RU2614464C2 - Spacecraft control method for flying around moon - Google Patents

Abstract

FIELD: aviation.

SUBSTANCE: method comprises undocking the SC from Earth orbital space station (OSS) and transferring to flight path to the moon. Then SC is placed into selenocentric orbit. After being there a specified time the SC is transferred to the flight path to Earth in a plane coinciding with the plane of the original OSS low earth orbit at a specified docking point. In order to accomplish that, SC orbital plane change is performed on the selenocentric orbit at a predetermined angle. Further, SC drifts down until the height of the OSS orbit by several brakings in the Earth's atmosphere. Then the SC is docked again with OSS.

EFFECT: possibility of multiple flights, for example, between near-earth and near-lunar OSS at relatively low reference speed input and in a time of about 15 days.

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Description

The proposed control method can be used in space technology when organizing the moon around a spacecraft (SC), located, for example, as part of a near-Earth orbital station (OS). It is assumed that, after the Moon’s flight, the spacecraft returns to its initial near-Earth orbit for subsequent docking with the OS [1. "Moon. Step to the Solar System Development Technologies ”under. ed. V.P. Legostaeva, M., RSC Energia, 2011].

A known control method, selected as an analogue in which the moon is circled using the Zond-7 spacecraft, is launched into the reference orbit by the Proton launch vehicle (LV). After launching into near-Earth orbit, the Zond-7 spacecraft performs a take-off impulse for flying around the Moon along a return trajectory [2. IN AND. Levantovsky "The mechanics of space flight in an elementary exposition", M., Science, 1980]. The main disadvantage of this control method is that the spacecraft after the moon’s flight enters the Earth’s atmosphere with subsequent landing in a given area and, therefore, the use of this spacecraft is many times impossible.

There is a known method of controlling the spacecraft for the Moon’s flyby, selected as a prototype, which includes applying to the spacecraft in the initial low Earth orbit an impulse for a flight to the moon of duration t ₁ , an impulse to transition to a selenocentric orbit, in which the spacecraft performs a flight of duration t ₂ and an impulse for a return flight to the Earth with a duration of t ₃ [2]. The spacecraft (SC) Apollo-12, launched to the reference orbit using the Saturn-5 LV, was considered as a spacecraft. After the launch, the spacecraft performs a take-off impulse for the flight to the moon. After transferring to the selenocentric orbit of the spacecraft and performing the number of turns around the moon specified in the flight program, the spacecraft performs a take-off impulse for a flight to Earth with subsequent entry into the atmosphere and landing in a given area, which, like the analogue, eliminates its repeated use and is the main disadvantage.

The objective of the invention is the implementation of the flyby of the moon, followed by the return of the spacecraft to the initial near-earth orbit for docking with the OS and the possibility of reuse of the spacecraft.

The technical result of the invention is the possibility of working out a spacecraft intended for multiple flights between the near-Earth OS and the OS located in the orbit of the Moon.

The technical result is achieved due to the fact that in the spacecraft control method during the Moon’s flyby, including the application to the spacecraft in the initial near-Earth orbit, a pulse for a flight to the Moon of duration t ₁ , a pulse for transition to the selenocentric orbit, in which the spacecraft performs a flight of duration t ₂ and an impulse for a return flight to the Earth with a duration of t ₃ , in contrast to the known method, after completing a flight to the Earth, the spacecraft is returned to the plane of the initial near-earth orbit, for which they determine continue flax t ₂ according to the formula

,

,

where ϕ ₁ is the angle between the Earth-Moon line and the plane of the initial near-Earth orbit at the time of application of the take-off pulse,

ω _ОЗ is the angular velocity of the precession of the plane of the initial near-Earth orbit,

ω _L - the angular velocity of rotation of the Moon relative to the Earth,

t ₄ is the time interval necessary for matching the height of the orbit of the spacecraft with the height of the initial near-earth orbit,

and in one of the apexes of the selenocentric orbit, a pulse is applied to the spacecraft to rotate the line of nodes at an angle Δϕ in the direction perpendicular to the plane of the orbit, determined by the formula

,

,

where ϕ ₂ is the angle between the Moon-Earth line and the plane of the selenocentric orbit at the time of the spacecraft’s arrival to the Moon,

ϕ ₃ is the angle between the Moon-Earth line and the plane of the selenocentric orbit at the time of application of the impulse for the return flight to the Earth,

Δϕ _d is the correction angle determined by calculation, fending off perturbations of the selenocentric orbit from the Earth and the Sun and differences between the projections of the angles ϕ ₂ and ϕ ₃ on the plane of the Earth's equator from their true values.

