Orbits for dummies

Question

In a certain universe a perfectly spherical, uniformly dense planet is found to be in a stable orbit around a stable star. The rest of the universe is empty space with no silly stuff like dark matter. The planet has been in orbit for millions of years. Would the orbit be a perfect circle? If not why not?

Answer 1

The stable orbits around a star are given by the Kepler's laws oft planetary motion. In general these are ellipses with the center star in one of the two foci. Circular orbits are the special case when there is only one focus.

For a orbit with a given radius, there is only one speed which allows a circular orbit. If you have a starting condition where the orbit radius and the velocity does not match the conditions for a circular orbit, the gravitational force will not stay perpendicular to the veliocity. This causes the orbit to be an ellipse.

Answer 2

According to Newton's theory of gravity, the orbit would be an ellipse, which could take the form of a perfect circle. However, Einstein's theory of General Relativity tells us that this elliptical orbit would very gradually decay due to the emission of gravitational waves, and perhaps also precess. The Wikipedia page on the two-body problem in general relativity looks like a good reference on the topic.

Answer 3

In the Earth-Moon system, the mass of the Moon is sufficiently large and it is sufficiently close to raise tides in the matter of Earth. Because of this tidal friction can occur which dissipates energy. Enormous amount of power are involved in this process (of $\approx$ TW) and part of this causes the Moon to constantly being promoted to a slightly higher orbit (and Earth to be decelerated in its rotation). The Moon moves farther away from Earth at a rate of $\approx$ 40 mm/year. Now while it may start off in a perfect circle (but this would require very precise initial conditions) the planet will gradually move away from the star (it's essentially a very hot fluid) then if the orbit is changing it can't be in an exact circular orbit (if it started off from one) anymore.