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Major and Minor Axis
All elliptical orbits have a major and minor axis. The major axis is a line drawn across the longest part of the ellipse and a minor axis is a line drawn across the shortest part. In a circular orbit, the major and minor axis are the same value. Furthermore, the closer they are to being equal, the more circular the orbit is.
Eccentricity
The eccentricity is a measurement, always between 0 and 1, of how elongated or how circular an ellipse is. A perfectly circular orbit has an eccentricity of 0. As the eccentricity moves toward 1, it becomes flatter until it eventually becomes a parabola at 1 itself. The eccentricity can be found by dividing the distance between the foci by the major axis of the orbit.
Perihelion and Aphelion
When the planet is closest to the sun in its orbit it is said to be at "perihelion," and when it is farthest it is said to be at "aphelion." In a perfectly circular orbit, there is no specific aphelion and perihelion, since the planet is always be at an equal distance away from the sun no matter where it is in its orbit. To determine how close to being a circle an ellipse is, look for an aphelion and a perihelion that have similar values.
Kepler's First Law
Kepler's first law states that "orbits are ellipses with the sun at one focus," with the other focus being an empty placeholder. The empty focus is symmetrical to the sun, placed on the major axis at an equal distance away from the edge of the ellipse as the sun. To create a circular orbit, you would place the sun at the center and have only one focus. The closer the two foci are together on the major axis, the more circular the orbit would be.
Kepler's Second Law
Typically, on an elliptical orbit, as the planet moves closer to the sun it speeds up, and slows down again as it reaches aphelion. In a circular orbit the planet would go around the sun at the same speed throughout. The more similar the speed of the planet throughout its orbit, the more circular it will be.