1. Not finding help here? Sign up for a free 30min 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!

Troublesome Equation

  1. May 11, 2004 #1

    Kurdt

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Just looking for some advice on where my maths is going wrong with this. I have the following equation.

    [tex] L_{orb}=(\frac{GD}{M})^\frac{1}{2}M_sM_p [/tex]

    and information that the time derivatives of L and M are zero. Also M_s varies with time along with D. I am supposed to arrive at the following equation.

    [tex] \frac{\dot{D}}{D}=-2(1-\frac{M_s}{M_p})\frac{\dot{M_s}}{M_s}[/tex]

    I first brought the M over to be on the same side as the L as when I take the time derivative they will be 0 and then after taking the time derivative of what is left on the left hand side and rearranging a little I can only get

    [tex]\frac{\dot{D}}{D}=-2\frac{\dot{M_s}}{M_s^2}[/tex]

    Any pointers as to where my maths fails. I realise it could have something to do with a substitution of variables but I'm assuming not as it seems unlikely at the minute and I wouldn't like to type out all the possibilities :wink: . Any help is much appreciated.
     
    Last edited: May 11, 2004
  2. jcsd
  3. May 11, 2004 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    What's r and b?
    (This looks like some sort of spin equation in a gravitational field, but..)
    And M? Do you mean [tex]M_{p}[/tex]?
     
  4. May 11, 2004 #3

    Kurdt

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    sorry r and b was supposed to be part of the subscript I will change it and M is the sum of M_p and M _p.
     
  5. May 11, 2004 #4

    Kurdt

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Its just basically the orbital angular momentum in the Roche model of binary stars which I am studying at the minute. Trying to extract useful information on the rate of orbital decay.
     
  6. May 11, 2004 #5

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Remove the [tex]G^{\frac{1}{2}}[/tex] over as well.
    Then we have:
    [tex]0=\frac{\dot{D}}{2\sqrt{D}}M_{s}M_{p}+\sqrt{D}\frac{d}{dt}(M_{s}M_{p})\rightarrow\frac{\dot{D}}{D}=-2\frac{\frac{d}{dt}(M_{s}M_{p})}{M_{s}M_{p}}[/tex]

    The desired expression is now readily obtained
     
  7. May 12, 2004 #6

    Kurdt

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Thanks for your help. I knew it was something simple that I'd missed.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Troublesome Equation
  1. Wave equation (Replies: 4)

Loading...