# Eccentricity & Orbits of Planets

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• 0:02 What is Eccentricity?
• 0:58 Eccentricity of the Planets
• 2:20 Example Calculation
• 4:03 Lesson Summary

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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this lesson, you should be able to explain what eccentricity is and calculate the eccentricity of an orbit given relevant distance measurements. A short quiz will follow.

## What Is Eccentricity?

When you think about eccentricity, perhaps you think of your crazy aunt who climbed on the roof during Thanksgiving waving a pair of pantyhose. But did you know that planets can be eccentric, too? In physics, eccentricity is a measure of how non-circular the orbit of a body is. A particularly eccentric orbit is one that isn't anything close to being circular.

An eccentricity of zero is the definition of a circular orbit. When the eccentricity increases above this, but hasn't reached a value of 1, the orbit is elliptical. At an eccentricity of exactly 1, the object is on a parabolic trajectory, and an eccentricity of greater than 1 makes it a hyperbolic trajectory. These names come from parameters of conic sections since every orbit is one type of conic section or another.

But are eccentric orbits common in the universe? What about in our solar system?

## Eccentricity of the Planets

The planets are generally not especially eccentric. The Earth has one of the least eccentric orbits, at 0.017, though Venus and Neptune are even more circular. In fact, almost all the planets are below 0.1 eccentricity. Only one planet in our solar system is particularly eccentric: Mercury with an eccentricity of 0.21. The dwarf planet Pluto also has an eccentricity of 0.25. Pluto's orbit is especially wild because it's also at an angle compared to the plane the other planets orbit in.

But how do we determine these numbers? How are they calculated?

A more specific definition of eccentricity says that eccentricity is half the distance between the foci, divided by half the length of the major axis. The major axis is shown on this diagram and these are the two foci. The eccentricity of this orbit is wildly exaggerated so the two foci are nicely far apart. In a circular orbit, the two foci are both at the same point, right in the middle of the circle.

Here is the definition of eccentricity in equation form: e = c / a. So all you have to do is plug the numbers into the equation and solve. Since this is a ratio, you can use whatever unit you wish for distance, the standard SI unit of meters, or non-scientific units like miles, or astronomical distance measurements like astronomical units. Whatever you happen to have on hand.

## Example Calculation

Okay, let's go through an example. Let's say you have a planet which we'll call Planet X, and that planet is orbiting its star in an eccentric orbit. At its closest approach it is 2 astronomical units away from the star and at its furthest approach, its 3.2 astronomical units away from the star. What is the eccentricity of the orbit?

The issue with this question is that you're not given numbers to plug into the equation directly. You really have to draw a diagram to figure out what to plug in. Here is a diagram of an orbit and here are the distances we're given: 2 AU on closest approach and 3.2 AU on furthest. We need to figure out half the distance between the foci, marked here, and half the length of the major axis, marked here.

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