# Homework Help: Differentiation of conic section equation

1. Aug 31, 2014

### tauon

1. The problem statement, all variables and given/known data

I do not understand how the authors got the time derivative of equation 1.5-4 in the form given at 2.5-2.

2. Relevant equations

3. The attempt at a solution

$$\frac{d}{dt}\frac{p}{1+e cos\sigma}=-\frac{p}{(1+ecos\sigma)^2}(-esin\sigma\dot\sigma)=\frac{pe\, sin\sigma\dot\sigma}{1+2e\,cos\sigma+e^2cos^2\sigma}$$

?

I tried various rewrites using trigonometric identities, but the equation just got so complicated that it'd take me a long time to typeset it in this post.

2. Aug 31, 2014

### tauon

Never mind. I got the derivation. I also found out I am blind/can't read.

3. Sep 13, 2014

### geoffrey74

Hi tauon! I'm curious if you could share how you got the derivation, or which textbook your above excerpt is from. I'm trying to get to equation 2.5-2 from this excerpt, but seem to be getting stuck the same spot you were. Thanks!

4. Nov 27, 2014

### tauon

Hi. This might be very late now, but I didn't check this thread since I got the solution. :p
In case someone runs into it in the future, this is the derivation I used

Oh, and the excerpt is from "Fundamentals of Astrodynamics" (authors Roger Bate, Donald Mueller, and Jerry White) the 1971 edition.

Last edited: Nov 27, 2014