WHY THE ORBITS OF PLANETS ARE ELLIPTICAL?

This description ignores the relatively negligible gravitational effects of other planets (because of mass) and stars (because of distance).

An object, a concentration of mass, is hurled away from a star a result of some energetic event. This can have three different results. Objects that receive an initial energy above a certain threshold escape the star’s gravity and experience some alternative fate (unknown to us for the purposes of this discussion).

[1] Objects that receive an initial energy below a certain threshold fall back into the star. But there is a certain middle range of initial energy that results in an orbiting planet. For objects that receive this level of energy the escape momentum eventually falls below the gravitational attraction between the planet and the star. As the planet again approaches the star, the planet’s velocity (momentum) increases. At a certain moment, the acceleration due to gravity and the momentum come to be equal. At that moment the planet will be in a circular orbit around the star. The distance from the star at which this happens is a function of the initial energy and the mass of the object. This is also the closest the planet gets to the star. Beyond this point as the planet continues to “fall”, it continues to be accelerated by gravity. The resulting increased momentum now causes the planet to again move away from the star. All things being equal (and they are not, see first sentence), this phase will result in the complete restoration of the original energy and the system will recur.

Here is another way to explain the energy exchange.
At some point the initial energy is all used up and the planet begins to fall back toward the star. As it falls to the star it accelerates acquiring momentum (which is another way of saying that it is reacquiring the energy it gave up in overcoming gravity). In the course of returning to the star it acquires enough energy to allow it to avoid falling into the star.






[1] The mass of the object must also be a part of the equation. Couldn’t there still be objects way beyond what we presently consider the boundaries of our solar system that will in fact someday come back as additional planets?[1] The mass of the object must also be a part of the equation. Couldn’t there still be objects way beyond what we presently consider the boundaries of our solar system that will in fact someday come back as additional planets?