Kepler’s Laws

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 second law says that the line connecting the center of the Sun to the center of the planets “sweeps” equal areas in equal time intervals , so we can understand that the rate of change of area as a function of time is constant for all planets. This can only be possible if the translational speeds of the planets are variable, and should be higher in the perihelion region and lower in the aphelion region.

• 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