# Help deriving this elliptical orbit equation?

help deriving this elliptical orbit equation??

Hi guys, this is my first post on these boards. just found out about this forum and im really happy because i often find i need a place like this to ask questions and my prayers are answered!

im a physics/computer science major in my second year at the University of the Witwatersrand in Johannesburg, South Africa.

any way.. enough history..

i need help deriving this equation for an elliptical orbit :

$$\frac{(x + ae)^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$$

where e is the eccentricity and for an ellipse e < 1

i cant find anything useful in my books and dont even know where to start.

any help would be awesome! thanks!

-skiz

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David Morin's book on mechanics explains very clearly on how to derive this equation

hmm i dont have david morin's book on mechanics..

any tips on how to go about deriving this? am i supposed to use the geometry of an ellipse?

bah

I assume that you are doing a course in Introductory Mechanics. The book by Kleppner & Kolenkow is really good for such a course. However in that book, the authors have begun from Law of conservation of energy and angular momentum and have derived the polar form of the equation. I believe that this is a good way to do this as it begins from conservation principles.

tiny-tim
Homework Helper
Welcome to PF!

Hi skiz! Welcome to PF! Is this a mechanics question (find the orbit of a particle in an electric or gravitational field), or a geometry question (find the equation for an ellipse)?

Assuming it's mechanics, start with Newton's second law, and remember that the force perpendicular to the "radius" vector is zero. hey tim, thanks for the welcome!

yeah its a mechanics course. Our first 6 months are split between "Classical Mechanics" and "Modern Physics/Relativity"

i find modern physics and relativity really interesting and easy to grasp but classical mechanics is kicking my ass...

tiny-tim
Homework Helper
Hi skiz! Just remember that nearly all classical mechanics boils down to good ol' Newton's second law …

force in a particular direction = (rate of) change of momentum in that direction … and in each case you just have to work out which direction gives you the best information (in this case, it's the "transverse" direction).