What Is the Weight of a Satellite Orbiting Mars?

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The discussion focuses on calculating the weight of a satellite orbiting Mars, emphasizing the relationship between gravitational force and kinetic energy. Weight is defined as the gravitational force exerted by Mars on the satellite, which can be derived using the formula GmM/R^2. The kinetic energy of the satellite, given as 3.0x10^10 J, is related to its mass and velocity through the equation KE = 0.5 mv^2. For a satellite in circular orbit, the centripetal force equals the gravitational force, allowing for the determination of weight using the equations provided. Understanding these concepts is crucial for solving the problem effectively.
GrkFizzix
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Hi Guys I am in year 12 and have my exam shortly would just like to ask a question to do with gravity.

A small satellite orbits Mars. It has a kinetic energy of 3.0x10^10 J, and is at a constant distance of 8.0x10^7 m from the center of Mars. What is the weight of the satellite at this height?
 
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How is weight defined?

ehild
 
it gives no further explanation but I am guessing mg?
 
No, mg is at the surface of Earth. I asked what you have learned about weight, as there are two different definitions and one says that the orbiting bodies are weightless. Here, I think weight is meant as the gravitational force of Mars on the satellite.

To get the force of gravity at distance R from Mars, you can use the equations for the kinetic energy related to the centripetal force along a circular orbit. If m is the mass of the satellite and M is that of Mars, and G is the gravitational constant, the gravitational force is GmM/R^2. The kinetic energy is KE= .5 mv^2.
For a circular orbit, the centripetal force = the force of gravity, and this is the weight of the satellite.

The centripetal force is mv^2/R,

mv^2/R = GmM/R^2.

Go ahead.


ehild
 

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