假定宇航员乘坐宇宙飞船到某行星考察,当宇宙飞船在靠近该星球表面空间做匀速圆周运动时,测得环绕周期为T,当飞船降落在该星球
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GM=V^2R (1) 2PI*R/V=T (2) F=GMm/R^2(3) 由(1),(2)得GM=4PI^2*R^3/T^2 即G^2M^2=16PI^4*R^6/T^4(4) (3)变形得F^3=G^3M^3m^3/R^6 (5) -----------(5)*(4)即得F^3=16PI^4GMm^3/T^4 ------ M=3T^4/16PI^4Gm^3

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