Calculating orbital radius and speed of an asteroid in the asteroid belt

[aligass2004]

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.

 

[Astronuc]

Please show the work so we can understand one's method. What value of g was used? Remember the sun is the principal source of the gravitational field for this problem.


Also, please refer to - http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html#c6

http://hyperphysics.phy-astr.gsu.edu/hbase/orbv.html

 

[aligass2004]

I used 9.81 for the value of g.

 

[D H]

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?

 

[aligass2004]

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

 

[D H]

You were trying to use one of Kepler's laws here,

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

but you did it wrong. Where did you get that equation from? Look over your text and your notes.