Unformatted text preview: more details). Loss of satellite to a perturbinof satellite to a perturbing body If we have a satellite mass m, at a distance d from its primary mass M 1 , then a second large body of mass M 2 distance D from M 1 produces a perturbing acceleration on m of: A - B = [GM 2 /(D-d) 2 ] - GM 2 /D 2 or approximately 2GM 2 d/D 3 between orbiting body and primary (d << D). The gravitational aceleration b is given by: b = GM 1 /d 2 Thus, the instability limit, when the perturbation starts to be of the same order as the primary's effect, is given by: d = (M 1 /2M 2 ) 1/3 D as long as M 1 << M 2 . If M 1 >> M 2 we must use the exact relation: d 3 (2D-d) = (M 1 /M 2 )D 2 (D-d) 2 If we take the earth-moon system with the sun as perturber then d is about 1.7 10 6 km, four times the current orbital radius....
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- Fall '10
- Astronomy, Natural satellite, Celestial mechanics, Orbital resonance