0139611 = 359.98604 degrees. The average solar movement in the sidereal year is therefore 359.98604 / 365.2422 = 0.9856091 degrees per day. Because of the 50.26 ″ it takes 20.4 minutes longer to reach a full 360 degrees to cover. This period corresponds to the length of a sidereal Year, which, based on the stars, lasts 20.4 minutes longer. 360 / 0.9856091 = 365.25636 days (length of the sidereal year). At the tropical end of the year, the earth completed in relation to the sun 365,2422 days, but in relation to the stars, it led one additional rotation as the sidereal time is around 4 minutes daily runs faster.

Average apparent sun movement per day of the tropical year: 360 / 365.2422 = 0.9856473 degrees × 4 minutes = 3 minutes 56.55536 seconds (Progress from sidereal time per day compared to solar time: 3 min. 56.55536 sec.), That is 365.2422 days × 3 min. 56.55536 in the year Sec. = 1440 min. = 1 day. 365.2422 sunny days therefore correspond 366.2422 sidereal days.

1 middle sunny day = 366.2422 / 365.2422 = 1.002737909 sidereal days 24 hours 3 minutes and 56.55536 seconds

1 middle sidereal day = 365.2422 / 366.2422 = 0.997269566 sunny days = 23 hours 56 minutes 4.09054 seconds  

On December 12th at 12 noon the sun culminates with any star in the geographic local meridian (north-south circle - upper figure). On December 31st, the star already culminated at 8 a.m., because the sun continued to move around 4 × 30 days = 120 minutes or 30 degrees as a result of its apparently eastern movement. The star culminates earlier and accordingly moves westward away from the sun. Therefore, new constellations always appear in the eastern sky over the course of the year. Local star time key "O" ( Fig. 19).

attachment

Constellations north of the sky equator

Constellations south of the sky equator (marked with *) enclose it)

Longitude and latitude

Christian chronology accounts for the calendar years Christ's birth. The one with the setting of the calendar commissioned monk Dionysius Exiguus (500-556) was wrong 5 years. In addition, the number "0" between 1 v. BC and AD 1 disregarded; therefore the astronomical distinguish mathematical count from historical.

1900 AD (hist.) = 1900 (astronomical) 1 AD (hist.) = 1 (astronomical) 1 of Chr. (Hist.) = 0 (astronom.) 2 of Chr. (Hist.) = 1 (astronom.) 13,000 BC Chr. (Hist.) = 12 999 (astronom.)

Historical years before BC are to be reduced by 1 and enter negative.

Date entries from October 15, 1582 relate to the Gregorian, before that on the Julian calendar.

The precise entry to one degree is generally sufficient. For more precise entries with arc minutes and seconds accuracy The following examples are used:

Geographical coordinates of the Cologne Cathedral (Dachreiter):
50 ° 56'33 "north latitude and 6 ° 57'33" east longitude.

Entry in the form:

Geogr. Latitude: 50.5633 Geogr. Length: 6.5733

After the number of degrees, a separating decimal point (never use commas when entering the latitude and longitude), then the values for arc minutes and arc seconds.
Southern latitude Cape Town: -33 ° 58′06 ″.
Input: Latitude: -33.5806
Always enter southern latitude with a negative sign. Fill in missing positions:
56 ° 1'11 ″ = 56.0101; 1 ° 1′10 ″ = 1.0110; -0 ° 0′1 ″ = - 0.0001.

The longitude is counted from the prime meridian in Greenwich: 180 degrees positive in an easterly direction (e.g. 139 ° 45 ′ east longitude Tokyo) and 180 degrees negative to the west (e.g. -73 ° 58 ′ west Length New York). The western longitude always gets one negative sign. Always input in sexagesimal form; Degree., Arc minutes and arc seconds (°, ′, ″).

Always enter only universal time. The Central European Time (CET) applicable in Germany must therefore be reduced by 1 hour before entering (2 hours for summer time).
6:30 p.m. 9 sec. CET = 5:30 p.m. 9 sec. UT (world time).
Fill in missing digits with a zero: 2:30 a.m. 1 s = 2,3001; 0 o'clock 0 m 1 s = 0.0001.

The height of the center of the globe receives the desired height above the horizon; through the azimuth indication the instrument is turned in the chosen direction. The entry under azimuth and altitude is also in sexagesimal Shape possible.

Input:

Azimuth: 45.3145 Height: 20.1530

The center of the globe is 20 ° 15'30 ″ above Horizon and the compass 45 ° 31′45 ″ (southwestern starry sky appears).

