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!

Given the Mass & Orbital Period, Find the Gravitational Force

  1. Oct 26, 2014 #1
    1. The problem statement, all variables and given/known data
    A large telescope of mass 8410 kg is in a circular orbit around the earth, making one revolution every 927 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth?
    [itex]M_E = 6.0x10^{24} kg[/itex]
    [itex]m_s = 8410 kg[/itex]
    [itex]T_s = 927 min = 55,620 s[/itex]
    [itex]G = 6.67x10^{-11} Nm^2/kg^2[/itex]

    2. Relevant equations
    [itex]T^2 = \frac {4{\pi}^2 r^3}{GM_E} \Rightarrow r = \sqrt[3]{\frac {T^2 GM_E}{4\pi^2}}[/itex]
    [itex]F_G = \frac {GM_E m_s}{r^2}[/itex]

    3. The attempt at a solution
    [itex]r = \sqrt[3]{\frac {T^2 GM_E}{4\pi^2}} = \sqrt[3]{\frac {(55,620 s)^2 (6.67x10^{-11} Nm^2/kg^2)(6.0x10^{24} kg)}{4\pi^2}} = 3.1532x10^7 m[/itex]

    [itex]F_G = \frac {GM_E m_s}{r^2} = \frac {(6.67x10^{-11} Nm^2/kg^2)(6.0x10^{24} kg)(8410 kg)}{(3.1532x10^7 m)^2} = 3385 N[/itex]

    Is there a simpler equation to get the radius? Am I doing it right?

    Last edited: Oct 26, 2014
  2. jcsd
  3. Oct 26, 2014 #2


    User Avatar

    Staff: Mentor

    Your results look good. I don't know if there's a simpler way to get to the radius unless you memorize some fact about another radius and period. For example, if an object could orbit at the Earth's surface it would have a period of 84.5 minutes. Then knowing the Earth's radius you could set up the ratio:
    $$\left( \frac{927}{84.5} \right)^2 = \left( \frac{r}{6378 km} \right)^3$$
    and solve for r.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted