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Satellites in Circular Orbits

by Whotto
Tags: circular, orbits, satellites
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Mar3-09, 03:39 AM
P: 16
1. The problem statement, all variables and given/known data

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.

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.

2. Relevant equations

I have no clue. Maybe this?

v = sqrt(GM/r)

F = G (m1m2/r2)

a = v2 / r

a = 4pi2r / T2

3. 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!
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Mar3-09, 06:16 AM
P: 34
[tex]v = \frac{2{\pi}r}{T}[/tex]

Should help you in the second part if you equate it to another equation with known variables.
Mar3-09, 06:19 AM
P: 1,810
Start with Kepler's 3rd law.

Mar3-09, 02:14 PM
P: 16
Satellites in Circular Orbits

Thanks! I got #2 with the formula T = ( 2 pi r3/2 ) / sqrt(GMe).

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

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