What is the Orbital Speed of a Satellite in a Circular Orbit?

[Whotto]

Homework Statement

#1
A satellite is in a circular orbit around an unknown planet/ The satellite has a speed of 1.70 x 10⁴ m/s, and the radius of the orbit is 5.25 x 10⁶ m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 8.60 x 10^6 m. What is the orbital speed of the second satellite.

#2
The moon orbits the Earth at a distance of 3.85 x 10⁸ m. Assume that this distance is between the centers of the Earth and the moon and that the mass of the Earth is 5.98 x 10²⁴ kg. Find the period for the moon's motion around the Earth. Express the answer in days and compare it to the length of a month.

Homework Equations

I have no clue. Maybe this?

v = sqrt(GM/r)

F = G (m₁m₂/r²)

a = v² / r

a = 4pi²r / T²

The Attempt at a Solution

# 1: Well, I know there is something that the two satellites could be compared to, but I can't figure what. I tried a futile stab at the question by using v₁² / r = v₂² / r but that didn't give me the right answer.

The answer at the back of the book is 1.3 x 10⁴ m/s.

# 2: I don't even know how to get started on this question...I know I have radius and mass of the Earth, and I need to find the period.

Any help towards these questions would be greatly appreciated!

 

[Briggs]

$$v = \frac{2{\pi}r}{T}$$

Should help you in the second part if you equate it to another equation with known variables.

 

[skeptic2]

Start with Kepler's 3rd law.

 

[Whotto]

Thanks! I got #2 with the formula T = ( 2 pi r^3/2 ) / sqrt(GM_e).


But I still don't get #1. Can I get some more pointers?