The online planetary motion simulations will show us the differences between the different ways of interpreting the motion of the planets throughout history. We will see the geocentric theory, the Copernican theory and Kepler’s laws.

Planetary motion has been the subject of study and understanding since ancient times. Two of the most influential theories in this field were the geocentric theory, which was predominant in antiquity and the Middle Ages, and the Copernican theory, proposed by Nicolaus Copernicus in the 16th century. Subsequently, Kepler’s laws provided an accurate mathematical description of planetary motion.

**Geocentric theory and Copernican theory.**

**Geocentric theory**. The geocentric theory, also known as the Ptolemaic model, was based on the ideas of Claudius Ptolemy, a Greek astronomer and mathematician who lived in the 2nd century. According to this theory, the Earth was at the center of the universe and all other celestial objects, including the Sun, Moon and planets, revolved around it in circular orbits.

**Copernican theory**. The Copernican theory, also known as the heliocentric model, was proposed by Nicolaus Copernicus in the 16th century. According to this theory, the Sun was at the center of the solar system and the planets, including the Earth, revolved around it.

Although the geocentric theory was widely accepted for centuries, the Copernican theory provided a simpler and more elegant explanation of planetary motions.

**Kepler’s Laws**

Subsequently, Johannes Kepler, a 17th-century German astronomer and mathematician, developed three empirical laws that describe planetary motion precisely:

**Kepler’s first law (law of orbits)**. The planets describe elliptical orbits around the Sun, where the Sun occupies one of the foci of the ellipse.

**Kepler’s second law (law of areas)**. The radius joining the planet to the Sun sweeps equal areas in equal times. This implies that the planets move faster when they are closer to the Sun (at their perihelion) and slower when they are farther away (at their aphelion).

**Kepler’s third law (law of periods)**. The square of the orbital period of a planet is proportional to the cube of its mean distance from the Sun. This law establishes a mathematical relationship between the period of revolution of a planet around the Sun and its mean distance from the Sun.

These laws allowed Kepler to accurately describe and predict the motions of the planets, laying the foundation for future developments in the field of astronomy.

In summary, the online planetary motion simulations on this page help us to understand the motion of the planets and teach us which have been the different theories that have explained it throughout history.

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- Copernicus
- Kepler
- Kepler II

## The Copernican theory versus the geocentric theory

The Copernican theory states that, in the solar system, the Sun is at the center and the planets move around it. This theory replaced the existing one, which believed that the Earth was at the center and that the other planets and the Sun moved around it..

## Kepler’s Laws

Kepler’s first law says that the orbit of the planets of the solar system is an ellipse with the Sun at one of its foci. Kepler’s second law says that a line joining the sun with any one of the planets sweeps an equal area per unit time. Kepler’s third law says that the square of the orbital period of any planet is proportional to the cube of the semi-major axis of its orbit.

## Kepler’s Laws II

This simulation of Kepler’s Laws allows you to discover the principles of Kepler’s Laws in detail. You can explore how the velocity and position of a planet affect its motion and orbit and discover how Kepler’s Laws apply to different bodies in the solar system. What is meant by the “swept area of a planet’s orbit”? You can find out this and much more with this simulation.