Why do planets have elliptical orbits?

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Why do planets have elliptical orbits?

In: Physics
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Because that’s [one of the four possible] shape[s] that ~~is~~[are] caused by attraction toward a point whose strength is proportional to one divided by the square of the distance to that point.

Gravity follows an inverse-square law, so the strength of gravity is inversely proportional to the square of the distance between the two masses. When you crunch the numbers on this, all possible orbital paths turn out to be conic sections.

A conic sections is just the surface you get if you chop through a(n infinite) cone with a plane. There are four of these. Cut horizontally and your get a circle. Cut at a slight angle and you get an ellipse. (A circle is really just a special ellipse.) Cut at an angle parallel to the slope of the cone and you get a parabola. Cut steeper, and you get a hyperbola.

The first two of these are closed curves, i.e. they are loops. These are the orbits that planets have. The other two are open curves (i.e. they go off to infinity). These are the orbits that some comets have if they pass the sun once and never return.

If they started perfectly circular they would stay that way. They dont, and the imperfections mean at some point gravity is stronger along the planets path, and will speed the object up. This creates an even larger imperfection in the circle, and it just goes from there. Hopefully this is a bit of an easier way to understand it without all the complex crap about systems at equilibrium.

If the universe were perfect, then maybe all of the planets could orbit in perfect circles around their parent stars.

But the universe, as it turns out, is very complicated and rarely works out so nice. In our solar system, there are eight planets (plus or minus Pluto) and millions of other tiny moons, asteroids, comets, and other junk. Everything with *mass* (so… basically everything but light) has *gravity*, which means that everything in the solar system pulls on everything else.

Imagine a million ropes tied to you, and each of them is pulling in a different direction. Some pull harder than others, though, depending on the mass of the thing doing the pulling.

The Sun contains the vast majority of the mass in the solar system, so you can just pretend that there’s only one thing pulling on the Earth. But it’s not a perfect approximation, because the Moon is there, too, and it’s gravity affects the earth enough to create tides. Jupiter is the largest planet in the Solar System, and it does have a measurable pull on the Earth, even from tens of millions of miles away.

So, even if the Earth’s orbit started out as a perfect circle, it’s not going to stay that way. In a perfectly circular orbit, a planet would move at a constant speed during their orbit. But a little tug from Jupiter might be enough to speed the Earth up a little bit (maybe only a few meters per second). But now the Earth is moving faster, which means it now has more *energy*. Energy, and this other thing called *angular momentum* like to be conserved, though. That basically means that the little bit of energy that the Earth gained has to go somewhere. Specifically, it goes into the orbit—in order to compensate for the increase in energy, **the orbit actually has to get bigger.**

The current position of the Earth acts kind of like an “anchor” point for the orbit’s expansion. If Earth gets a little bit faster, the orbit will stretch out *away from its current position*. A stretched out circle becomes… an ellipse!

This also means that the Earth will be ever so slightly further away from the sun at the opposite end of its orbit, since we stretched the orbit out a bit.

So, after the 4.5 billion-year lifetime of the Earth, its been pulled and tugged every direction by all the different planets in the solar system, which are constantly causing the Earth’s orbit to stretch and squeeze in different directions. The difference is extremely small, but it’s important when we’re trying to send stuff to other planets, where the difference of a few feet might mean landing a probe on Mars and crashing into the surface.

Because if they had triangular orbits, then when they were on the “side”, the gravity due to the sun would deflect their path off of a straight line. The same is true for any polygon, so they must be curved.

Just to add something to the other answers:

A comprehensive answer is not really possible in ELI5. Gravity follows an inverse-square law, and that does result in elliptical (or paraboical) orbits, but WHY that is the result is not easy to explain.

Back in the day, Isaac Newton had to invent a whole new branch of mathemathics for this.