I'm thinking of a system like an object in orbit around a planet. Say a 100kg mass orbiting the earth. If I were to impart 1 m/s to the object down toward the center of the mass it is orbiting, what would happen?
What I'm assuming is that the object would move closer to the earth which would cause an increasing imbalance of the objects orbital speed and its altitude. This would cause it to feel an increasing acceleration away from the planet, come to a stop, and eventually begin accelerating towards its proper altitude.
Inertia being what it is, it seems that this would set up an oscillation centered on the altitude/speed balance. I'm assuming in most cases this would decay into a stable altitude.
How can the period of the oscillations be calculated? Are there stable resonances possible in this modality and how can they be found?
If we were to plot the
y value of a circular orbit over time we would get a nice sin wave. What I'm effectively wondering is if an oscillation can be added to that, a la:
Is it possible to create such an oscillation in the object's orbital altitude with a downward impulse?