The graticules of the 3 coordinate systems horizon / equator / ecliptic are selected in the form: "Degree networks: 0.0.0". The first zero before the comma refers to the degree network for the horizontal system, the second on the equator and the third Zero on the ecliptic system.  

Coordinate systems Horizontal system

The position of a star can be determined by height and direction determine. This is either calculated or with angle measuring instruments (meridian circle, theodolites, Sextants etc.) measured.

The plumb line points upwards to the zenith and points downwards the vertical to the nadir of the site. Zenit and Nadir are the poles of the horizontal system. The runs at the north pole of the earth Plumb line parallel to the earth's axis, so that the zenith of the horizon and the north pole of the sky - polar star at the zenith. The horizon and equator are therefore at the geographical north or south pole at the same level.

example

Date: 1.2.2000 Geographic latitude: 90 (North Pole)
Longitude: 10 Time: 12 degree network: 90.90.0

The 4 red arches converging at the zenith appear, as do the 4 green ones converging in the North Pole Right ascension sheets (0, 6, 12, 6 p.m.).

Azimuth: 0.0 Height: 90.1

Since the sky equator and horizon are identical at the north pole, move all stars are parallel to the horizon; can neither open nor perish. The sky revolution can only be parallel to the horizon so the sun, moon and planets can only be there as a result their own movement rise and fall.  

The horizon level, zenith and nadir are the guiding points of the Horizontal system, as well as the geographic poles and the equatorial plane form the guiding points of the geographic coordinate system. The angular distance from the east or west point becomes parallel to Horizon level measured and called nautical amplitude. The angular distance from the east or west point when opening or Fall down the horizon becomes astronomical labeled morning and evening width.

The horizon coordinates determine the position of a star at the sphere only for the moment because azimuth and Altitude change due to the sky revolution. As having an angle measuring instrument (theodolites) is rare, simple aids are sufficient if necessary such as a ruler, ruler or tape measure, around azimuth and height to determine. Hold a ruler at arm's length against the Sky, 1 cm corresponds to one degree.

Is the azimuth for the rise of the sun z. B. N 70 degrees O, can from the east point 90-70 degrees = 20 degrees (morning distance 20 degrees) measured to the north and the sunrise point determined.

Every circle passing through Zenith and Nadir is a great circle. These great circles intersect the horizontal plane vertically or vertical; hence the term vertical or vertical circles. The running through the east, zenith, nadir and west point, the great circle marking the east-west direction carries the Description "First vertical".

The great circle running through the south, zenith, north and nadir point, which determines the north-south direction of the horizon, is the geographical meridian (longitude) of our location (red north-south line when entered under degree network 90.0.0 - Fig. 20).

The azimuth is measured parallel to the horizontal plane and shows the direction of the stars. This angle is counted astronomically from the south point over the west in a full circle (0 ... 360 degrees) (south 0 °, west 90 °, north 180 ° and east 270 °), but can also be specified quadrantally, e.g. B. S 50 ° W. Stars in the first vertical have an azimuth of 90 ° (west direction) or 270 ° (east direction). The circles of heights and latitudes of the apparent celestial sphere are small circles, but are also called parallel parallels, azimuthal circles or Almucantarate. All stars on the same almucantar have the same height or the same azimuth on the vertical circle ( Fig. 21).

The entered longitude or local meridian forms the sky meridian (north-south line) by the Culminate stars between rising and setting. Your walk due to the southern local or celestial meridian, the upper, the lower culmination through the northern celestial meridian.  

Coordinate system of the sky equator 1st order coordinates Fixed equatorial system: declination ( δ ) and hour angle ( t )

The hour angle ( t ) a star is its angular distance from the geographically fixed location or celestial meridian (north-south line) of the selected location; it is therefore called a fixed equatorial system [hour angle ( t ) = Local star time minus right ascension].

If the hour angle is 0 hours, the star culminates in the upper, at 12 hours in the lower local meridian. The hour angle indicates the time before or after culmination. There is a star in the eastern sky 45 degrees before the north-south circle (sky meridian), its hourly angle is 3 hours east (1 hour = 15 degrees).

The declination (deviation) is the angular distance from the earth or sky equator and therefore corresponds to the latitude. The sun's declination reaches z. B. Values between + 23.5 ° (Beginning of summer) and -23.5 ° (beginning of winter). With a declination of +10 degrees it makes its daily orbit due to the sky change by the zenith of all earth locations of latitude 10 degrees.

