Mechanics

# Kepler’s Laws

Kepler’s laws describe how planets move around the Sun and satellites around planets.

The German astronomer Johannes Kepler (1571-1630), after a lifetime of study, deduced three laws that explain planetary motion and make us understand how the universe is structured. Kepler ‘s laws can be used to study the movement of planets around the Sun and the movement of natural and artificial satellites around planets.

Kepler was able to deduce the three laws from numerous astronomical data collected by his predecessor, Prince Tycho Brahe, and through his own observations.

• Kepler’s 1st Law – Law of Orbits

The law of orbits says that the trajectory of planets around the Sun or the trajectory of satellites around planets has an elliptical (oval) shape and the body being orbited occupies one of the foci of the ellipse.

Kepler’s first law does not exclude the possibility of circular trajectories, since the circle is a special case of an ellipse .

In the case of the planets’ trajectory around the Sun , the point at which they are closest to the star is called perihelion , and the point at which they are farthest away is called aphelion .

See that the Earth’s translational motion around the Sun forms an ellipse, and the Sun is at one of the foci (edge) of the ellipse

• Kepler’s 2nd law – Law of areas
• Kepler’s 3rd Law – Law of Periods

In his third law, Kepler says that the square of the period of revolution (T) of the planets is directly proportional to the cube of the average radii (R) of their orbits. Therefore, we have:

The constant in question depends on the constant of universal gravitation (G = 6.7 x 10 – 11 Nm 2 /kg 2 ) and the mass of the body being orbited. In the case of the Solar System, using the period of revolution of the planets in Earth years and the average radius of the orbits in astronomical units , the value of the constant for all planets must be very close to 1. The table below shows the relationship of the third law of Kepler and the planets of the Solar System.

*AU = Astronomical Unit – corresponds to the average distance from the Earth to the Sun