Universal Gravitation question

1. Jun 1, 2010

GrkFizzix

Hi Guys im 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?

2. Jun 1, 2010

ehild

How is weight defined?

ehild

3. Jun 1, 2010

GrkFizzix

it gives no further explanation but im guessing mg?

4. Jun 2, 2010

ehild

No, mg is at the surface of Earth. I asked what you have learnt 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.