RU2709951C1 - Method of controlling movement of a space object during flight from an earth orbit to a moon orbit - Google Patents

Abstract

FIELD: astronautics.

SUBSTANCE: invention relates to interplanetary flights, for example, when space objects (SO) are delivered to a station located on high near-moon orbit. Method includes flight from the Earth to the Moon along trajectory with flight of the Moon at specified height, where first braking pulse is performed to transfer SO to initial near-moon orbit. Aposelenium of this orbit is located in the vicinity of Moon's gravisphere (60–75 thousand km). Due to gravitational perturbations, mainly from the Earth, through the revolution the pericynthion height of this orbit changes to the height of target orbit pericynthion. In this pericynthion the second brake pulse is performed to form the target elliptic (or circular) orbit around the Moon.

EFFECT: reduction of total characteristic speed for launching of space object from transitory trajectory to target, mainly high near-moon orbit.

1 cl, 6 dwg

Description

The proposed control method can be used in space technology when launching a space object (KO) located in near-Earth orbit into a given high near-moon orbit.

To fly to the Moon from the Earth’s orbit, it is necessary to perform a take-off pulse, the value of which, depending on the height of the near-Earth orbit, varies from 3050 to 3200 m / s. Upon arrival to the moon, the KO trajectory represents a selenocentric hyperbolic orbit. To enter the lunar orbit with the given parameters, additional operations must be performed.

A known control method, selected as an analogue (Fig. 1), in which to bring the spacecraft to a given near-moon orbit by means of a take-off pulse ΔV ₁ , a trajectory of the moon is formed at a given distance. The point of passage at a given distance from the moon is at the same time a point of a given orbit. In the vicinity of this point, a braking impulse ΔV ₂ is performed to transfer the spacecraft from the trajectory of the moon's flight into a given orbit around the moon, [1. IN AND. Levantovsky, "The mechanics of space flight in an elementary exposition", Science, 1980].

Despite the simplest and fastest transition to a given orbit, the disadvantage of this method is the significant value of the braking impulse ΔV ₁ , which requires high fuel consumption. In conditions of fuel shortage, this factor can be critical. Let us determine the momentum ΔV ₁ in terms of the characteristic velocity for transferring the spacecraft into a circular lunar orbit with a height of H = 10 thousand km:

,where μ is the gravitational parameter of the moon,

,

r is the radius of the orbit of the moon and r = H + r _L , where r _L = 1737 km is the radius of the moon [1],

Таким образом, подставляя в формулу необходимые значения получим ΔV_Σ1=ΔV₁=667 м/с.ν _∞ - entry speed (speed at infinity) at the pericenter with a height of H = 10 thousand km of a selenocentric hyperbolic orbit during a flight from Earth to the Moon 4.5 days will be

Thus, substituting the necessary values in the formula, we obtain ΔV _Σ1 = ΔV ₁ = 667 m / s.

A known method of controlling the motion of the spacecraft during the flight from the orbit of the Earth to the orbit of the moon (Fig. 2), selected as a prototype [2. Gordienko E.S., Ivashkin V.V. “Using a three-pulse transition to launch a spacecraft into the orbits of an artificial moon satellite,” Space Research, 2017, Volume 55, No. 3, p. 207-217], including the execution of the spacecraft of the take-off pulse for the flight from the Earth to the moon along the trajectory with the passage relative to the moon at a given height, upon reaching which a braking pulse is performed to transfer the spacecraft to an elliptical orbit around the moon. In contrast to the analogue, this method uses three pulses to translate the QO into a given orbit. With the first inhibitory impulse, the CO is transferred to a transition elliptical orbit with a population height of Hα ₁ . Then, a second impulse is executed in the apostillation, which is already accelerating, raising the height of perisulation to the height of perisulation of the target orbit Нπ ₂ . And finally, after the arrival of KOs in perioperations with the third inhibitory impulse, the KOs are transferred into orbit with the height of the population Нα ₂ . If the target orbit is circular Hα ₂ = Hπ ₂ .

