What Is the Weight of a Satellite Orbiting Mars?

[GrkFizzix]

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?

 

[ehild]

How is weight defined?

ehild

 

[GrkFizzix]

it gives no further explanation but I am guessing mg?

 

[ehild]

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