Stationary model of the solar system

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"Artificial Lunar Satellites (ALS), spacecraft launched into orbit around the Moon; the movement of the ISL is determined mainly by the gravity of the Moon. The first ISL is the Soviet automatic station "Luna-10", launched on March 31, 1966. When launching the ISL, the last stage of the launch vehicle is first launched into orbit of the Earth's satellite, and then, by additionally turning on the jet engine, it is transferred to the flight orbit to the Moon. The speed of a spacecraft when launching from near-Earth orbit is somewhat less than parabolic (see Space speeds); it corresponds to a very elongated ellipse with an apogee reaching the orbit of the Moon or lying beyond it. The lowest possible speed when launching from orbit at an altitude of 200 km above the Earth's surface is about 10.92 km/sec (parabolic speed at this altitude is 11.015 km/sec); the flight time to the closest vicinity of the Moon in this case is about 4.74 days. At launch speeds of 10.93 and 10.96 km/sec, the flight lasts about 3.5 and 2.6 days, respectively. At a distance of about 66,000 km from the center of the Moon, the spacecraft enters the sphere of influence of the Moon's gravity. In the case of flight trajectories, the selenocentric (relative to the Moon) speed of the spacecraft at the boundary of this sphere is no less than 0.8 km/sec, which significantly exceeds the parabolic speed for the Moon at this distance (0.38 km/sec). Under these conditions, the spacecraft, in the case of passive (uncontrolled) motion, circles the Moon, moving relative to it along a hyperbola, and then leaves the sphere of influence of the Moon and returns to the Earth. In order for the spacecraft to move into the orbit of the Moon's satellite, the onboard jet engine is turned on for a short time, upon command from the Earth, giving it a braking impulse (see figure).

The ISL orbit is similar to the orbits of the satellites of all planets and, to a first approximation, is an ellipse with a focus at the center of the Moon. The point of the orbit closest to the center of the Moon is called periseleniya, and the most distant point is called aposeleniya. The selenocentric speed vk of the motion of the ISL in a circular orbit of radius r and the period T of its revolution in an orbit with an average distance r from the center of the Moon are determined by the formulas:

where R is the radius of the Moon (1738 km). The selenocentric parabolic velocity at a distance r from the center of the Moon is equal to

Significant disturbances in the movement of low (several hundred km above the lunar surface) ISLs are caused mainly by the non-centrality of the lunar gravitational field, due to the complex shape of the Moon and the uneven distribution of matter inside it; less significant disturbances are due to the gravitational influence of the Earth and the Sun. The main consequence of the disturbances is almost periodic changes in the shape of the orbit, and at the same time the altitudes of the peri-settlement and a-settlement, and the peri-settlement gradually decreases and the ISL falls on the Moon.

The first ISL - the Soviet automatic station "Luna-10" - when entering the trajectory to the Moon, had a speed of 10.87 km/sec (at an altitude of about 270 km above the Earth). After 3.5 days, the station, rounding the Moon, passed at a minimum distance of about 1000 km from its surface and at that time had a selenocentric speed of about 2.1 km/sec. By turning on the braking engine, the speed was reduced to 1.25 km/sec, and the station moved into orbit around the Moon with an apopulation altitude of 1017 km and a periselenium altitude of 350 km. The orbital inclination was 71°54¢ to the equator of the Moon. The active period of the existence of Luna-10, during which information about the readings of on-board instruments was transmitted from the station and trajectory measurements were carried out, lasted from April 3 to May 30, 1966. During this time, the ISL made 460 revolutions around the Moon; due to the disturbance of the peri-settlements, it rose to a height of 378.7 km, and the a-settlements dropped to a height of 985.3 km. In this case, the disturbances caused by the non-centrality of the lunar gravitational field exceeded the disturbances due to the Earth's gravity by 5-6 times, and the latter exceeded the solar ones by 180 times. Theoretical calculations showed that after 6.5 months the resettlement should have reached a distance of 2150 km from the center of the Moon, and then began to descend so that the fall of Luna 10 to the Moon should have occurred in 2.5 years.

In total, in 1966–69, 5 Soviet (Luna series) and 5 American (Lunar Orbiter series) ISLs were launched. The goals of the launches were: a) direct studies of the properties of the surface of the Moon and cislunar space using on-board scientific equipment, as well as photographing the surface of the Moon; b) study of the gravitational field of the Moon, as well as the features of the shape and internal structure of the Moon on which this field depends, clarification of the mass of the Moon based on trajectory measurements and analysis of disturbances in the movement of the ISL. Thus, the Luna-10 ISL was equipped with spectrometers for studying gamma radiation and infrared radiation of surface lunar rocks, a device for recording fluxes of charged particles coming from the Sun and cosmic radiation, a recorder of meteoric particles in cislunar space, a device for detecting magnetic fields of the Moon; on the Luna-11 ISL, in addition, radio astronomy equipment for the study of long-wave space."
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