Depending on the height of the settlement Hα _{1 of the} transitional elliptical orbit, using this method, it is possible to reduce fuel consumption for launching into a circular near-moon orbit with a height of H = 10 thousand km per 100 ÷ 250 m / s. According to the calculations, at the height of the population of the transitional elliptical orbit Нα ₁ = 50 thousand km and the date of arrival to the Moon 01.12.27, the value ΔV _Σ3 will be:

those. 225 m / s less than with a single-pulse circuit.

For population heights from 15 to 45 thousand km, ΔV _Σ3 will be from 565 to 459 m / s, which is less than 102 to 208 m / s in comparison with a single-pulse scheme.

The main disadvantage of this control method is still a significant total magnitude of the pulse ΔV _Σ3 for translating the _spacecraft into a given orbit.

The technical result of the invention is an additional reduction in the cost of the total characteristic speed for transferring the TO into a given orbit.

The technical result is achieved due to the fact that in the method of controlling the motion of the spacecraft during the flight from the Earth’s orbit to the moon’s orbit, which includes the execution of the spacecraft of the take-off pulse for the flight from the Earth to the moon along the trajectory with the passage relative to the moon at a given height, after which a braking pulse is performed to translate CR in an elliptical orbit around the Moon, in contrast to the known one, defines an elliptical orbit with a population in the vicinity of the moon’s gravisphere and a height Hα in the range 60–75 thousand km, which due to gravitational of perturbations from the Earth through the turn, the height of the resettlement will change to the value of the height of the resettlement of the target orbit Нπ, then the braking impulse, which is applied to the CO, is adjusted by the value of the height of the settlement Нα, and the final braking pulse is performed through the round, when passing the resettlement of height Нπ, to form the target elliptical orbit around the moon.

The proposed method will consider an example. Let a circular orbit 200 km high be considered as a near-Earth orbit of the KO. Consider the problem of flying KO into a circular orbit around the moon with an altitude of 10 thousand km. The flight scheme includes a take-off impulse ΔV ₁ , which forms a passage near the Moon along a hyperbole of a selenocentric orbit at a distance of about 100 km, a braking impulse ΔV ₂ for transferring a space object into a transitional highly elliptical orbit around the Moon. Then, through a flight orbit in this transitional orbit, a pulse ΔV ₃ is performed for the final transition of the spacecraft to a given orbit around the moon.

The technical result in the proposed control method is achieved due to the fact that the populations of the transitional highly elliptical orbit with a height of Hα, selected in the range of 60–75 thousand km, are located in the vicinity of the Moon’s gravisphere (~ 66 thousand km) [4. E.V. Tarasov, "Cosmonautics", Engineering, 1977]. After performing the braking pulse, ΔV ₂ KO from the hyperbolic transit orbit is transferred to a transitional elliptical orbit around the Moon. With a correctly selected height of the population of Hα in the transitional orbit, due to gravitational perturbation from the Earth through the orbit, the height of the population increases to a predetermined value (in our case, Hπ = 10 thousand km). In addition to an increase in the height of perisulation, a monotonic decrease in the height of the population of the transitional orbit is observed, which, in turn, reduces the magnitude of the pulse ΔV ₃ , which finally forms the orbit around the moon. Thus, it is possible to reduce the number of transition pulses from three to two and further reduce the costs of the characteristic velocity for transition to a near-moon orbit. The decrease in ΔV _Σ2 compared with the belliptic transition occurs due to:

- reduction of the brake pulse ΔV ₂ , because the populations of the transitional orbit increases from 20 ÷ 50 thousand km to 60 ÷ 75 thousand km,

- pulse exceptions in the settling of the transitional orbit, because the formation of the pericenter of a given orbit is provided by the disturbing influence of the Earth’s gravitational field,

- reduction of the brake pulse ΔV ₃ , because in addition to the height of perisulation, due to disturbances from the Earth, the height of the population of the transitional orbit decreases.

