Central Force Problem: Nature of Orbit when Force is Halved | Homework Help

[neelakash]

Homework Statement

A particle moves in a circular orbit under the action of a force
f(r)=-(k/r^2).If k is suddenly reduced to half its value, what would be the nature of the orbit?

Homework Equations

e=sqrt[1+(2*L^2*E)/(mk^2)]

The Attempt at a Solution

My attempt:
Clearly,the particle moves under attractive central force.Now,for the circular orbit,eccentricity e=0 and as the motion is bound,the energy is negative.
If k is reduced to k/2, eccentricity changes to
e=1+(8*L^2*E)/(mk^2)=6*L^2*E/(mk^2)

Since e becomes negative as E is negative,no motion is possible.

Am I correct?

 

[berkeman]

I didn't check your math, but your solution for e being negative sounds reasonable. But that doesn't mean "no motion is possible". It means that something happens to the formerly circular motion of the particle. Think about it in a real-life physical sense. The particle is moving around in a circle, the central force is suddenly cut in half, describe how the particle moves next...