Solving Satellite Speed Problem: Draw Path for Faster & Slower Orbits

[impendingChaos]

Homework Statement

When a satellite is at the desired altitude over the equator or Jupiter its velocity has the correst direction but the speed is (a) slightly faster that the correct speed for a circular orbit of the radius and (b) is slighly slower than the correct speed for a circular orbit of the radius

The question then offers two spheres to represent the planet and the path if the satellite had the proper speed, one must now draw the new path of the satellite for both cases.

The Attempt at a Solution

I believe that in instance (a), the path would be greater from the accepted path of the sattellite with proper speed, for a time, but would then return to the original path of the correct sattelite speed once it has circled the planet due to gravity, forming an ellipse around the circular orbit of the correctly sped satellite.

I feel the same will happen for instance (b) except the ellipse will form inside the path for a satellite of the correct speed.

My friends believe this is incorrect and the sattelite will (a) spiral away from the planet outwards (away form the correct path) and (b) spiral inwards (inside the correct path)

Simply need some hint to help me justify which is correct.
Thx.
C.N.

 

[andrevdh]

Planetary (and satellite) motions are generally descibed by conic sections. Which type of orbit it follows is determined by the total mechanical energy of the satellite. The other fact to consider is that its radial speed is zero at the point in consideration. This suggests that the satellite will be at the symmetrical point of the orbit, eg. if it is an elliptical orbit it will either be at aphelion or perihelion.