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Calculation of the cancel-point between Gravity Fields of
the Earth and the Moon
Let Me = the mass of Earth,
Mm = the mass of the Moon,
de = the distance from Earth to the small test mass
of unit mass
dm = the distance from the Moon to the small test
mass of unit mass
Fe = the force due to Earth's gravity on the unit
mass
Fm = the force due to the Moon's gravity on the
unit mass
D = the distance between Earth and the Moon = 384,000 km
G = universal gravitational constant.
The force of gravity between the Earth and the unit mass is
expressed by the law of universal gravitation:
Fe = G Me / de2
Likewise Fm = G Mm / dm2
Then, at the point where the two fields cancel, we have Fe
= Fm
(1) Thus G Me / de2 = G
Mm / dm2
(2) But Me = 83 Mm
So, Equations 1 and 2 imply de = 9.13 dm
But D = de + dm
Thus de = 346,000 km and dm =
38,000 km.
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