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  • Die säkularstörungen einer aussenstationsbahn

    Paper ID



    • H G L Krause







    The well-known methods of investigation on the influence of the oblateness of a planet on the motion of its inner satellites as well as the influence of other perturbations from celestial bodies on such motion cannot be applied for the case of the artificial satellite;, as these investigations treat circular orbits with almost no inclination towards the equatorial plane. A method is developed to investigate secular perturbations for satellite orbits with any excentricity and inclination. It is found that the inclination plays a more essential role than the excentricity. Subject of the investigation is the motion of an artificial satellite at a mean distance of I669 km from the surface of the earth making one revolution about the earth in 1 h 59 min 40*34 sec. The orbit of this satellite shall have an excentricity of 0.2 and an inclination of 45° towards the equatorial plane. The oblateness of the earth results in l) a regression of the line connecting the ascending and descending knots thus, that one such revolution of this line takes 105 d 1 h 17 min., 2) a clockwise motion of the line of apsides taking 4 a 346 d 20 h 34 min for a full motion through 36O0, 3) a reduction of the time neccessary for one full revolution of the artificial satellite about the earth by 2.3 sec. For approximately circular orbit of the artificial satellite in the equatorial plane there results a full revolution of the knots as well as the line of apsides in 80 d 8 h 23 min. The attraction of the equatorial belt results in a, reduction of the time necessary for a full revolution of the artificial satellite by 14.8 sec. The influence of Moon und Sun on the orbit of this satellite is very small. However, the influence of the Moon is 2.2 times as large as that of the Sun., Both results in a regression of knots and line of apsides which takes several thousend years for a full motion through 360°, for a full revolution. The artificial satellite offers a possibility of proving the general relativity theory by Einstein. This theory requires a progression of the line of apsides by 9*82 are sec per year for an excentricity of 0,2 (that of the Mercur). The Mercur planet showing this effect in its greatest extent in this solar system, has a progression of 42.6" per centenniurn only. This is 23 times smaller as that of the artificial satellite with 9*82". This effect may be proved with an unmanned space station if no forces and moments act upon this station. Naturally there will be considerable difficulties as the velocity of the satellite is l/20° or 180" per second in the sky and. at the same time it can be seen only through telescopes during the night if no rader tracking is employed. The diameter of the satellite of 60 m appears under a mean angle of only 1.54"* Assuming for the satellite an albedo (reflectivity) of that of the moon and taking an effective radius of 20 m, the satellite appears in our sky as a star with the magnitude of the 6th order.