We will consider the proposed method by the example of a spacecraft docked to the OS located in the initial near-Earth orbit. The technical result in the proposed control method is achieved due to the fact that after separation from the OS and the application of the take-off impulse, the spacecraft is transferred to the flight path to the moon. Upon reaching the lunar orbit, a braking impulse is performed to transfer the spacecraft to the selenocentric orbit. After the specified time spent by the spacecraft in this orbit, an impulse is executed for the return flight to the Earth. After a flight to the Earth, due to several decelerations in the Earth’s atmosphere, it switches to the so-called brake ellipses [2], gradually reducing the height of the orbit up to the height of the orbit of the OS. Then the SC again docked to the OS.

The specified time spent in the selenocentric orbit is necessary for the planes of the orbits of the OS and the spacecraft to coincide after the completion of the braking of the spacecraft in the Earth's atmosphere. The spacecraft performs a take-off impulse from the initial plane of the near-Earth orbit. Due to the rotation of the moon with an angular velocity ω _Л ~ 13.2 ° / day, the flight to the moon in this coordinate system is performed with a certain anticipatory angle ϕ ₁ ~ 27 ° [3. "Fundamentals of the theory of spacecraft flight", ed. G.S. Narimanova, Mechanical Engineering, Moscow, 1972] between the Earth-Moon line and the plane of the original orbit. Due to the off-center nature of the Earth’s gravitational field, the initial near-Earth orbit where the OS is located has an angular precession velocity of the plane ω _{ОЗ of} about 5 ° per day [3]. Therefore, during the time consisting of the flight time to the moon t ₁ , the time spent in the selenocentric orbit t ₂ , the return flight to the Earth t ₃ , and the time after the return flight until the spacecraft returns to the OS orbit plane t ₄ , the initial plane of the OS orbit due to the precession will turn around

in a clockwise direction, when viewed in projection onto the plane of the equator of the Earth from the North Pole. Now consider the rotational motion of the moon. By the beginning of the return flight, the Moon-Earth line will unfold relative to the initial position of the plane of the original OS orbit by an angle ϕ _L , calculated by the formula

To combine the planes of the orbit of arrival and the orbit of the OS, it is necessary that the Moon-Earth line at the time of departure, be in the plane of the original near-Earth orbit, i.e. ϕ _L = 180 ° -ϕ _OZ .

Solving this equation, with respect to t _2, one can obtain the admissible time spent by the spacecraft in a selenocentric orbit

For optimal return to Earth with minimal fuel costs, it is necessary that at the moment of application of the impulse for departure, the lead angle between the Moon-Earth line and the plane of the selenocentric orbit is ϕ ₃ ~ 60–70 ° [3]. If the spacecraft speed, formed by the geometric addition to the spacecraft’s orbital speed in the selenocentric orbit of the take-off impulse and the linear velocity of the moon (~ 1 km / s), does not exceed the geocentric parabolic speed, then the spacecraft turns to the Earth some time after it leaves the sphere of action of the moon and its trajectory will be close to the direction of the Moon-Earth line [3].

Suppose that after the flight to the Moon, the angle between the plane of the selenocentric orbit and the Moon-Earth line will be ϕ ₂ ~ 75 ° [3], which corresponds to the transition to the polar selenocentric orbit. While in the selenocentric orbit t ₂ , the Moon-Earth line will rotate at an angle ω _Л ⋅t ₂ and the actual angle between the Moon-Earth line and the selenocentric orbit will be: 180 ° -ϕ ₂ -ω _Л ⋅t ₂ , provided that the planes of the ecliptic and the equator of the Earth coincide.

