Planetary motion. Geocentric theory, Copernican theory and Kepler’s laws

15/04/2026

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

This Thematic Unit is part of our Earth Sciences collection

Epicycle

Imaginary circle used in the geocentric model to explain the apparent motion of the planets.

Focus

One of the two interior fixed points that define the shape of an orbital ellipse.

Geocentric Model

Ancient theory that placed the Earth at the center of the universe with celestial bodies revolving around it.

Heliocentric Model

Astronomical theory that places the Sun at the center of the system and the planets revolving around it.

Kepler’s First Law

Law of ellipses: planets describe elliptical orbits with the Sun at one of their foci.

Kepler’s Second Law

Law of areas: the radius vector joining the Sun and a planet sweeps out equal areas in equal times.

Kepler’s Third Law

Harmonic law: the square of the orbital period is proportional to the cube of the average distance to the Sun.

Retrograde Motion

Apparent change in a planet’s movement where it seems to move backward in its orbit from Earth.

Semi-major Axis

Half of the longest diameter of an ellipse, used to define the size of an orbit.

Planetary motion

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 is a more detailed development of the heliocentric model. It 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 three laws of planetary motion

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.

Epicycle

Imaginary circle used in the geocentric model to explain the apparent motion of the planets.

Focus

One of the two interior fixed points that define the shape of an orbital ellipse.

Geocentric Model

Ancient theory that placed the Earth at the center of the universe with celestial bodies revolving around it.

Heliocentric Model

Astronomical theory that places the Sun at the center of the system and the planets revolving around it.

Kepler’s First Law

Law of ellipses: planets describe elliptical orbits with the Sun at one of their foci.

Kepler’s Second Law

Law of areas: the radius vector joining the Sun and a planet sweeps out equal areas in equal times.

Kepler’s Third Law

Harmonic law: the square of the orbital period is proportional to the cube of the average distance to the Sun.

Retrograde Motion

Apparent change in a planet’s movement where it seems to move backward in its orbit from Earth.

Semi-major Axis

Half of the longest diameter of an ellipse, used to define the size of an orbit.

Explore the exciting STEM world with our free, online, simulations and accompanying companion courses! With them you’ll be able to experience and learn hands-on. Take this opportunity to immerse yourself in virtual experiences while advancing your education – awaken your scientific curiosity and discover all that the STEM world has to offer!

Planetary motion simulations

Copernicus
Kepler I
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 three laws I

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 three 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.

Giants of science

“If I have seen further, it is by standing on the shoulders of giants”

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Galileo Galilei

1564

–

1642

Galileo Galilei revolutionized astronomy by observing planets, Jupiter’s moons, and advocating heliocentrism.

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Isaac Newton

1643

–

1727

Isaac Newton formulated the law of universal gravitation and the three laws of motion, founding classical mechanics.

“If I have seen further, it is by standing on the shoulders of giants”

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“Equipped with his five senses, man explores the universe”

Galileo Galilei

1564

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Galileo Galilei revolutionized astronomy by observing planets, Jupiter’s moons, and advocating heliocentrism.

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Test your knowledge

How did the understanding of planetary motion evolve from the geocentric model to the Copernican model?

For many centuries, planetary motion was explained through the geocentric model, which placed Earth at the center of the universe. This idea, developed by Claudius Ptolemy in the 2nd century, proposed that the Sun, Moon and planets moved around Earth in circular orbits. Although widely accepted, the model required increasingly complex adjustments to match observations. In the 16th century, Nicolaus Copernicus introduced a major shift: he placed the Sun at the center of the system and stated that Earth was just another planet orbiting it. This heliocentric model offered a simpler and more coherent explanation of planetary movements. The transition from geocentrism to heliocentrism marked a fundamental change in astronomy, opening the way for more accurate descriptions of celestial motion and preparing the ground for Kepler’s later mathematical laws.

Why were Kepler’s three laws a decisive breakthrough in the study of planetary motion?

Johannes Kepler formulated three empirical laws that provided a precise mathematical description of planetary motion. His first law established that planets move in elliptical orbits with the Sun at one focus, replacing the long‑held belief in perfect circular paths. The second law stated that the line connecting a planet to the Sun sweeps out equal areas in equal times, meaning planets move faster when closer to the Sun (perihelion) and slower when farther away (aphelion). The third law showed a proportional relationship between a planet’s orbital period and its average distance from the Sun: the square of the period is proportional to the cube of the distance. These laws allowed astronomers to predict planetary positions with great accuracy and represented a major step forward in understanding the mechanics of the solar system.

Why did people believe for so long that Earth was at the center of the universe?

Because from the ground it looks like everything moves around us: the Sun rises and sets, the Moon crosses the sky and the planets change position. Without telescopes or advanced knowledge, it seemed natural to think Earth was still and everything else moved around it. That’s why the geocentric model lasted for centuries.

What did Copernicus change about how we understand the solar system?

Copernicus proposed that the Sun, not Earth, was at the center of the system. He explained that Earth is a planet that orbits the Sun just like the others. This idea made the motions of the planets easier to understand and avoided the complicated corrections needed in the geocentric model.

What are Kepler’s laws used for?

They are used to describe exactly how planets move around the Sun. The laws explain that orbits are elliptical, that planets change speed depending on how close they are to the Sun and that there is a mathematical relationship between how long a planet takes to orbit and how far it is from the Sun. Thanks to these laws, astronomers can predict planetary motion with great accuracy.