Proving Elliptical Trajectory Acceleration Vector Passes Through Focus

  • Thread starter Thread starter aim1732
  • Start date Start date
  • Tags Tags
    Trajectory
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
2 replies · 3K views
aim1732
Messages
428
Reaction score
2
If a particle's trajectory is defined by the law x=acos[pt] and y=bsin[pt] where t is parameter of time then we have to prove that it's acceleration vector passes through the focus of the conic----ellipse in this case as can be clearly seen.
If we write out the position vector in the vector notation and differentiate twice we get a=-p2r and this clearly is directed towards the centre of the axes system and not the focus.Any ideas?
 

Discussion

Physics news on Phys.org
aim1732 said:
If we write out the position vector in the vector notation and differentiate twice we get a=-p2r and this clearly is directed towards the centre of the axes system and not the focus.
Correct.

Any ideas?
Ideas regarding what? I assume you are trying to prove Kepler's first law. The given equation does not describe a planet's motion. You need to find the right equation.
 
have to prove that it's acceleration vector passes through the focus of the conic----ellipse in this case as can be clearly seen.

I meant this.