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!

Period of revolution of two double stars

  1. Nov 10, 2013 #1
    1. The problem statement, all variables and given/known data
    Two double stars of the same mass as the sun rotate about their common center of mass. Their separation is 4 light years. What is their period of revolution?


    2. Relevant equations
    Lagranian = T - U = [itex]\mu\dot{r}^{2}/2[/itex] + [itex]\vec{L}^{2}/2\mu r^{2}[/itex] - [itex]Gm_{1}m_{2}/r[/itex]
    F = ma = m[itex]\omega^{2}[/itex]r = [itex]Gm_{1}m_{2}/r[/itex]


    3. The attempt at a solution
    Tried to solve this using the orbital equation , but I'm off by a power of 10. I've also tried using F = m[itex]\omega^{2}[/itex]r = [itex]Gm_{1}m_{2}/r[/itex] and solving for the period using [itex]\omega[/itex] = [itex]2\pi r/T[/itex] but I'm not sure where I'm going wrong. Since the question asks for the period of two double stars, does this mean that the reduced mass is [itex]\mu[/itex] = [itex](2m_{1})(2m_{2})/(2m_{1} + 2m_{2})[/itex] = [itex]4m^{2}/4m[/itex] = m since all the masses are the same? I'm assuming that two double stars means 4 separate stars acting in pairs. I'm not really sure where to go with this problem.
     
  2. jcsd
  3. Nov 10, 2013 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Aren't there a couple of things wrong with the RHS? It's dimensionally wrong for a force, no? And is r standing for the same distance each side?
     
  4. Nov 10, 2013 #3
    Oops, yeah.

    F = m[itex]\omega^{2}[/itex]r = [itex]Gm_{1}m_{2}/r^{2}[/itex]

    I believe? Since [itex]\omega^{2}[/itex] = [itex]a/r[/itex], I substituted for acceleration and set the only acting force on the stars as their gravitational attraction towards each other. Am I missing something else?
     
  5. Nov 10, 2013 #4
    And assuming a circular orbit, r = .5d, where d is the separation between the stars.
     
  6. Nov 10, 2013 #5

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    If the separation is d, what force does each experience?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Period of revolution of two double stars
  1. Period of a star (Replies: 7)

Loading...