With the optimal date of the flight from Earth to the Moon, the total momentum ΔV _Σ2 for transition to a circular lunar orbit with an altitude of 10 thousand km can be about 335 m / s, which is compared to the method described in the prototype and when setting the height of the population of the transitional orbit Hα ₁ = 50 thousand km is 107 m / s less.

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

in FIG. 1 shows a scheme for launching an analog into a circular lunar orbit according to a single-pulse scheme;

in FIG. 2 shows a scheme for launching a prototype into a circular near-moon orbit with a belliptic transition according to a three-pulse scheme;

in FIG. 3 shows a scheme for launching into a circular lunar orbit according to the proposed control method according to a two-pulse scheme;

in FIG. 4 shows the cost graphs of the total characteristic velocity ΔV _Σ3 and the excretion time for a belliptic transition;

in FIG. 5 shows the cost graphs of the total characteristic velocity ΔV _Σ2 and the heights of the settlement Hα of the transitional orbit for the proposed two-pulse scheme depending on the date;

in FIG. Figure 6 shows the change in the height of the perioperation Нπ and the population Нα of the transition elliptical orbit during the orbit due to gravitational perturbations from the Earth.

In FIG. 1 shows a scheme for launching into a circular lunar orbit according to a single-pulse scheme. Initially, the spacecraft (1) with a take-off impulse ΔV ₁ (2) from a near-earth orbit is transferred to the flight path to the moon with a passage relative to the moon at a distance corresponding to the height Нπ ₂ (3) of a given circular near-moon orbit. After arriving at a given distance, the spacecraft performs a braking impulse ΔV ₂ (4) to transition to a given circular orbit.

In FIG. Figure 2 shows a scheme for launching into a circular lunar orbit according to a three-pulse scheme. Initially, the spacecraft (1) with a take-off pulse ΔV ₁ (2) from the near-earth orbit is transferred to the flight path to the moon with a passage relative to the moon at a given minimum distance Нπ ₁ (5). After arriving at a distance of Нπ _{1, the} KO performs a braking pulse ΔV ₂ (4) to transfer the KO to a transitional elliptical orbit around the Moon (6) with a population (7) inside the moon's gravisphere (8). Then, the spacecraft continues to fly in this orbit until it arrives at the populations (7), where the accelerating impulse ΔV ₃ (9) is performed, which forms an orbit with re-population at a given height Нπ ₂ (3) of a circular near-moon orbit. After this, the flight continues until it arrives at the relocation, where the braking impulse ΔV ₄ (10) is performed, which completes the transfer of the spacecraft to a given circular near-moon orbit.

In FIG. 3 shows a scheme for launching into a circular lunar orbit according to the proposed method. Initially, the spacecraft (1) with a take-off impulse ΔV ₁ (2) from the near-earth orbit is transferred to the flight path to the moon with a passage relative to the moon at a given minimum distance Нπ ₁ (5). After arriving at a given distance, the spacecraft performs a braking impulse ΔV ₂ (4) to transfer to a transitional elliptical orbit around the moon (6) with a population (7) in the vicinity of the lunar gravity sphere (8) and a height in the range of 60-75 thousand km. Then, the spacecraft continues its flight in a transitional orbit until the next arrival in the peri-settlements. Due to gravitational perturbations from the Earth, the initial transitional orbit (6) changes and through the orbit takes the form (11) with a height of percussion Нπ ₂ (3) corresponding to the height of percussion of the target orbit. Then, in an overpopulation with a height of Нπ ₂ (3), a braking impulse ΔV ₃ (10) is performed, which completes the transition of the CR to a given circular near-moon orbit.

