## brinethery 3 years ago Scientists want to place a 2800.0 kg satellite in orbit around Mars. They plan to have the satellite orbit at a speed of 2695.0 m/s in a perfectly circular orbit. Here is some information that may help solve this problem: mass of mars = 6.4191 x 10^23 kg radius of mars = 3.397 x 10^6 m G = 6.67428 x 10^-11 N-m^2/kg^2 What radius should the satellite move at in its orbit? (Measured frrom the center of Mars.)

1. Algebraic!

$G\frac{ M _{mars} }{ r^2 } = \frac{ V^2 }{ r}$

2. Algebraic!

$G\frac{ M _{mars} }{ V^2 } = r$

3. brinethery

@Algebraic! Thank you very much, just one quick question... why is little m (mass of satellite) not included?

4. Algebraic!

yeah, it's a bit weird to think about... but there you have it: the force due to gravity is proportional to satellite mass as is the centripetal force... so, it's immaterial what the satellite's mass is...

5. Algebraic!

This is actually only approximately true though, for satellite mass << mass of mars... if the satellite is very massive then mars and the satellite both orbit the center of mass of the system... but that's not a concern here.

6. brinethery

Thanks... I feel like I need some major hand-holding through this chapter we're doing :-(

7. Algebraic!

No problem:)

8. brinethery

I'd give ya 3 medals if I could. My dad and I just went through the derivation and I can see that the little m on each side cancels out. I will live another day!

9. Algebraic!

:)

10. Algebraic!

for sparta!

11. brinethery

I have one more question having to do with this problem: I could open up a new thread if you want me to? What should the speed of the orbit be, if we want the satellite to take 8 times longer to complete one full revolution of its orbit?