Determination of the orbits of Venus, the Earth, and Mars from 1962- 1978 radar observations of Venus and Mars

Kislik, M. D.; Kolyuka, Yu. F.; Kotel'Nikov, V. A.; Petrov, G. M.; Tikhonov, V. F.

doi:10.3367/ufnr.0131.198007h.0511

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“…This is accounted for by a persistent raising of precision of astronomical observations and discovery of such systems as the double pulsar PSR 1913+16 (Hulse and Taylor, 1975). The present techniques allow to measure the periodic and secular corrections to the Newton equations of motion of the order of (v/c) 2 (see Kislik et al, 1980 andWeisberg andTaylor, 1984) as well as the secular radiation correc tions to the order (v/c) 5 (Weisberg and Taylor, 1984) where v is a cha racteristic velocity of the bodies. It seems possible that the effect caused by terms of order (v/c) 1 * may be measured in a near future (Sha piro, 1979).…”

Section: Introductionmentioning

confidence: 99%

Equations of motion for isolated bodies with relativistic corrections including the radiation reaction force

Grishchuk¹,

Kopeikin²

1986

Symp. - Int. Astron. Union

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We have derived in an explicit form the equations of motion for two spherically-symmetric non rotating bodies in the slow motion approximation. The equations include relativistic corrections of order (v/c)2, (v/c)4 and (v/c)5 to the newtonian equations of motion. It is shown that the equations depend on the only parameter characterizing each body, namely on its relativistic mass, regardless of its internal structure and degree of compactness. This means that the equations can also be applied to bodies with a strong internal gravity, such as neutron stars and black holes. It is shown that in the (v/c)2 and (v/c)4 approximations the equations can be derived from a Lagrangian. The Lagrangian is given in an exact form. The integration of the equations of motion is performed by the method of osculating elements. The formulae for secular change of the semi-major axis and eccentricity coincide precisely with the standard ones whose derivation is based on a calculation of the energy flux in the outgoing gravitational waves.

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Section: Introductionmentioning

confidence: 99%