In FIG. Figure 4 shows the graph of the characteristic velocity expenditures for a three-pulse transition according to a three-pulse scheme (12) to a polar (orbital inclination of 90 °) near-moon circular orbit with an altitude of H = 10 thousand km and a graph of the orbital time (13) depending on the value of the population height of the transitional orbit. The calculations were carried out during the flight to the Moon for 4.5 days after the issuance of a take-off impulse from a near-Earth circular orbit with a height of 200 km and an inclination of 51.6 °. The date of arrival to the Moon at a height of Hπ ₁ = 100 km - 12/01/27. Also, for comparison, the characteristic velocity costs obtained on the same date using a single-pulse circuit (14) are presented. The graphs show that a single-pulse circuit requires a larger total characteristic speed.

In FIG. Figure 5 shows the cost graph of the total characteristic velocity ΔV _Σ2 (15) for transition to a circular lunar orbit with a height of H = 10 thousand km according to the proposed method, when starting from the Earth from a circular orbit with a height of 200 km and an inclination of 51.6 ° depending on the date. The range of dates of departure from Earth from 11/26/27 to 01/01/28 was considered, which obviously exceeds the duration of the lunar month (~ 27 days). A graph of apocalyptic heights for each considered date is also presented (16). It can be seen from graph (15) that the ΔV _Σ2 value has a cyclic character with a period corresponding to the lunar month and the minimum value reaches 335 m / s, which is ~ 110 m / s lower than the minimum value for the belliptic transition at Hα ₁ = 50 thousand km . It can be seen from graph (16) that the initial height of the population of the transition ellipse, depending on the date, varies from 63.5 to 74.5 thousand km, i.e. located in the vicinity of the moon’s gravisphere.

In FIG. Figure 6 shows the graphs of changes in the altitude of the settlement (17) (dashed line) and perisulation (18) (solid line) of the transitional lunar orbit during flight according to a two-pulse scheme. The graph corresponds to the date of arrival to the Moon on 12/01/27. As can be seen from graph (17), the population height after the first braking impulse ΔV ₂ in the overpopulation of the hyperbolic orbit jumps up to 71 thousand km. Then, during a revolution, under the influence of gravitational perturbations from the Earth, the population height decreases by 20 thousand km to 51 thousand km. From the graph (18) it can be seen that per revolution the height of the perioperation of the transitional orbit increases to a predetermined height of 10 thousand km. In the overpopulation, a braking impulse ΔV ₃ is performed, which decreases abruptly the height of the population to 10 thousand km and, thus, the transition to a circular near-moon orbit is completed.

Consider an example. Suppose we need to bring the spacecraft to a high circular moon orbit with an altitude of 10 thousand km. This is most easily accomplished using a single-pulse circuit, as shown in FIG. 1. For this, the value of the height of the perisulation of the transit hyperbolic orbit should be equal to the height of the final circular orbit, ie Нπ ₁ = 10 thousand km. During the passage of the overpopulation, a braking impulse of about 667 m / s is performed, which leads to the formation of a circular orbit 10 thousand km high.

биэллиптический переход становится оптимальнее гомановского перехода. Так как радиус орбиты Луны 1737 км, то при высотах окололунных орбит свыше 30 тыс. км оптимальнее становится биэллиптический переход. Биэллиптический переход не с круговой, а гиперболической орбиты траектории пролета Луны, позволяет получить энергетический выигрыш и при меньшей высоте конечной круговой орбиты [2]. Как показано в [2], при переходе на круговую орбиту высотой около 4.5 тыс. км суммарные затраты на переход будут меньше, чем при одноимпульсной схеме на 200 м/с. Для круговой орбиты высотой 10 тыс. км, в зависимости от высоты апоселения переходной эллиптической орбиты, можно уменьшить суммарные затраты от 100 до 250 м/с, что и показано на фиг. 4. Естественно, что в этом случае увеличивается время выведения на заданную орбиту от 1.5 до 4-х суток.It is possible to reduce these costs by using a belliptic transition for an interorbital transition in the central gravitational field of a celestial body [3. R.F. Appazov, O.S. Sytin, "Methods of designing the trajectories of carriers and satellites of the Earth", Nauka, 1987]. According to [3], with the ratio of the initial and final radius of the orbits