For an optimal return flight to the Earth, it is necessary to rotate the plane of the selenocentric orbit by the angle Δϕ to provide the optimal angle ϕ ₃ at the time of departure, i.e.

As you know from the course of descriptive geometry: if the sides of the angle are not parallel to the projection plane, then the angle is projected onto this plane with distortion. Since the plane of rotation of the Moon is in a plane close to the plane of the ecliptic, which makes the angle ε≈23.5 ° with the plane of the equator of the Earth, the projection of the angles will slightly differ from the values of the plane angles between the Moon-Earth line and the plane of the selenocentric orbit. This mismatch at a given angle ε will amount to several degrees. It is also possible that this formula may differ due to a change in the position of the plane of the selenocentric orbit (up to several degrees) due to the influence of the gravitational field of the Earth and the Sun, which can manifest itself in a highly elliptical selenocentric orbit. All of the above requires introducing into the formula for determining the rotation angle Δϕ the correction angle Δϕ _d , determined by calculation and reaching values up to 10 °. Thus, the formula for determining the rotation of the plane of the selenocentric orbit finally has the form:

The invention is illustrated in FIG. 1 ÷ 6, where

in FIG. 1 shows the flight diagram of the analogue - flyby the moon using the spacecraft "Probe-7",

in FIG. 2 shows the flight diagram of the prototype - a flight to a lunar orbit according to the spacecraft "Apollo-12",

in FIG. 3 is a diagram explaining the determination of the most favorable conditions for the departure of the prototype flight to Earth,

in FIG. 4 illustrates the flight scheme of the spacecraft according to the proposed method,

in FIG. 5 shows the projection of the angle ϕ ₂ on the plane of the equator of the Earth,

in FIG. Figure 6 shows a diagram with successive passes at a given distance from the Earth and subsequent exit into orbit of the OS.

In FIG. 1-6 marked the following items:

угла ϕ₂, 16 - линия Луна-Земля, 17 - плоскость экватора Земли, 18 - плоскость вращения Луны вокруг Земли, 19 - угол ε наклона эклиптики, 20 - угол u положения Луны, 21 - атмосфера Земли, 22 - импульс перехода КА на орбиту околоземной ОС.1 - the initial near-Earth orbit, 2 - the departure impulse to the Moon, 3 - the direction of the Moon’s movement, 4 - the spacecraft return trajectory after the Moon’s flight, 5 - the braking impulse, 6 - the selenocentric orbit, 7 - the departure impulse for the flight to the Earth, 8 - the trajectory flight to the Earth, 9 - anticipatory angle ϕ ₁ , 10 - angle ϕ ₂ , 11 - lead angle ϕ ₃ , 12 - angle of rotation ϕ _OZ , 13 - angle of rotation of the moon ϕ _L , 14 - angle of rotation of the plane Δϕ, 15 - projection

angle ϕ ₂ , 16 is the Moon-Earth line, 17 is the plane of the Earth's equator, 18 is the plane of rotation of the Moon around the Earth, 19 is the angle of inclination ε of the ecliptic, 20 is the angle u of the position of the Moon, 21 is the Earth’s atmosphere, 22 is the momentum of the spacecraft transition to near-Earth orbit.

In FIG. Figure 1 shows the trajectory of the lunar flyby using the Zond-7 spacecraft in a frame of reference rotating with the Earth-Moon line. After the launch, the spacecraft is in the initial near-earth orbit (1). At a given point in the orbit, a take-off impulse (2) is applied to the SC, after which the SC flies around the Moon from the direction of its movement around the Earth (3) and flies back to the Earth along the return path (4) with subsequent landing in a given area.

In FIG. Figure 2 shows the flight diagram of the prototype - a flight to a lunar orbit according to the spacecraft "Apollo-12" scheme also in the reference system rotating together with the Earth-Moon line. After the application of the take-off impulse (2), the spacecraft flies to the vicinity of the Moon, where, after the issuance of the inhibitory impulse (5), it passes into the selenocentric orbit (6). After ~ 4 days, when conditions arise for an optimal flight to Earth with minimal fuel costs [3], the spacecraft performs a take-off impulse (7) and returns to Earth along the arrival path (8) with subsequent landing in a given area.

