# Centripetal Acceleration in Satellites Question

1. Nov 12, 2007

### sarahhhh

1. The problem statement, all variables and given/known data

What provides the force that causes the centripetal acceleration of a satellite in orbit?

2. The attempt at a solution

I'm really confused about the answer to this question because in class my teacher only taught us how to solve satellite problems if we are given the distance and we have to find speed .
Can someone please help me.. or just explain what i would need to know to get the answer to this problem! thanks sooo much!!!!

2. Nov 12, 2007

### hotcommodity

The force that provides the centripetal acceleration for a satellite orbiting in uniform circular motion (that is, the satellite has the same speed at every point on its orbit) is the gravitational force:

$$F_{grav} = G \frac{M_Em}{r^2}$$

Where G is the gravitational constant (this is easy to find, its probably in the cover of your text book), ME is the mass of the earth, m is the mass of the satellite, and r is the distance between the center of the Earth and the satellite.

You know by Newton's Second Law that this gravitational force must equal the mass of the satellite times the centripetal acceleration, and the centripetal acceleration in terms of speed is:

$$a_c = \frac{v^2}{r}$$

And so we have:

$$G \frac{M_Em}{r^2} = m \frac{v^2}{r}$$

And now you can solve for the speed. Does that help?

3. Nov 14, 2007

### sarahhhh

yes! thank you so much :)