Understanding the Elliptical Shape of Planetary Orbits

The orbits of the planets are described as ellipses. This term, derived from Kepler's First Law of Planetary Motion, states that planets move in elliptical orbits with the Sun at one of the two foci. An ellipse is a closed curve symmetric about two axes, and it can be thought of as a stretched circle.

The Elliptical Path of Planets

The paths of the planets are approximately elliptical in shape, with the Sun positioned at one of the two points called foci. Some orbits are more circular than others. For instance, Venus has a nearly circular orbit with an eccentricity of 0.007, which is very close to zero, making it the most circular orbit of the planets. On the other hand, Pluto has a much more elliptical orbit with an eccentricity of 0.268.
Haley's Comet, known for its long and relatively elliptical orbit, has an eccentricity of 0.967. An eccentricity of 1 represents a straight line rather than an ellipse.

The Definition of an Ellipse

Picture an ellipse as a flattened circle, but the Sun is not at the center but rather at one of the two points, each called a focus and collectively referred to as foci. The mathematical definition of an ellipse is the locus of all points that bear the following relationship to two separate points called the foci: the sum of the distances from any point on the ellipse to the two foci is a constant.

For the Earth's orbit around the Sun, we can identify two points: a point near the center of the Sun that we could call point A and another point outside the Sun called point B. No matter where the Earth is in its orbit, if you add the distance from the Earth to A to the distance from the Earth to B, the sum remains constant, making the Earth's orbit an ellipse.

The Reason for Elliptical Orbits

The reason planets travel in elliptical orbits is deeply rooted in the nature of gravity and the conservation of energy. The strength of gravity diminishes as the square of the distance between two bodies. If a planet were moved to a point that is twice as far from the Sun, the force of gravity on the planet would only be one-fourth as much.

If an object moves in a direction perpendicular to the central body, it either has the exact amount of energy to remain at that distance and continue its perpendicular motion, or it has too little or too much energy to remain at the same distance from the central body. If it has too little energy, it will begin to "fall" towards the central body. At some point, the potential energy has been converted to kinetic energy, and the object is in a downward path. It will continue to have its potential energy converted to kinetic energy as it "falls," and eventually, it will be moving in a direction perpendicular to the central body. However, at that point, it will have too much energy to travel in a circle and will start moving upward, with its kinetic energy being gradually converted back to potential energy as it moves further away from the central body. This continual exchange between kinetic and potential energy keeps the object moving in an elliptical path.

Other Shapes in the Solar System

Consider the path of a thrown ball. When you throw a ball, it travels along a path that approximates a parabola, but this is only an approximation. Two vertical lines are not actually parallel, and the end of a very long ellipse approximates a parabola. If you slice a cone with a plane parallel to its center line, you get a parabola. However, if you tilt that plane slightly, it will come out of the cone at some point and form an ellipse. If you slice it perpendicular to the axis, you get a circle. As you tilt a plane from horizontal to vertical, the slice will go from a circle to an ellipse and finally to a parabola.

In nature, no object ever travels in a perfect circle or in a perfect parabola, as it is impossible to achieve both the exact perpendicular direction and the exact velocity. Thus, the circle and the parabola are mathematical ideas that we use in physics, but they do not exist in nature. The paths of bodies moving under the force of gravity are always ellipses or hyperbolas, never perfect circles or parabolas.

Conclusion

The elliptical shape of planetary orbits is a fascinating aspect of our solar system, best explained through the laws of Kepler and the fundamental nature of gravity. Understanding these concepts deepens our appreciation for the intricacies of celestial mechanics and the beauty of the universe.