::Interactive Astronomy::

Kepler's Laws of Planetary Motion

These laws governing planetary motion were discovered by Kepler (1571 A.D. to 1630 A.D.) after his studies of his mentor's ( the Danish astronomer Tycho Brahe) meticulous data acquired through observing planetary movement. These laws are one of the fundamental laws governing planetary motion.

Kepler’s three Laws of Planetary Motion

Kepler's First Law: The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.

The planet follows the ellipse in its orbit. This also means that the planet to Sun distance is constantly changing during the planet’s orbit.

Why are the orbits elliptical and not circular? More about elliptical orbits

Kepler's Second Law: The area between the planet and the Sun (in blue) consists of equal areas of the ellipse and the planet travel these areas in a constant and equal time throughout, around the ellipse.

This means that a planet carries out its elliptical orbit with varying angular speeds. The point where the planet is nearest to the Sun is named as the perihelion period while that of greatest separation is named as the aphelion period. Thus, abiding Kepler's second law, the planet moves fastest when it is in perihelion and slowest when it is in aphelion.

Kepler's Third Law: The squares of the periods of revolution of the planets are proportional to the cubes of their mean distances from the sun.

P=orbital period (same time units) R=semi-major axes (same distance units)

Kepler's Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit.

This explains the difference in orbital periods of different planets with different orbit radiuses. For e.g. Mercury = innermost planet = 88 days orbital period while Pluto = outermost planet = 248 years orbital period.

Planets have elliptical orbits because it is not possible to have a perfect circle. This is because there are other planets that would gravitationally affect the orbit and cause it to be immediately non-circular by constantly shifting the objects position. After a stable gravitational orbit type has been established, the orbit is usually in the form of an ellipse. Nevertheless, it is still inversely related to Kepler’s three laws and gravity.

When an astronomical object passes into our solar system, there would be four circumstances, based on Kepler’s three laws and the principles of gravity.

The four theoretical choices:

hyperbolic
elliptical
circular
spiral

A hyperbolic orbit happens is when an object comes in from space towards the Sun possessing so much energy that it rotates around the Sun, and flies back into space, changing its course, like a horseshoe. The object never flies back. If it does, then it is an object which has an elliptical orbit around the sun with an extremely high eccentricity, which is rather impossible as the far-out distance would be impossible for our sun to capture in the first place.

An elliptical orbit happens is when the object comes in but does not have enough energy to pull itself away from the Sun's gravity, thus being captured in an elliptical orbit. The eccentricity of the orbit depends on the object's initial energy.

A circular orbit happens when the object has the exact amount of energy to be captured in a perfectly circular orbit, which is rather rare.

A spiral collision happens when the object does not have enough energy to establish any form of orbit and would spiral towards the Sun and be disintegrated. Usually, most asteroids and comets have this end when their orbits become unstable due to several factors like internal collisions, or an extra body in the solar system causing orbital disruptions.