# Finding the radius in the universal gravity equation

## Homework Statement

G= 6.67 *10^-11
M= 5.97*10^24 kg
m= 430 kg
Orbital speed=6800m/s
I'm supposed to find radius of satellite orbit.

## The Attempt at a Solution

I don't know where to start because in order to find radius, I have to find period as well

gneill
Mentor
Assuming a circular orbit, what force is providing the centripetal force to maintain that circular motion?

What equations are relevant?

Fg= G*M*m/r^2, v=2Pi(r)/T, acent=v^2/r
I'm not sure what force maintains circular motion. I would assume gravity

gneill
Mentor
Fg= G*M*m/r^2, v=2Pi(r)/T, acent=v^2/r
I'm not sure what force maintains circular motion. I would assume gravity
Gravity is correct. It's providing the centripetal force.

There's an equation for centripetal force that involves the velocity but not the period T. Do you know what it is?

I don't think so. I know there's F=mv^2/r, but I would still have two unknowns, Fg and r.

SammyS
Staff Emeritus
Homework Helper
Gold Member
I don't think so. I know there's F=mv^2/r, but I would still have two unknowns, Fg and r.

Do you have an expression for gravitational force? (I assume that's what you mean by Fg.)

gneill
Mentor
I don't think so. I know there's F=mv^2/r, but I would still have two unknowns, Fg and r.
Yes. That's good for ##F_c##. You've already stated an equation for ##F_g##. Try equating them. Can you solve for r?

I don't think so. I know there's F=mv^2/r, but I would still have two unknowns, Fg and r.

You said the centripetal force must be
F = mv^2/r

You said the gravitational force is
Fg = G Mm/r^2

When asked what force maintains orbit you said “I assume gravity”

You said “I would still have 2 unknowns”

So that’s 2 equations in 2 unknowns. Hmmm ... what to do, what to do?