Mechanics

# Laws of Planetary Motion

The laws of planetary motion convinced the scientific community about the reality of the heliocentric model, which claimed that the Earth revolved around the Sun.

Johannes Kepler, a German physicist, disciple of the Danish astronomer Tycho Brahe, was responsible for developing the laws of planetary motion, laws that convinced the scientific community about the reality of Nicolaus Copernicus’ heliocentric model, which stated that the Earth revolved around the Sun.

The laws of planetary motion are known as Kepler’s Laws, and they have the following definitions:

Kepler’s 1st Law
Planets move in elliptical orbits and the Sun is located at one of the foci.

Kepler’s 2nd Law
The line segment drawn from the Sun to any planet describes equal areas in equal times.

This means that:

• The speed of the planets around the Sun varies;
• The speed of planets is greater when they are at perihelion (closer to the Sun) than when they are at aphelion (far from the Sun);
• The translational movement is varied, being able to be accelerated or delayed.

Kepler’s 3rd Law
The square of the period of revolution of each planet around the Sun is directly proportional to the cube of the average distance of that planet from the Sun.

Kepler’s third law can be mathematically described by the equation:

T² = k.r³

Where:
T = period of revolution
K = proportionality constant
R = distance from the Earth to the Sun (semi-axis)
• The longer the semi-axis, the longer the period, ie, the longer the year of the planet.

In addition to confirming Copernicus’ theories, Kepler’s Laws showed the accurate representation of the orbit of the planets, that is, almost circular ellipses.

They are also valid for any body that gravitates around another with a much greater mass, such as artificial satellites that move around the Earth.