2nd order coordinates Movable equatorial system: right ascension ( α ) and declination ( δ )

The geographical longitude and latitude circles in the sky projected form the spherical right ascension and Declination circles. The earth equator becomes the sky equator, North and south poles of the earth to the north and south poles of the apparent Celestial sphere, the axis of the earth to the celestial axis, around which the Starry sky to the west in the opposite direction turns. Once a day longitude and latitude are correct Right ascension circles. The right ascension of the Stars then always corresponds to the longitude 0:00 local time in Greenwich.  

In order to create a geographical location-independent coordinate, a zero meridian was also defined on the sphere. Since this prime meridian participates in the daily rotation of the sky, it is called the 2nd order moving or equatorial system. This zero hour circle is the right ascension circle running through the celestial poles and spring point, which is always at 0:00 local sidereal time in the north-south circle at a height of 90 degrees - latitude above the horizon ( Fig. 22).

The right ascension increases to the east. Is the right ascension of a star equal to the local star time, the star culminates in the celestial meridian of the location. Stars exactly on the North-south line have the right ascension of local sidereal time, which is displayed after pressing the "O" key. Reach a star in the south (upper culmination) or north (lower culmination) its highest or lowest level or below the horizon in the local meridian, one speaks of his culmination (lat. culmen = 'summit').

The prime meridian of the sky in the local meridian (culmination of the Spring time), local sidereal time is 0 o'clock. To The hour angle of the spring point is 3 hours 45 degrees or 3 hours east. His hour angle with the north The south circle of the location is therefore the sidereal time of the location. The right ascension length of a star from the spring point is given in time since the north-south circle of the site (e.g. Greenwich prime meridian) and the prime meridian of Celestial sphere (0 o'clock hour circle of the spring point) against each other due to the sky revolution move.

The sky equator (declination circle 0 degrees) always runs through the east and west point of the horizon. The height of the north and the South Pole above or below the horizon is always the same latitude of the chosen location.

Coordinate system of the ecliptic

There is a geocentric and heliocentric system to distinguish. The geocentric ecliptic system exists the positions of the stars as they are on Earth Skies are visible during the heliocentric system Positions related to the center of the sun.  

Geocentric ecliptical longitude and latitude

The plane of the earth's orbit serves as the basic or reference plane of the ecliptical longitude ( λ ) and latitude ( β ). The earth orbit plane projected onto the sky is the ecliptic (Greek eclipse = 'disappear'. Eclipses of the sun and the moon can only occur near the ecliptic ( Fig. 23).

The earth's orbit runs through the center of the sun and the center of the earth, so that the ecliptical latitude of the sun is always 0 ° 0 '. The axis of rotation is not exactly perpendicular to the orbital plane, but is currently inclined at 23.5 degrees. The equatorial and earth orbital plane (ecliptic) therefore form a variable angle over the millennia with the extreme values of 22-24 degrees ( Fig. S.).

The ecliptical length becomes from the spring point (0 degrees Aries) counterclockwise on the ecliptic level to the east measured in the direction of the apparent movement of the sun. The stellar prime meridian (intersection of the ecliptic and Equatorial plane) the sun passes around March 21st. The sun passage through the spring point is independent of the calendar. 1582 fell the beginning of spring on March 10th. After the introduction of the Gregorian Calendar reform again on the 21st  

From the prime meridian (spring point) the ecliptical length becomes counted along the ecliptic, the right ascension on the Equatorial plane. At the beginning of spring each exceeds Sun the sky equator (earth equator projected on the sky) to the north (right ascension 0 o'clock, declination of the sun 0 degrees, ecliptical longitude 0 degrees, ecliptical latitude always 0 ° 0 ′).

Their northern deviation from the equator reached the highest level at +23.5 degrees at the beginning of summer (Tropic of Cancer) around June 21 ( Fig. 24).

All great circles that run through the ecliptical north and south poles and intersect the ecliptic vertically are ecliptical longitude circles. The ecliptical latitude ( β ) is measured along the ecliptical longitude circles positively in the north and negatively in the south.

Examples

Date: 21. 3rd 2000 Geogr. Width: 50 Geogr. Length: 9 Time: 11:27 Gradual network: 30.90.90 Azimuth: 0.0 Height: 30.1

On March 21st the sun is in the spring point (0 degrees Aries) in the local meridian Frankfurt / Main (50 ° Br. and 9 ° ÖL). The right ascension circle 0 o'clock is in the north-south circle. The local star time is the time of the respective right ascension circle in the local meridian. At 0 o'clock local time always happens the spring point 0 ° Aries, at 6 o'clock the solstitial point 0 ° Cancer, 12 o'clock the equinox point 0 ° Libra, at 6 o'clock the Solstitial point 0 ° Capricorn the local meridian, whose longitude was entered.

