Kinetic energy of space probe problem

AI Thread Summary
To determine the kinetic energy required for a 10-kg space probe to reach a maximum distance of 4.0 million meters from Planet Zero's center, the gravitational potential energy must be calculated for two positions: the surface (2.0 million meters from the center) and the desired height (4.0 million meters). The initial potential energy is calculated using the formula U = (GMm/radius), while the mechanical energy at the maximum height is given by E = - (GMm/2d). The key is to find the difference in gravitational potential energy between these two configurations. Careful attention to the calculations and signs is crucial to arrive at the correct kinetic energy value. Accurate calculations will yield the necessary kinetic energy for the probe's launch.
chouZ
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Homework Statement


Planet Zero has a mass of 4.0*10^23 kg and a radius of 2.0*10^6 m . With what kinetic energy should a 10-kg space probe be launched vertically from the surface of Zero so as to achieve a maximum distance of 4.0*10^6 m from Zero's center?

The Attempt at a Solution


I found the initial potential Energy, U=(GMm/radius planet Zero) and then the mecahnical energy at the end, E= - (GMm/2d)

its not right..HELP!
 
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I think most likely you are not using the right values for the distance.

The question is effective asking for the difference in gravitational potential of two configurations, and they are:

1. The space probe on the surface of this planet (distance of 2.0x10^6 from center)
2. The space probe at a distance off the surface (distance of 4.0x10^6 from the center)

Try doing the calculations carefully again.
 
How do you know it isn't right? What did you get for your final value? Be careful of your signs.
 
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