Mathematical Modelling of Copernicus and Kepler

Copernican Model

Copernicus was a Polish astronomer who proposed a heliocentric model of the universe.
His heliocentric model proposed that the Sun, not the Earth, was the centre of the universe.
In this model, the Earth and the other planets orbited around the Sun in circular orbits.
He suggested that the apparent daily rotation of the sky was due to the Earth’s rotation on its axis.
His model simplified the explanation for the apparent retrograde motion of planets.

Kepler was a German astronomer and mathematician who used the detailed observations made by Tycho Brahe to refine Copernicus’ model.
His laws of planetary motion supplemented Copernicus’s heliocentric model.
Kepler’s First Law states that planets move in elliptical orbits, with the Sun at one focus of the ellipse.
Kepler’s Second Law, often referred to as equal areas in equal times, implies that a planet’s speed varies during its orbit, moving fastest when it is closest to the Sun (perihelion) and slowest when it is furthest from the Sun (aphelion).
Kepler’s Third Law, the harmonic law, relates the planet’s distance from the Sun (semi-major axis of its orbit) and its orbital period stating that the square of the orbital period is proportional to the cube of the semi-major axis.

The mathematical models of Copernicus and Kepler revolutionised our understanding of the solar system.
They paved the way for a mechanistic understanding of the universe, which was later solidified by Newton’s laws of motion and law of universal gravitation.
The Copernican model, though not entirely correct, was significant as it challenged the geocentric model, prompting a paradigm shift in astronomy.
Kepler’s laws are still used today to study planetary motion and to calculate trajectories of spacecraft and satellites.

Copernicus reintroduced the concept of a heliocentric universe where the Earth and other planets move in circular orbits around the Sun.
Kepler refined this model and proposed three laws of planetary motion which provided an accurate description of the planets’ elliptical orbits.
The work of Copernicus and Kepler led to a complete reimagining of the universe and laid the groundwork for Newton’s laws of motion and universal gravitation.