- #1
tv2le
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A) If the moon of mass mM has radius RM and the distance between the centers of the Earth and the moon is REM, find the total gravitational potential energy of the particle-earth and particle-moon systems when a particle with mass m is between the Earth and the moon, and a distance r from the center of the earth. Take the gravitational potential energy to be zero when the objects are far from each other. Take the mass of Earth as mE.
B)There is a point along a line between the Earth and the moon where the net gravitational force is zero. Use the expression derived in part (a) to find the distance of this point from the center of the Earth in meters.
The attempt at a solution: In Part A, I was able to find that U= -GmEm/r - GmMm/(REM-r)
For Part B, do I just set the equation for potential energy equal to 0? I tried that, and got stuck, because I end up with 2 unknown variables (distance from Earth and distance from moon), so what would the second equation be to help solve for both of these variables?
B)There is a point along a line between the Earth and the moon where the net gravitational force is zero. Use the expression derived in part (a) to find the distance of this point from the center of the Earth in meters.
The attempt at a solution: In Part A, I was able to find that U= -GmEm/r - GmMm/(REM-r)
For Part B, do I just set the equation for potential energy equal to 0? I tried that, and got stuck, because I end up with 2 unknown variables (distance from Earth and distance from moon), so what would the second equation be to help solve for both of these variables?