Gravity and Energy -- Two masses above two different planets

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SUMMARY

The discussion focuses on the relationship between gravitational potential energy (GPE) and kinetic energy (KE) for two masses on different planets. The user has calculated the gravitational acceleration (g) of the foreign planet and the final velocity (Vf) of the ball, establishing that GPEiA equals KEfA. They seek assistance in determining the mass of the ball, noting that the ratio of the two masses is sufficient for solving the problem. The conversation highlights the importance of momentum conservation during the interaction of the two objects.

PREREQUISITES
  • Understanding of gravitational potential energy (GPE) and kinetic energy (KE)
  • Familiarity with the concepts of momentum and impulse
  • Basic knowledge of physics equations related to energy and motion
  • Ability to work with ratios and proportions in physics
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  • Research the principles of gravitational potential energy and kinetic energy equations
  • Study momentum conservation in elastic and inelastic collisions
  • Explore the concept of mass ratios in physics problems
  • Learn about gravitational acceleration variations on different celestial bodies
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Students and educators in physics, particularly those studying mechanics and energy conservation principles, as well as anyone interested in solving problems involving gravitational forces and mass ratios.

jstelpend
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Homework Statement
Hello, I have been stuck on this problem.

A ball with an unknown mass (mA) is initially 11.9 meters above the surface of a foreign planet. A box with an unknown mass (mE) is initially some distance (hE) above the surface of the Earth. The ball and box both have the same GPE relative to the surface of their respective planets.

The foreign planet has a mass of 8.7 x 10^24 kg and its radius is 6.35 x 10^6 meters.

Both the ball and the box are dropped from rest and caught by someone on the surface of the respective planets. The person on the foreign planet and the person on the Earth both apply the same amount of impulse on their respective objects.

Find hE initially. (6.67*10^-11 to be used for G and 9.8 to be used for g of Earth. Also, ignore air resistance)
Relevant Equations
Conservation of energy, gravitational acceleration, Fg = GMm/d^2???, pi = pf
So far, I have found g of the foreign planet, Vf of the ball, and realize that GPEiA = KEfA (Am I right here?). Thus, since GPEiA = GPEiE, GPEiE also equals KEfE. I also understand that, since the same impulse is applied to catch the objects, both objects have the same momentum at the moment that they are caught.

I am stuck on finding the mass of the ball which, I believe, will allow for me to solve the entirety of the question.

I appreciate all help and thank, in advance, those who decide to reach out!
 
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jstelpend said:
I am stuck on finding the mass of the ball
Seems to me that you don't need to know the two masses, only their ratio.
 

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