How can the acceleration of a body in an ellipse always point towards a focus?

AI Thread Summary
The discussion centers on proving that the acceleration of a body moving at constant speed in an elliptical path is always directed towards one of the foci. Participants express frustration over the complexity of deriving a vector equation for a particle's elliptical motion. Suggestions range from tedious mathematical approaches to more complex calculations that require deeper understanding. The lack of shared methodologies hinders collaborative problem-solving. Clearer communication of individual efforts is needed to facilitate progress in the discussion.
prabhat rao
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prove that the acceleration of a body moving with constant speed in ellipse is always directed towards one of the focus .
I have tried but my efforts have gone in vain
 
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Can you write me a vector equation for the path of a particle traveling in an ellipse?
 
Hootnannty indicates our problem! I can think of several ways of doing this, some involving simple but VERY tedious mathematics (I wouldn't want to do it that way!), others involving short calculations but much deeper mathematics. If you don't show us anything of your work (you tell us you have made efforts but don't describe them), we don't know what methods you can use.
 

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