# Homework Help: Planet Orbits, finding radius HELPP

1. Jan 27, 2010

### thussain93

1. The problem statement, all variables and given/known data
The planet mars has a mass of 6.418*1023kg and completes an orbit around the sun in 687 days. The sun has a mass of 1.99 * 1030kg. what is the average radius of the orbit of mars?

2. Relevant equations
Force Gravity = G*(m1m2)/r2
Force Centripital = mv2/r

G = 6.67 * 10-11

3. The attempt at a solution
I tried plugging in the numbers into the Universal gravitaiton formula where m1 was the mass of mars * m2 which is the mass of the sun * Universal gravitation. I didn't know what to use as Force Gravity.
with the force centripital formula, you have 2 masses. how could i go about finding the velocity of mars if i dont have the radius??
thanks for the help

2. Jan 27, 2010

### rl.bhat

Re: Planet Orbits, finding radius HELPP!!

G*M*m/r^2 = m*v^2/r. Or
G*M/r= v^2.....(1)
In the problem time T to completes an orbit around the sun is given.
So velocity v = 2*pi*r/T...(2)
Substitute the expression of v in eq.1 and solve for r.

3. Jan 27, 2010

### thussain93

Re: Planet Orbits, finding radius HELPP!!

for when i plug in equation 1, would i take the square root of the whole left side??

4. Jan 27, 2010

### rl.bhat

Re: Planet Orbits, finding radius HELPP!!

G*M/r= v^2.....(1)
G*M/r= (2*pi*r/T)^2.....(2)
If you simplify, you get
G*M*T^2= 4*pi^2*r^3.
Convert days to seconds and solve for r.

5. Jan 27, 2010

### thussain93

Re: Planet Orbits, finding radius HELPP!!

I got an answer with over a billion km lol seems kinda big even for planets but whatever

thanks alot