How Does Height Above Earth Affect Satellite Weight?

AI Thread Summary
The weight of a satellite decreases with height above the Earth due to the weakening gravitational force. At 12.8 million meters above the Earth's surface, the standard gravitational acceleration of 9.81 m/s² is not applicable. Instead, the gravitational force can be calculated using the formula F = GMm/d², where G is the gravitational constant, M is the Earth's mass, m is the satellite's mass, and d is the distance from the Earth's center. This approach provides a more accurate weight for the satellite at that altitude. Understanding the impact of altitude on gravitational force is crucial for precise calculations in satellite dynamics.
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Homework Statement


What is the weight of a 200 kg satellite 12.8 * 10^6 m above the surface of the Earth.


Homework Equations


F = mg


The Attempt at a Solution


F=200 (9.81)
F = 1962 N

I thought this was a basic weight problem, but I was confused on whether the height above the Earth affects the weight.
 
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The gravitational force gets weaker as you go further out from the center of the Earth. The g = 9.81 value will not be accurate. You could use the basic gravitational force formula F = GMm/d² (M=mass of Earth, m = mass of satellite, d = distance from center of Earth to center of satellite) or you could use the F = mg with g = GM/d².
 

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