Central force problem
Central force F=-ar/(r^3) & Central potential energy,U=-(a/r)
Find the nature of orbits if (i)a>0 and (ii)a<0
If we remember the attractive central force E=E(r) diagram,i.e.the one showing the graph of U_eff,we only need to know E_total=K+U.
Where only PE is given.
Then K=a/r and U=-(a/r)
Then in positive and negative both caes we get a parabolic orbit.
Please check if i am correct.
That's one possibility...
Originally Posted by kolahalb
Doesn't the form of the force law look familiar? That should lead you to what the correct answer should be. Now you have to prove it.
There is the problem.The -ve force obviously corresponds to elliptical path...
But I am getting total energy 0.
But I annot understand where did I go wrong?
OK,thank you.I got it.
Hence total energy E=K+U= -(1/2)(a/r)
Then,F=+b/r where b=-a>0
K is itrinsically positive.So,total energy positive.
hence hyperbolic trajectory.