Physics
Scientific paper
Sep 1958
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1958rspsa.247...49k&link_type=abstract
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 247, Issue 1248, pp. 49-72
Physics
28
Scientific paper
The equations of motion of a satellite in an orbit over an oblate earth in vacuo are solved analytically, by a perturbation method. The solution applies primarily to orbits of eccentricity 0\cdot 05 or less. The accuracy of the solution for radial distance should then be about 0\cdot 001%, and the error in angular travel about 0\cdot 001% per revolution. The earth's oblateness has four main effects on the motion: (1) The orbital plane, instead of remaining fixed, rotates about the earth's axis in the opposite direction to the satellite, at a rate of 10\cdot 00(R/{r})3\cdot 5 cos α deg./day, where α is the inclination of the orbital plane to the equator, R the earth's equatorial radius and {r} the satellite's mean distance from the earth's centre. (2) The period of revolution of the satellite, from one northward crossing of the equator to the next, is 14\cdot 5 surd (R/{r}) sin2α sec greater for an inclined orbit than for an equatorial orbit. (3) The radial distance r from the earth's centre changes. For a given angular momentum the mean r is 14\cdot 1 R/{r} nautical miles greater for a polar orbit than an equatorial one. Also, during each revolution r oscillates twice, the amplitude of the oscillation being 0\cdot 94(R/{r})sin2α n. miles. (4) The major axis of the orbit rotates in the orbital plane at a rate of 5\cdot 00(R/{r})3\cdot 5 (5 cos2α - 1) deg./day. Thus it rotates in the same direction as the satellite if α < 63\cdot 4 degrees, or in the opposite direction if α > 63\cdot 4 degrees. A brief comparison is made between theory and observation for Sputniks 1 and 2.
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