Kepler's Laws, Ellipses, and Eccentricity

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  • 0:01 The True Shape of…
  • 0:30 Ellipses and Foci
  • 1:35 (Semi) Major Axis and…
  • 3:25 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov

Artem has a doctor of veterinary medicine degree.

This lesson will discuss Kepler's First Law of Planetary Motion; define an ellipse, focus, major axis, semimajor axis, and eccentricity; and explain what they have to do with astronomy.

The True Shape of Planetary Orbits

If you ever hear someone say that Earth moves around the sun in a circle, you can bet them a good chunk of change that this isn't true. Thanks to the brilliant mathematician Johannes Kepler, we know that Earth and the other planets in our solar system do not move around the sun in a circle. You'll find out what shape they actually take as we take a look at Kepler's First Law of Planetary Motion and its key components.

Ellipses and Foci

Kepler's First Law of Planetary Motion says that the orbit of a planet around the sun is an ellipse, with the sun at one focus. An ellipse is a curve surrounding two points called foci, so that the total distance from one focus to a point on the ellipse and back to the other focus is constant for every point on the curve. A focus, singular for foci, is simply one of two fixed points from which an ellipse can be generated.

Let's focus on the screen to see how it's done (please see the video beginning at 01:07 to see this demonstration).

Take two thumbtacks, a corkboard, and a loop of string. The thumbtacks stuck in the board represent our foci. Tie the string around the thumbtacks in a loop. Then, take a pencil and push it tight against the string as you move the pencil around. If you keep the string tight as you move the pencil, you'll trace out an ellipse. You can change the shape of the ellipse by changing the length of the string or by changing the distances between the foci.

(Semi) Major Axis & Eccentricity

The maximal diameter of an ellipse is the line that passes through the two foci, and it's called the major axis. Half of the major axis is the semimajor axis. Considering planets move around the sun in an ellipse, the semimajor axis is equal to a planet's average distance from the sun, with the sun located at one focus of the ellipse and nothing located at the other focus.

An ellipse has a critical component called eccentricity (or little e), the extent to which an orbit deviates from a circle. Eccentricity is equal to the distance between the two foci of an ellipse divided by the major axis.

Eccentricity
image showing different eccentricities

Eccentricity tells us the shape of the ellipse and its value ranges from 0 to 1. As the images on the screen show you, an ellipse with 0 eccentricity is a circle and as the eccentricity nears 1, the shape of the ellipse becomes almost a straight line. Basically, the greater the eccentricity, the more elongated the ellipse.

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