In FIG. 3 in a projection onto the plane of the Earth’s equator, a diagram is presented explaining the definition of optimal conditions that allow the prototype to fly to Earth with a minimum fuel consumption. The spacecraft performs a take-off impulse from the initial plane of the near-Earth orbit (1), represented by the line of intersection of this plane with the plane of the earth's equator. Due to the rotation of the moon with an angular velocity ω _Л ~ 13.2 ° / day, the flight to the moon in this coordinate system is performed with a certain anticipatory angle ϕ ₁ (9). After reaching the Moon, the spacecraft passes to the selenocentric orbit (6), the plane of which is represented by the line of intersection of this plane with the lunar equator and forming an angle ϕ ₂ (10) with the Moon-Earth line. For optimal return to Earth, it is necessary that at the moment of application of the pulse for departure (7), the lead angle ϕ ₃ (11) is ~ 60–70 °.

In FIG. 4 also, in a projection onto the plane of the Earth's equator, the spacecraft flight scheme according to the proposed method is explained. For the full spacecraft flight time, including the flight to the moon, being in a selenocentric orbit (6), the spacecraft’s return flight to the Earth, and the time of transition from the brake ellipses to the orbit with the OS orbit height, the plane of the original OS orbit (1) will rotate along the Earth's equator by an angle ϕ _OZ (12). For the planes of the orbits of the spacecraft and the spacecraft to coincide at the time of the spacecraft docking with the spacecraft, it is necessary that by the time the return departure begins, the angle ϕ _ОЗ (12) corresponds to the angle ϕ _Л (13), i.e. at the time of departure, the Moon-Earth line was in the plane of the initial near-Earth orbit (1), which it would occupy at the time of the spacecraft docking with the OS. This condition determines the duration of the spacecraft in selenocentric orbit. At the same time, for the spacecraft to fly to Earth with minimal fuel costs, it is necessary that the angle ϕ ₃ be equal to the optimal ~ 60 ÷ 70 ° at the time of departure, which requires the rotation of the plane of the selenocentric orbit (6) to the angle Δϕ (14).

(15) угла ϕ₂ (10), образованного линией Луна-Земля (16), обозначаемой ОО', и плоскостью селеноцентрической орбиты (6), обозначаемая линией О'В, на плоскость экватора Земли (17), представленной треугольником КВВ'. Плоскость вращения Луны вокруг Земли (18) близка к плоскости эклиптики и наклонена под углом ε (19) к плоскости экватора Земли. Положение Луны относительно узла Ω определяется углом u (20).In FIG. 5 shows the projection

(15) the angle ϕ ₂ (10) formed by the Moon-Earth line (16), denoted by ОО ', and the plane of the selenocentric orbit (6), denoted by the line О'В, to the plane of the Earth's equator (17), represented by the triangle of HVE'. The plane of rotation of the Moon around the Earth (18) is close to the plane of the ecliptic and tilted at an angle ε (19) to the plane of the Earth's equator. The position of the moon relative to the node Ω is determined by the angle u (20).

In FIG. Figure 6 shows the spacecraft’s transition from the return trajectory (4) due to successive passes in the Earth’s atmosphere (21) to the initial orbit of the near-Earth OS (1). The spacecraft enters the Earth’s atmosphere with the 2nd space velocity. After the first deceleration of the spacecraft in the atmosphere, it passes into an elliptical orbit. Successive atmospheric passes are carried out until the next apogee of the orbit reaches the orbit height of the orbital station N _OS . Then, at the apogee of the orbit, an impulse (22) is performed for the final transfer of the spacecraft to the orbit of the near-Earth OS with subsequent docking with it.