the belliptic transition becomes more optimal than the homanic transition. Since the radius of the Moon’s orbit is 1737 km, at heights of the near-moon orbits of more than 30 thousand km, the belliptic transition becomes more optimal. A belliptic transition not from a circular, but from a hyperbolic orbit of the trajectory of the passage of the Moon, allows one to obtain energy gain at a lower altitude of the final circular orbit [2]. As shown in [2], in the transition to a circular orbit with an altitude of about 4.5 thousand km, the total cost of the transition will be less than with a single-pulse circuit at 200 m / s. For a circular orbit with a height of 10 thousand km, depending on the height of the population of the transitional elliptical orbit, the total costs can be reduced from 100 to 250 m / s, as shown in FIG. 4. Naturally, in this case, the time to launch into a given orbit increases from 1.5 to 4 days.

If the populations of the transitional elliptical orbit are located in the vicinity of the moon’s gravisphere, then the influence of the Earth’s gravitational field will begin to perturb this orbit in such a way that through the orbit in such an orbit the height of the population will increase, and the height of the population will decrease. With a correctly selected height Hα _{1 of the} transitional orbit, as shown in FIG. 6, through the turn, the perisulation height will change from Нπ ₁ to Нπ ₂ and without an acceleration pulse in the orbit settling, as provided for by a three-pulse scheme. Thus, in order to bring KOs to a given orbit, it is sufficient to carry out the impulse of forming a given height of the population of Hα ₂ during repeated passage of the perioperation.

The combined decrease in the height of the settlement and the increase in the height of the resettlement during the flight of the spacecraft during the flight makes it possible, in comparison with the three-pulse scheme, to reduce the total cost of the characteristic speed to bring it to a given near-moon orbit. So, shown in FIG. 5, the total costs of the characteristic speed when choosing the optimal date for the flight show a decrease of more than 100 m / s.

As for the three-pulse scheme, the duration of the two-pulse transition will increase to 6.5 days due to the flight during the orbit in a transitional elliptical orbit with a large initial population height Hα ₁ , but in the case of an unmanned spacecraft flight this factor is not critical.

It should also be noted that the gravitational perturbation from the Earth during the flight in a transitional elliptical orbit will also change the inclination of a given orbit. In the example, depending on the date, this deviation ranged from 15 to 25 degrees. This perturbation can be countered by changing the initial inclination of the orbit of arrival to the Moon by the desired value (~ 15–25 degrees).

The proposed method will reduce the total characteristic speed for the launch of TO in a high circular lunar orbit. So, if we take the consumption of the characteristic speed for elimination according to a single-pulse scheme as a unit of measurement, then the consumption by the prototype method will be from 66 to 85%, and by the proposed method 50%. When delivered to a high circular near-moon orbit of a spacecraft with a mass of 7 tons, an additional increase in the payload compared to the three-pulse scheme can be about 250 kg.

The proposed method can be used for the delivery of goods to a promising station located in a high circular lunar orbit.

Claims (1)

A method for controlling the motion of a space object during a flight from orbit around the Earth to an orbit around the Moon, including the spacecraft performing a take-off impulse for a flight from Earth to the Moon along a path with a passage relative to the Moon at a given height, after which a braking pulse is performed to transfer the space object to the target an elliptical orbit around the Moon, characterized in that they define an elliptical orbit with a population of height Hα in the range of 60–75 thousand km in the vicinity of the moon’s gravisphere, which t of gravitational perturbations from the Earth through the orbit, the altitude of the perisulation will change to the value of the altitude of the population of the target orbit Нπ, then the braking impulse, which is applied to the space object, is adjusted by the value of the height of the population Нα, and the final braking impulse is performed through the revolution when the passage of height is carried out by Нπ to form the target elliptical orbits around the moon.

Images