Date: 20th 3rd 2000 Geogr. Width: 50 Geogr. Length: 9 Time: 11.31 Degree network: 90.30.0 Azimuth: 289.0 Height: 40.1

The declination circles run at 50 ° north latitude diagonally to the horizon. The sky equator intersects them Horizon level always below the angular amount of Complementary latitude of the place (90 degrees - latitude = Height of the sky equator above the horizon in the north-south Circle). They move during their day and night arc the stars on declination circles parallel to the Sky equator run.  

Which day and night arc do the stars describe for places on the earth's equator (latitude 0 degrees)?

The sky equator then cuts the horizon under one 90 degree angle - latitude = 90 degree.

Date: 20th 3rd 2000 Geogr. Latitude: 0 Geogr. Length: 9 Time: 11.31 Degree network: 90.30.0 Azimuth: 289.0 Height: 40.1

The stars go up and down vertically. Around March 21 and September 23 at noon the sun is at the zenith of a geographical location Latitude 0 °. The starry sky rotates around the north-south axis the celestial sphere that is on the latitude 0 ° in the plane of the horizon (height of the celestial north pole above the Horizon = the geographical latitude of the place - at the earth's equator = 0).

At the North Pole, the sun rises on March 21 and reaches the Summer begins around June 21st the Tropic of Cancer. The ½ year old does not begin until the beginning of autumn around September 23 Polar night. The height of a star at the geographical north or south pole is equal to the declination.

Date: 21. 6. 1995 Geogr. Latitude: 70.40 Geogr. Length: 23.40 (hammerfest) Time: 22.2824 Degree network: 90,30,90 Azimuth: 180.0 Height: 40.1

At the beginning of summer, the sun sets north of the Arctic Circle not under even during their lower culmination (24-hour polar day). The yellow ecliptic arch lies a few more degrees above the horizon of Hammerfest, so that the sun remains visible at midsummer night.

At what horizon point (morning distance) the sun rises on March 21 (beginning of spring), June 21 (beginning of summer), Sept. 23 (beginning of autumn) and Dec. 21 (beginning of winter) open?  

Messier catalog

The French astronomer Charles Messier (1730-1817) hired one Catalog of easy-to-find objects. The original Catalog ends with M 103. In 1921 C. Flammarion added the sombrero Galaxy added. Objects 105-107 were created by H.S.Hogg in 1947 recorded; No. 108 and No. 109 by Owen Gingerich 1960 added. NGC / I. = number in Dreyer's New General Catalog or index catalogs.

Supernova in 1054

The Chinese chronicle of the Sungh dynasty reports about a new star 900 years ago that was seen even during the day. In North America, Indios reproduced the supernova explosion of AD 5/7 1054 in two petroglyphs ( Fig. 28).

The rock painting shows the narrow crescent moon near the supernova (on July 5, 1054). The nebula in the Taurus constellation carries the Name Messier 1 (M 1 - Cancer Nebula).

Date: 5th 7. 1054 Geogr. Latitude: 36 Longitude: -112 (Northern Arizona) Time: 12 (4:32 a.m. mean local time) Graticule: 0.0.0 Azimuth: 270.1 Height: 25.1

The waning moon is 4 degrees north ( Fig. A).

The increasing sickle was in conjunction with M 1 on 4 April 1055 ( Fig. B). The Indios were good observers of the sky, after the waning sickle was visible on July 5, 1054 next to the supernova ( Fig. A), they painted the increasing sickle in the nearby cave in the closest approximation to M 1 9 months later.

Date: 4th 4.1055 Geogr. Latitude: 36 Geogr. Length: -112 Time: 5.30 a.m. (10 p.m. 2 min. Mean local time - 3. 4. 1055) Graticule: 0.0.0 Azimuth: 90.1 Height: 25.1

Claims (1)

The celestial globe is characterized by its novel electronic design, which enables the globe to be used like an instrument.
The real-time sequence for 30,000 years reflects the stars' own movement, their daily rise and set - with continuous date and time information. Information about stars, planets, nebulae, star clusters and galaxies is available by clicking on them The planetarium circuit - again with the date and time lapse - shows the planetary movements with their standstills, returns and loops. The movement sequence here is 3 seconds, 1 day. Magnifications, graticules, meteor shower, lines connecting the stars to a constellation can be selected.
As a tool for scientists, historians, navigators, as a learning device for students, schoolchildren and everyone, it also surpasses an elaborate and complicated projection planetarium in terms of its scientific usability.
The precession movements of the earth's axis and the resulting changes in the position of the stars can be traced back over thousands of years.
The invention has for its object to faithfully reproduce the events and changes in the sky over a large period of time in terms of date, time and geographical location in the past, present and future.