Orbits of Space Vehicles

the trajectories of spacecraft. They differ from the orbits of natural celestial bodies primarily in the presence of powered legs, in which the spacecraft’s reaction engine operates. However, the orbits of space vehicles are often understood to mean only legs of passive (non-powered) flight. The orbits of spacecraft are studied in astrodynamics.

A distinction is made among fly-by orbits, satellite orbits, and hard and soft landing orbits, depending on the nature of motion of the spacecraft. In a fly-by orbit, a spacecraft moves with a hyperbolic velocity with respect to the celestial body under investigation and, after approaching the body, leaves its vicinity. Correction of a fly-by orbit by means of thrust impulses is usually accomplished before the rendezvous; it is usually not done on the approach leg, when the spacecraft is in passive flight. Satellite orbits of spacecraft are characterized by elliptical velocities with respect to the celestial body under study. To place a spacecraft in a lunar or planetary orbit, the craft’s velocity must be reduced to elliptical velocity during approach to the celestial body, which is accomplished by jet braking. A high relative velocity of the spacecraft at the moment of contact with the celestial body is characteristic of a hard landing. A spacecraft is usually destroyed by a hard landing. Hard-landing orbits are particular cases of fly-by or satellite orbits in which part of the orbit passes below the surface of the celestial body and collision with the surface terminates the spacecraft’s motion. A landing in which the spacecraft’s relative velocity at the time of contact with the surface does not attain values that result in the craft’s destruction is called a soft landing. A soft landing is accomplished by braking jet thrust on the descent leg of the orbit or by a parachute system, if the celestial body has a sufficiently dense atmosphere.

Spacecraft orbits are chosen and computed in advance in accordance with the spacecraft’s mission. The problems of economical fuel consumption and increasing the payload of the spacecraft play a major role in selecting the orbits of spacecraft; therefore, efforts are made to maximize the use of the gravitational force of the body under study to change the trajectory as necessary. An example is the flight of the unmanned interplanetary probe orbited on Oct. 4, 1959, by the third Soviet space rocket. At the time of rendezvous with the moon, the unmanned interplanetary probe passed at a distance of 6,500 km from the lunar surface and photographed the far side of the moon; under the attraction of the moon, its trajectory was bent and the probe returned to earth from the direction of the northern hemisphere. Passing at a distance of 4,700 km from the surface of the earth, the probe transmitted the photographs to earth.

Since spacecraft have small dimensions and weight, their orbits are appreciably affected not only by gravitational forces but also by atmospheric resistance of the earth or planets and light pressure, which have virtually no effect on the motion of natural celestial bodies. Perturbations caused by atmospheric resistance and the compression of the earth are most noticeable in the motion of artificial earth satellites. Under the action of atmospheric resistance the orbit gradually decreases in size—a secular decrease in the semimajor axis and eccentricity takes place in such a way that the altitude of the orbital perigee decreases far more slowly than does the altitude of the apogee. The decreased orbital dimensions result in a reduction in the period of revolution of the satellite around the earth and an acceleration of the apparent motion of the satellite. The closer the orbit to the surface of earth, the faster such orbital changes take place. For a circular orbit with an altitude of the order of 150–160 km or less, the changes occur so quickly that the satellite cannot make a complete revolution and falls to earth.

The compression of the earth causes two principal effects in the motion of artificial earth satellites: rotation of the orbital plane of the satellite around the earth’s axis, which takes place in a direction opposite the motion of the satellite (retrograde motion of the line of nodes of the orbit), and rotation of the orbit itself in its plane (motion of the apsis line). The rate of motion of the nodal line is equal to zero if the orbital plane is perpendicular to the plane of the earth’s equator. The direction of motion of the line of apsides depends on the inclination of the orbit to the equatorial plane and coincides with the direction of motion of the artificial earth satellite in orbit if the inclination of the orbit is i < 63°26′; if the inclination is greater, the line of apsides will move in a direction opposite that of the orbital motion of the satellite.

The selected (calculated) orbit of a spacecraft is not achieved precisely because of inevitable deviations in engine operation from the calculated operating conditions during launching and corrections. The orbit changes continuously under the action of perturbing forces. Therefore, the task of measuring the spacecraft’s apparent motion and of determining the parameters (elements) of the actual orbit from the measurements arises. Radio engineering methods of observation, which make it possible to determine the distance to a spacecraft and the craft’s radial velocities, are the most widely used. The motion of spacecraft that are close to the earth, such as artificial earth satellites and lunar probes, is also measured according to observations that make it possible to determine the angular coordinates of a spacecraft (usually in the right ascension and declination or in azimuth and altitude). Laser range finders are also used to make such measurements. The refined values of the orbital parameters, or elements, are used to calculate the corrective impulses and to predict the motion of the spacecraft (to calculate the ephemerides) during successive observations of the spacecraft.