Just looking for some advice on where my maths is going wrong with this. I have the following equation.(adsbygoogle = window.adsbygoogle || []).push({});

[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 . Any help is much appreciated.

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# Troublesome Equation

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