Why Are Orbits Of Planets Elliptical?

 

We know that the planets move in elliptical orbits around the sun. This was discovered by Johannes Kepler in the 17^th century. He laid out three laws which describe the motion of planets around the sun. But why elliptical orbits? Why not circular orbits? What is so special about ellipses?

Just like most of the scientific problems in the 17^th century, this was also answered by Sir Isaac Newton. He discovered the law of gravitation and through this law, he could explain why orbits are elliptical.

The gravitational force between two objects, in this case, the sun and the planets, depends inversely on the square of the distance between them. Newton figured out using calculus that under the influence of an inverse square force, a body will travel along a conic section and in case of planets, it is an ellipse.

What happens when the orbit of a body follows different conic sections? For that, we need to know what are conic sections. Depending on how you cut a cone, you get different 2D shapes. These are called conic sections. Different conic sections are shown in the figure.

Conic sections are characterized by their eccentricities. Eccentricity of a conic section, in the simplest language, is a non negative real number which describes the shape of the section. A circle has eccentricity 0, ellipse between 0 and 1, parabola 1 and hyperbola greater than 1.

From the figure, we can clearly see why some of the orbits cannot describe the orbit of a planet. If any planet or object had parabolic or hyperbolic orbits, they would be long gone from our solar system. In other words, they are ejected out of the solar system.

Circles are just a special case of ellipse. But the eccentricity of 0 is extremely hard to attain and maintain in nature and hence we do not get circular orbits.

Let us come back to ellipses now. On earth, when you throw a ball horizontally, the ball follows a parabolic path as the velocity of the ball carries it horizontally and gravitational force pulls it downwards (the mass of the ball is very low as compared to earth).

If you throw the ball with a greater force, it will travel more distance while still following a parabolic path to the ground. Now consider you throw a ball with so much force that it does not land but curve around the curvature of the earth. This is because the gravitational force of the earth will pull it downwards while its velocity will make it move forward. This results in an orbit. The ball will come back to the place where it started and will continue to move in the same path unless a force is applied to in opposite direction. The ball is said to be in orbit around the earth.

The ball that is orbiting around the planet will follow an elliptical path as it is the most stable orbit possible. What is meant by a stable orbit? The orbit that requires the least energy to go around the earth is said to be stable. Circular orbits, as stated above, are hard to attain and maintain.

Consider another similar example. This time, instead of throwing the ball, you are dropping it from a considerable height. Drop the ball such that it does not drop on to the earth but moves very close to it (We are ignoring air resistances in all of our examples). The ball will fall in such a way that it will be trapped around an orbit around the earth. The orbit, as you can guess it, is elliptical because it is stable.

Inertia (in this case, the tendency to keep moving in the direction of its velocity) and the gravitational force must combine effectively in order for orbits to occur.

In case of planets and the sun, the planets are the ball and the sun is the earth. The planets move with tremendous speeds. Due to the gravitational influence of the sun which is significantly more massive than the planets, they get trapped in an orbit around the sun. This orbit will more or less be an ellipse.

It must be noted that the orbits are not perfect ellipses. Due to the gravitational influences of other planets, the orbits are disturbed and hence we do not get perfect ellipses. Due to many different factors which can affect the velocity and gravitational forces, circular orbits are not seen in nature. The same reason applies to not seeing perfect elliptical orbits of planets.

The orbit of earth has an eccentricity less than 0.02 and that is as close to a circular orbit as we will ever get. All the calculations that I did in 11^th and 12^th grades, considering the earth’s orbit to be circular, were, therefore, very close to being correct.

CONCLUSION

Newton’s law of gravitation allows the orbits of planets to follow a path described by conic sections. Parabolic and hyperbolic orbits would mean solar system could not exist as things would escape the system very easily. Circles are not possible because they are very difficult to attain and maintain. This is mainly due to various factors like gravitational forces of different bodies affecting the velocity of the body. Ellipse is the most stable of all orbits as it needs least energy to maintain it. However, perfect ellipses are not possible due to the same reasons why circular orbits are not found.