## Homework Statement

The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 4.2 earth years. What are the asteroid's orbital radius and speed?

## Homework Equations

T = 2pi sqrt(r/g)

## The Attempt at a Solution

I tried manipulating the above equation to solve for r. I got 4.383, but it was wrong.

I used 9.81 for the value of g.

D H
Staff Emeritus
Why did you do that? You need to use the universal gravitational constant G, not the Earth's standard gravitational acceleration, g. Moreover, this equation,

$$T = 2\pi \sqrt{\frac r g}$$

is not quite. What are Kepler's laws?

I have no idea. We didn't discuss them in depth.

D H
Staff Emeritus
$$T = 2\pi \sqrt{\frac r g}$$