Archive of Astronomy Questions and Answers

Why does the gravity of the Earth and Moon balance at 40,000 miles from the Moon?

You can see this by solving the equation for 'd' :



  G M(earth)              G M(moon)
------------------   =  --------------
           2                 2
(  R - d  )                 d

which leads to:


 M(earth)          2               2
----------  =     R   - 2 R d  +  d
  M(moon)

and using M(earth) = 5.9 x 10^27 grams, M(moon) = 7.3 x 10^25 grams and R = 384401 kilometers. The ratio of the masses is 80.8 and the answer is D = 37,900 kilometers or 24,250 miles. An object located 37,900 kilometers from the Moon's surface along the Earth-Moon line would feel an acceleration towards the Earth of 0.3 centimeters/sec^2, and an equal acceleration towards the Moon. This is what a simple calculation would yield as an answer.