Possible Orbits in V = k r^4 Potential

[yxgao]

Assume energy greater than 0.
Consider cases in which k is either + or - and l is either 0 or +.


Using your tuition, what are the possible orbits?


k<0:
l=0: falls to the center
l=+: hyperbola or it falls to the center

k>0:
l=0: hyperbola
l=+: hyperbola or it falls to the center

what about circular orbits?

 

[yxgao]

Is this question more difficult than it sounds? There are no responses from anyone! :)

 

[M98Ranger]

In this potential, circular orbits are not possible since the potential is not symmetric. The only possible stable orbits are hyperbolas or falling to the center.