Planet Orbits, finding radius HELPP

[thussain93]

Planet Orbits, finding radius HELPP!

Homework Statement

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?

Homework Equations

Force Gravity = G*(m¹m²)/r²
Force Centripital = mv²/r

G = 6.67 * 10^-11

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 don't have the radius??
thanks for the help

 

[rl.bhat]

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.

 

[thussain93]

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

 

[rl.bhat]

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.

 

[thussain93]

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

thanks alot