Although the motion of planets was discussed by the ancient Greeks, their belief in a geocentric model of the universe significantly limited scientific progress in this field. In Greek astronomy, the epicycle method was employed to explain the complex motions of planets; from a mathematical perspective, this method can be regarded as an early form of Fourier series. However, this approach served only to describe observed motions rather than to explain their physical causes.
A fundamental turning point in the understanding of planetary motion occurred in the sixteenth century. In 1543, Nicolaus Copernicus proposed in his work De Revolutionibus Orbium Coelestium that the planets, including the Earth, move around the Sun. Although this heliocentric model was revolutionary from a scientific standpoint, Copernicus still assumed that planetary orbits were perfect circles. Over time, increasingly precise astronomical observations revealed that this assumption was insufficient.
In 1600, Johannes Kepler became the assistant of Tycho Brahe, the most accurate observational astronomer of his era. After Brahe’s death in 1601, Kepler began analyzing the exceptionally precise observational data he had collected and started formulating the laws governing planetary motion.
Kepler demonstrated that planets move around the Sun not in circular paths but in elliptical orbits, with the Sun located at one of the focal points of the ellipse. Furthermore, he proved that the line connecting a planet to the Sun sweeps out equal areas in equal intervals of time. These two fundamental laws were first derived from observations of Mars and were published in 1609 in Astronomia Nova.
However, Kepler’s laws were not immediately accepted. The first law was met with caution, while the second law remained under serious scrutiny by the scientific community for nearly eighty years.
Kepler’s third law was presented in 1619 in Harmonices Mundi. According to this law, the squares of the orbital periods of planets are proportional to the cubes of the mean radii of their orbits. Surprisingly, this law was accepted more rapidly than the first two.
In 1679, Robert Hooke wrote a letter to Isaac Newton, explaining planetary motion as the result of a force directed toward a central point. Although Newton did not respond directly to this letter, he began developing his own ideas based on mechanical phenomena observed on Earth. He noted that because the Earth rotates, an object dropped from the top of a tower should fall slightly away from the base rather than directly beneath it.
Newton initially described the object’s trajectory as a spiral moving toward the center of the Earth. Hooke, however, argued that under the influence of a central gravitational force, the trajectory should take the form of an ellipse and that the motion would be periodic. Newton acknowledged that his original sketch was incorrect, but he modified Hooke’s model under the assumption that gravitational force was constant.
Hooke later proposed that this gravitational force is inversely proportional to the square of the distance. Years afterward, he claimed priority for this idea and presented the letter he had sent to Newton as evidence.
The crucial historical insight was the realization that the motion of the Moon around the Earth and the motion of the planets around the Sun could be explained by the same universal law. For its time, this idea was profoundly revolutionary and formed the foundation of the law of universal gravitation.
Approximately fifty years later, Newton recalled these events and wrote (with his characteristic style of early modern English preserved):
“In the same year, I began to consider the application of Kepler’s laws to the orbit of the Moon and realized that it was possible to calculate the effect of a central force acting on spherical bodies. By establishing the relationship between the distances of planetary orbits from the center and the forces involved, I understood that their motion could be explained by this law.”
These reflections ultimately led to the formulation of the Law of Universal Gravitation, which laid the foundations of classical mechanics and modern cosmology.