Finding the radius in the universal gravity equation

[Madelin Pierce]

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.

Homework Equations

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]

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

What equations are relevant?

 

[Madelin Pierce]

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]

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?

 

[Madelin Pierce]

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

 

[SammyS]

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]

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?

 

[Cutter Ketch]

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

Everybody keeps asking if you have equations that you already wrote!

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?