A particle moves in a circular orbit under a force field given by \(\vec{F}(\vec{r})=-\frac{k}{r^2} \hat{r}\), where k is a positive constant. If the force changes suddenly to \(\vec{F}(\vec{r})=-\frac{k}{2 r^2} \hat{r} \), the shape of the new orbit would be
1
parabolic
2
circular
3
elliptical
4
hyperbolic