at what distance will the moon gravity be stronger than the earth gravity?
the earth-moon distance is 384403 km
2007-04-23 16:38:20 · 3 answers · asked by wills 3 in Science & Mathematics ➔ Physics
The point where the lunar gravity and Earth's gravity are equal is around 25,000 miles from the Moon.
It is the L1 Lagrangian point.
2007-04-23 17:01:52 · answer #1 · answered by J C 5 · 1⤊ 0⤋
The Earth masses 81.3 times the mass of the moon, so
-81.3GmM/d^2 = -GmM/(384403 - d)^2
81.3/d^2 = 1/(384,403 - d)^2
81.3(384,403 - d)^2 = d^2
81.3(147765666409 - 768806d + d^2) = d^2
80.3d^2 - 62503927.8d + 12013348679051.7 = 0
d^2 - 778,380d = - 149,605,836,601
d^2 - 778,380d + 151,468,922,984 = 151,468,922,984 - 149,605,836,601
(d - 389,190)^2 = 1,863,086,383
d = 389,190 - 43,163
d > 346,026 km from Earth center
2007-04-23 17:22:05 · answer #2 · answered by Helmut 7 · 2⤊ 0⤋
It won't. The earth is bigger.
2007-04-23 17:09:45 · answer #3 · answered by Anonymous · 0⤊ 2⤋