Kepler’s Three Laws
Johannes Kepler, a brilliant astronomer is the person who enformulated and wrote the laws that govern orbital physics. He wrote these in three elegant laws, known as Kepler’s Laws. These were derived from the observations of Tycho Brahe. They are as follows:
The Law of Ellipses : Kepler states that the orbit of a satellite around a star or host object is said to follow an orbital trajectory that is elliptic in nature. In this ellipse, we are said to have a the star or the host object at one of the foci.
The Law of Equal Areas: Kepler says that an object in orbit around a star sweeps out equal areas over equal periods. For example, let’s say we were to mark the planet on its orbit in the month of June (P1) and September (P2), a period of 4 months. Let’s also mark the points of the planet‘s position in its orbit at the months of January (P3) and April (P4), a period of 4 months. According to the second law, the triangle formed by the union of the points P1 and P2 and position of the sun is equal in area to the triangle formed by the union of the points P3 and P4 and the position of the sun. They are of equal areas.
The Relation between an object’s orbital period and orbital radii: According to Kepler, the orbital period (P) of a planet is related to its average or oral radii (r). The relation states that the square of the orbital period is directly proportional to the cube of the average orbital radii (P^2 ∝ a^3). He further states that this proportion depends on the mass of the object. Another variation of the relation, in the case of a planetary system where we take two planets, is
T1 r1
( — ) ^2 = ( — ) ^3
T2 r2
Where: T1 = Planet 1 Orbital Period
T2 = Planet 2 Orbital Period
r1 = Planet 1 Orbital Radius
r2 = Planet 2 Orbital Radius
