# Asteroid's orbital radius and speed

somebody help me start this question

The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 5 earth years. What is the asteroid's orbital radius and speed?

Thanks!!!

## Answers and Replies

I believe you need the mass of the sun, unless you are allowed to give your answer as a function of that variable. Use this formula:
$$T=\frac{2\pi r^{\frac{3}{2}}}{\sqrt{Gm_{sun}}}$$
where G is the universal gravitational constant and T is the orbital period.

is this right

Sirus said:
I believe you need the mass of the sun, unless you are allowed to give your answer as a function of that variable. Use this formula:
$$T=\frac{2\pi r^{\frac{3}{2}}}{\sqrt{Gm_{sun}}}$$
where G is the universal gravitational constant and T is the orbital period.
will the period be 31536000s. if it is, is this right:
r=[T*(sqrt(GM_sun)/2pi)]^(2/3)
[ 31536000*sqrt(6.67*10^(-11)*(1.99*10^(30)))/(2*pi)]^(2/3)

Check your period calculation again. Your method looks correct.

Sirus said:
Check your period calculation again. Your method looks correct.
opps
31536000*5?