# Gravity?

#### Andre36

Moon mass is 81 times smaller than Earth's mass. The distance between the center of the two planets is 60 times the radius of the earth. Q: At what point on the straight line connecting the two planets is the gravitational force between the moon and the earth equal?

#### benit13

Hi Andre! Welcome to the forum.

Here's some hints:

Do you know the equation that relates the gravitational force to the masses of the gravitating bodies? If so, write it down and think how the force varies as you travel along the line between the two masses. If not, look it up and write it down.

Now think about another mass (usually called a 'test mass') that travels from Earth to the Moon. What is the gravitational force on this test mass caused by the Earth? What is the gravitational force on this test mass caused by the Moon? How do these two forces change as the test mass goes on its journey?

Once you have these down, I think you'll be able to find your answer. Update us with how it's going

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#### HallsofIvy

The gravitational force between two masses, M1 and M2, at distance r apart, is $$\displaystyle \frac{GM1M2}{r^3}$$. Imagine a 'test mass" of mass 1 kg and let "M" be the mass of the earth, "R" the radius of the earth. Such a test mass at distance r from the center of the earth would feel a gravitational force $$\displaystyle \frac{GM}{r^2}$$ from the earth. Assuming that mass is on the line between the centers of the moon and the earth, its distance from the moon would be 60R- r and the mass of the moon is M/81. So the gravitational force on the object from the moon would be $$\displaystyle \frac{\left(\frac{GM}{81} \right ) }{(60R- r)^2}= \frac{GM}{81(60R- r)^2}$$. Set those equal and solve for r. (It will be in terms of R, of course. Both G and M will cancel.)

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