Physics Help Forum Gravity?

 Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum

 Jul 17th 2019, 01:24 AM #1 Junior Member   Join Date: Jul 2019 Posts: 1 Gravity? 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?
 Jul 17th 2019, 03:05 AM #2 Senior Member   Join Date: Oct 2017 Location: Glasgow Posts: 426 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 topsquark likes this.
 Jul 23rd 2019, 04:30 AM #3 Senior Member   Join Date: Aug 2010 Posts: 434 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.) Last edited by topsquark; Jul 23rd 2019 at 09:16 AM. Reason: LaTeX tweak

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