Why do planets that orbit the Sun have nearly circular orbit?

In school, we were taught that the orbits of planets were elliptical. However, the orbits appear to be circular. Why is this so? If, in fact, the orbits really are elliptical, how did we learn about them, and are there any laws that govern them?

First, let’s talk about the most basic facet of the solar system. There is the Sun at the center and the planets orbit the Sun. There are eight planets in our solar system, well nine if you are, like me, of a certain age. No, no, really, it’s just eight. There were real reasons to demote Pluto from planet to dwarf planet and the decision was perfectly sensible.

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Shape of Pluto’s Orbit

When Pluto was discovered in 1930, there was no accepted definition of the term planet. It was only in 2006 that a formal demarcation was offered. A planet has to: a) orbit the Sun; b) be big enough that gravity overcomes the strength of the material making it up, causing the planet to collapse more or less into the shape of a sphere, and; c) it has to clear its path of all other debris.

Pluto satisfies categories a and b, but not c. That’s because Pluto has an odd orbit compared to the other planets. While the orbit of the others is more or less circular, Pluto’s orbit crosses the orbit of the eighth planet and it dives off into a cloud of small objects, which means its path is not cleared. So, Pluto fails the planet test and we move on.

But the case of Pluto does bring up an important point and that is the shape of a planet’s orbit. The orbits of the planets look spectacularly circular, and they are, more or less. But they’re not. So, this brings us to the point where we re-examine some things that we once learned. The orbits of planets are, strictly speaking, ellipses.

This is a transcript from the video series Understanding the Misconceptions of Science. Watch it now, Wondrium.

You probably remember what an ellipse is. Basically, it’s a squashed circle, with one side longer than the other. A circle has a center and if you tie a string to the center and to a pencil, you can draw a circle. In contrast, an ellipse has 2 foci, which are 2 spots separated slightly from one another. If you take a string and tie it to both of the foci, you can draw the ellipse by kind of doing the same thing you did with the circle, and get a squashed circle.

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The Three Laws of Kepler

Now, it turns out that the orbits of the planets are pretty circular. It’s hard to see the difference with your eye. But they are actually ellipses, and this was first worked out in the early 1600s by Johannes Kepler. However, Kepler didn’t come up with the idea of the Earth going around the Sun. That honor is held by Aristarchus of Samos, a Greek philosopher who lived in the second century B.C.

Given the lack of proper instrumentation, the debate over whether the Earth or Sun was the center of the universe continued over many centuries. In 1543, Polish astronomer Nicolaus Copernicus published a mathematical treatise that promoted the idea of the Sun being the center of the solar system. But his treatment was complicated, and it was Kepler who used data to come up with the realization that the orbit of planets were ellipses.

In fact, Kepler came up with three laws. They are: 1) the orbit of a planet is an ellipse, with the Sun at one of the two foci; 2) the line connecting the planet and Sun sweeps out equal areas during equal intervals of time and; 3) the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. The semi-major axis is the distance from the center of the ellipse to the edge along the longest distance.

In a mathematical sense, the third law is the most interesting, as it allows astronomers to relate how long it takes for a planet to go once around the Sun to its distance from the Sun. Since this is a general astronomy discussion, let’s focus just on the first two laws.

Kepler’s first law means that the orbit of a planet isn’t always the same distance from the Sun. For instance, the closest the Earth gets to the Sun is 91 million miles or about 147 million kilometers. The term for the closest approach is called perihelion, which comes from the Greek term peri which means ‘near’ and the Greek word helios which means ‘Sun’. The term for when a planet is furthest from the Sun is called aphelion, from the Greek term apo which means ‘away from’.

When the Earth is at aphelion, it is nearly 95 million miles or about 152 million kilometers from the Sun. With a nearest distance of 91 million miles and a furthest of 95 million, the difference is small, only 4%. It also means that the foci are actually not that far apart, only about 4 million miles. To give some perspective, the radius of the Sun is about 430,000 miles and the distance between the Sun and Mercury is 29 million miles perihelion. So, this all says that the Earth’s orbit is pretty round, but it’s still, strictly speaking, elliptical.

In order to illustrate Kepler’s second law, it’s helpful to draw it with a highly-exaggerated ellipse. Kepler’s second law says that a line drawn from the Sun to the planet sweeps out an equal area for equal time. Because the distance between the planet and Sun is smaller at perihelion than at aphelion, it must mean that the planet moves faster at perihelion. For the Earth, the difference is 30 kilometers per second at perihelion and 29 kilometers per second at aphelion, or a little over half a mile per second difference.

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Newton’s Universal Law of Gravity

Kepler didn’t know why things were the way they were. He just used some precise observations and figured out what happened. The explanation for what Kepler hypothesized occurred in 1686, when British physicist Sir Isaac Newton presented to the Royal Society ideas that could explain the elliptical behavior by treating the Sun and planets as point-like masses, which means that the size and shapes of the Sun and planets didn’t matter, and by postulating that the force of gravity weakens as the square of the distance between the two objects.

The equation that embodies these ideas is called Newton’s universal law of gravity and it can be written as the force due to gravity equals G, which is just a constant, times the mass of the planet times the mass of the Sun, divided by the distance between them squared.

Taking this equation and others he had derived, Newton could calculate that the orbit of planets should be elliptical. It truly was a triumph of physics and astronomy.

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