### 11/21/2002

Why is Earth's orbit an ellipse and not a circle?

The Nerd responds: To explain why Earth's orbit is elliptical, I must first explain why the Earth orbits the sun at all. As most people know, the sun is the biggest source of gravity in our solar system. The gravitational force of the sun pulls objects straight to it just like the Earth pulls a rock you drop straight back to the ground. The rock doesn't start orbiting the earth when you pick it up and release it, so why don't planets, in the same way, just get pulled straight into the sun?

You probably can guess the answer: unlike the rock you drop, the planets are in motion. In fact, if instead of just dropping the rock, you instead tossed it with an incredible force (which, of course, you could never do without a rocket ship), the rock actually would go into orbit around the Earth. In this case, the force of Earth's gravity would continue to bend the rock's trajectory back to the ground, but the force from the rock's horizontal velocity would tend to keep it going parallel to the Earth's surface. If the horizontal force is enough, then the downward trajectory due to gravity would actually be less than the curvature of the Earth itself. The result is that the ground keeps falling away from the rock even as the rock bends towards the ground. Isaac Newton came up with a famous illustration of this effect, envisioning a cannonball being shot with such force that it enters into an orbit around our planet. I include it as Figure 1.

 Figure 1. Newton's illustration of a cannonball orbiting the earth

To maintain an orbit like the one shown in Newton's illustration requires a tremendous amount of momentum. Man made creations like the space shuttle get this momentum from its incredibly powerful rocket engines during liftoff. The momentum planets have come from their earliest origins.

Most scientists today believe the solar system formed from a giant "solar disc" that existed where the sun resides today. Without going into all the hows and whys of the beginning of the solar system, I will just say that this solar disc contained all the matter of our current solar system (and then some), and that it was spinning very rapidly. At some point, the solar disc flung off big chunks of itself. These big chuncks flew off away from the center of the solar disc. To make a long story short, what remained of the solar disc became the sun and the chunks that flew off became the planets.

 Figure 2.  The first orbits

The proto-planetary chunks are flung away from the disc at a great speed and start racing out of what will someday become the solar system. But counteracting the centripetal force that flung them away, is the powerful gravitational force of the solar disc. Even as the chunks are racing off into space, their trajectory is already being bent back towards the disc by the force of gravity. Some of these chunks were flung away so powerfully that the disc's gravity was insufficient to keep a hold of them and they flew right out of the solar system altogether. The stuff that remained started bending back towards the disc. But like the rock we envisioned throwing with incredible force, the momentum of the chucks was enough that they always slipped to one side of the disc instead of crashing straight into it. I provide an animated illustration of this in Figure 2.

Now, I can answer your original question. The elliptical nature of Earth's orbit is due entirely to the original force which tossed it away from the solar disc (now the sun). If the momentum of this toss had been greater, the Earth's orbit would have been more highly elliptical, or it might have been tossed completely out of the solar system forever. If it had been a slightly less violent toss, Earth's orbit might have been perfectly circular (and it really is very close to being circular) or if it had been even less violent, it might have spiraled right back into the disc and never become a planet at all.