1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Satellite Motion

  1. Jun 4, 2017 #1
    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 × 104 m/s, and the radius of the orbit is 5.25 × 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 × 106 m. What is the speed of the second satellite?

    2. Relevant equations

    Kepler's Laws of Planetary Motion -- T2/r3 = 4pi2 / GM

    v = sqrt (GM / r)

    3. The attempt at a solution

    There really isn't much conceptual work involved in this, so I might just be making an arithmetic mistake somewhere. But I've worked the problem out three times and gotten the same (wrong) answer every time...

    I used the v = sqrt (GM / r) -- plugged the values in for the first satellite and solved for the planet's mass which must be 2.274 x 1025 kg.

    Then I used that mass value for M in the same equation, switching out the radius value for the second satellite. I get that v = 1.3 x 104.

    But the answer is 1.3 x 10-7.

    Why is my answer so far off? Is the problem with the planet mass value or just in the calculations for the second satellite's speed? I think my process is right.
  2. jcsd
  3. Jun 4, 2017 #2


    User Avatar
    Science Advisor
    Gold Member

    This is clearly a typo in the answer key. There's no way orbital speed just barely higher would be 11 orders of magnitude lower.
    The numerical factor of 1.3 matches, so you're good there, and by eyeballing the distances involved the order of magnitude should be the same for both satellites - i.e. 10E4.
  4. Jun 7, 2017 #3
    Thanks! I did wonder about the small difference in the orbit radii, but wasn't sure if I was missing something.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted