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Satellites in Circular Orbits 
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#1
Mar309, 03:39 AM

P: 17

1. The problem statement, all variables and given/known data
#1 A satellite is in a circular orbit around an unknown planet/ The satellite has a speed of 1.70 x 10^{4} m/s, and the radius of the orbit is 5.25 x 10^{6} 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 10^{8} 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 10^{24} 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 (m_{1}m_{2}/r^{2}) a = v^{2} / r a = 4pi^{2}r / T^{2} 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 v_{1}^{2} / r = v_{2}^{2} / r but that didn't give me the right answer. The answer at the back of the book is 1.3 x 10^{4} 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! 


#2
Mar309, 06:16 AM

P: 33

[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. 


#3
Mar309, 06:19 AM

P: 1,803

Start with Kepler's 3rd law.



#4
Mar309, 02:14 PM

P: 17

Satellites in Circular Orbits
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? 


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