Mechanics

Kepler’s third law

Kepler’s third law shows the directly proportional relationship between the periods of revolution of the planets and the average radii of their orbits around the Sun.

Kepler enunciated three laws that determined the motion of the planets around the Sun.
Kepler ‘s third law is known as the law of periods and was formulated ten years after the law of areas ( Kepler’s 2nd law ). This law shows the directly proportional relationship between the period of revolution of a planet around the Sun and the mean radius of the planet’s orbit. It can be stated as follows:

The squares of the periods of revolution of the planets around the Sun are directly proportional to the cubes of the average radii of their orbits.

Therefore, calling T the period of revolution and R the mean radius of the orbit, we have:

2 = Constant
3         
  

This relationship shows that the farther a planet is from the Sun , the longer its time of revolution around the star. For all the planets in our Solar System, the above relationship has practically the same value. Note in the table below that when applying Kepler’s third law to planets, the values ​​will converge to 1.

* AU = Astronomical unit . Equivalent to the distance from the Earth to the Sun (1.48 x 10 8 km)

The value of the constant depends on the mass of the orbit’s central body, so for planets around the Sun the values ​​tend to 1, but for satellites around the Earth, for example, this relationship will be different from 1, since the mass of the Earth is infinitely less than the mass of the Sun.

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