Why is the orbit of planets around the sun elliptical?

Corey Houghton
By Corey Houghton
Questions and Answers

I study aerospace. During the lectures it was explained that the orbits move elliptically. Kepler’s first law also says this (but Kepler’s laws are empirical and thus don’t answer my question).

It was also explained by means of some equations and formulas that the planets do indeed have an elliptical orbit. A certain initial speed of the earth is assumed here and then it is indeed clear from these formulas that there is an elliptical orbit (a small additional question: where does this initial speed come from?). But still there was no real answer to my question.

Why just an elliptical orbit? Maybe the sun’s gravitational field isn’t evenly distributed? I can hardly imagine this. I haven’t been able to find a real answer on the internet either.

Asker: Jasper, 18 years old

Answer

If you solve Newton’s equations for a central attraction that decreases inversely with the square of the distance, you find that the orbits are conic sections, which is also the ‘initial velocity’; closed orbits are then ellipses. That’s the mathematic answer, and it may not be entirely satisfying.
The attraction of the sun is ‘central’, directed towards the sun. If you don’t have an initial velocity, or an initial velocity toward the sun, you’ll just fall on the sun. If you have a component of speed perpendicular to the direction to the sun (so your total speed is aimed next to the sun), then you will not end up directly at the sun. As you get closer to the sun, your speed increases. At a moment you arrive at your closest point to the sun, from then on your movement is slowed down again, but you fly on for a bit, until you have so little speed that you start to fall back in and accelerate again is becoming.
The ‘initial speed’ (actually the speed at any given moment) determines what your ellipse will eventually look like. If there is a large component toward the sun, it is a very elongated ellipse; if the speed is always perpendicular to the direction to the sun, then you are moving on a circle.

Why is the orbit of planets around the sun elliptical?

Answered by

Prof. dr. Christopher Waelkens

Astronomy

Catholic University of Leuven
Old Market 13 3000 Leuven
https://www.kuleuven.be/

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