Astronomy

Sir Isaac Newton verified and explained Kepler’s elliptical planetary orbits by the development of his law of universal gravitation.

Elliptical orbits are the most common orbits in the universe. They’re characterized by bodies which move faster when closer to what they’re orbiting, and slower when further away, with the orbited body at one of the two foci of the ellipse.

The difference in speeds is because the force of gravity is stronger when nearer the orbited mass, which we’ll call stars from here on out. The law of universal gravity says that so if the distance is smaller, the force is larger. Planets with elliptical orbits (a.k.a. all of them) have smaller gravitational forces when they’re furthest from their star, so they travel faster when they’re nearest the star.

The same effect is visible between orbits of different planets: Mercury is the fastest planet solely because being so close to the sun, it experiences the largest force of gravity. The slow planets are on the fringes of the solar system, where the force of gravity is small.

The orbits in our own solar system are nearly circular, such that Isaac Newton treated the placement of the Sun at the center of a circular orbit and found enough agreement to produce the law of universal gravitation .

Where do elliptical orbits come from? First, let’s investigate where circular orbits come from, which is when . This simplifies to . In other words, the radius and velocity have to be just right to be a circular orbit. If a body travels too fast or slow for the distance it is from the sun or star (or planet, in the case of a moon), then the orbit becomes elliptical.

That, in a nutshell, is why elliptical orbits are the most common kind in our universe. It’s impossible for us to speed up or slow down a planet to force it into a circular orbit.

Elliptical and circular orbits aren’t the only kind out there, though we grant that parabolic and hyperbolic paths can’t be termed orbits: they’re the paths a celestial body takes when passing through a gravitational field without being orbital material: they escape. Check out the relationships between the paths and velocities in the diagram below.

“C” is for circle, not cookie. “E” is for ellipse, in the sense of the longest elliptical orbit possible before the orbit changes to a parabolic path.