Gravitational Potential

Kin Long

2009-01-10 9:42 pm

What is the Gravitational Potential at the mid-point between the centres
of the earth and the moon?
(Mass of earth = 6.0x10^6 m , mass of moon = 7.4x10^30 kg , distanceof moon from earth = 3.8x10^8 m)
[It is impossible to use the universal gravitational constant (G) to calculate the answer.]

更新1:

Sorry,mass of earth is 6.0x10^24kg

回答 (1)

天同

2009-01-12 12:10 am

✔ 最佳答案

Gravitational potential = - GM/R
where G is the Universal Gravitational Constant
M is the mass of the object (either earth or moon)
R is the distance from the object.

Let 2r be the distance between the moon and the earth, thus
gravitational potential at the mid-point due to earth
= - GMe/r
where Me is the mass of earth
gravitational potential at the mid-point due to the moon
= - GMm/r
where Mm is the mass of the moon
The resultant gravitational potential
= - GMe/r - GMm/r = - (G/r)(Me+Mm)
try to substitute the corresponding values and calculate the answer.
[you better check the given data, the moon is by no means heavier than earth]

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