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

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SUMMARY

The acceleration of a body moving with constant speed along an elliptical path is always directed towards one of the foci of the ellipse. This phenomenon can be mathematically proven using vector equations that describe the motion of the particle in an ellipse. The discussion highlights the need for a clear vector equation to represent the path and emphasizes the complexity of the mathematics involved, suggesting that both tedious and advanced methods exist for deriving the necessary calculations.

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  • Understanding of elliptical geometry and properties
  • Familiarity with vector calculus
  • Knowledge of Newtonian mechanics
  • Ability to perform mathematical proofs
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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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