Consider an example. Let V _{1 be the take} -off impulse for the flight to the Moon (~ 3200 m / s), and the duration of the flight to the Moon t ₁ and back to the Earth t ₃ be 3.5 days. We also assume that the duration of the spacecraft on transition brake ellipses for matching the height of the orbit of arrival and the height of the orbit of the OS t ₄ - 1.5 days. Let us determine by the presented formula the necessary duration of stay in a selenocentric orbit t ₂ :

The momentum of the transition to the selenocentric orbit V ₂ depends on the parameters of this orbit. To save fuel, it is advisable to go into orbit with the highest possible settlement. In addition, turning the plane in a highly elliptical orbit will also require less cost. The most optimal would be a transition to a highly elliptical orbit with a period close to t ₂ . This orbit has a population of about 120 thousand km, but at the same time it is very unstable and the position of its plane is subject to strong influence from the gravitational fields of the Earth and the Sun. Consider the transition to orbit with a period close in value to half t ₂ , and with a population of about 55 thousand km In this case, V ₂ ~ 220 m / s.

We determine by the formula the value of the required rotation Δϕ of the selenocentric orbit:

A numerical calculation gives a value of about 52 °, which corresponds to the need to increase Δϕ by the value of the correction angle Δϕ _d ~ 11 °. Thus, the final formula for determining the angle of rotation of the plane of the selenocentric orbit is:

, отличающаяся по величине от угла ϕ₂, и в качестве примера представлена формула, по которой она определяется, справедливая на интервале ϕ₂>u:The need to introduce a correction angle Δϕ _d arises due to a change in the position of the plane of the selenocentric orbit due to the influence of the Earth and the Sun. This disturbance is stronger the more extended the orbit [2]. Also, in the angle Δϕ _d , the difference in the values of the angles ϕ ₃ and ϕ ₂ from their projections onto the plane of the Earth's equator is taken into account. In FIG. 5 shows a projection of an angle

, differing in magnitude from the angle ϕ ₂ , and as an example, the formula is presented by which it is determined, valid on the interval ϕ ₂ > u:

The most optimal point of application of the impulse to rotate the plane in one of the apexes of the selenocentric orbit relative to the equator of the moon. A numerical example shows that for an orbit with a population of about 55 thousand km, turning the plane of the orbit by an angle Δϕ = 52 ° will require a pulse of V ₃ ~ 255 m / s.

And, finally, the momentum of departure to Earth from this highly elliptical orbit will be V ₄ ~ 575 m / s.

Thus, minus the take-off impulse V _{1, the} necessary total impulse for performing a flyby will be:

If the selenocentric orbit is circular with an orbit height of about 100 km, then the total velocity V _Σ ~ 2750 m / s will be required.

The total duration of the flight will be:

In general, we can conclude that the proposed control method will allow to fly around the moon and return to the initial near-earth orbit with a fuel cost of just over 1 km / s.

Claims (11)

A method of controlling a spacecraft during a flyby of the Moon, including applying to a spacecraft in the initial low Earth orbit, an impulse for a flight to the Moon of duration t ₁ , an impulse for transition to a selenocentric orbit, in which the spacecraft performs a flight of duration t ₂ , and an impulse for the reverse trip to Earth duration t _3, characterized in that after the flight to the spacecraft earth plane is returned to the initial Earth orbit, which define n odolzhitelnost t ₂ according to the formula

where ϕ ₁ is the angle between the Earth-Moon line and the plane of the initial near-Earth orbit at the time of application of the take-off pulse, ω _ОЗ is the angular velocity of the precession of the plane of the initial near-Earth orbit, ω _L - the angular velocity of rotation of the Moon relative to the Earth, t ₄ is the time interval necessary for matching the height of the orbit of the spacecraft with the height of the initial near-earth orbit, and in one of the apexes of the selenocentric orbit, a pulse is applied to the spacecraft to rotate the line of nodes by an angle Δϕ in the direction perpendicular to the plane of the orbit, determined by the formula

where ϕ ₂ is the angle between the Moon-Earth line and the plane of the selenocentric orbit at the time of the spacecraft’s arrival to the Moon, ϕ ₃ is the angle between the Moon-Earth line and the plane of the selenocentric orbit at the time of application of the impulse for the return flight to the Earth, Δϕ _d is the correction angle determined by calculation, fending off perturbations of the selenocentric orbit from the Earth and the Sun and differences between the projections of the angles ϕ ₂ and ϕ ₃ on the plane of the Earth's equator from their true values.

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