Historical Development of Planetary Motion Theories

Posted on Oct 29, 2025 in Physics

1. Ptolemy’s Geocentric Model (2nd Century)

• Model geocentric: the Earth is at the center of the universe.
• All the planets and fixed stars move in circular orbits around the Earth.
• To explain the motion of the planets against the background of fixed stars (retrograde motion), it was necessary to introduce epicycles and deferents.
• Although mathematically complicated, the model fit well with observations and could be applied practically (navigation, predicting eclipses, etc.).

2. Copernicus and the Heliocentric Shift (16th Century)

• Heliocentric model: the Sun is at the center of the universe.
• All the planets orbit the Sun, except the Moon, which revolves around the Earth.
• The orbits of the planets were assumed to be circular, which required the maintenance of epicycles and deferents to adjust the model to observations.
• The model was much simpler than Ptolemy’s, but it conflicted with the dominant thought at the time and was rejected by the Church.

3. Galileo’s Telescopic Discoveries (17th Century)

• Used a telescope for the first time to observe the stars.
• Made findings that supported the heliocentric theory and contradicted the model of the universe that had been in force throughout the Middle Ages.
• Discovered spots on the Sun and mountains on the Moon (suggesting celestial bodies are imperfect, like Earth).
• Noted four satellites orbiting Jupiter (proving not all celestial bodies orbit the Earth).

4. Kepler’s Laws of Planetary Motion (17th Century)

After analyzing the experimental data collected by Tycho Brahe, Kepler proposed a planetary model based on three fundamental laws:

Kepler’s Three Laws

1. First Law (Law of Ellipses)

   The planets orbit the Sun describing elliptical orbits with the Sun located at one focus.

2. Second Law (Law of Equal Areas)

   The radius vector sweeps out equal areas in equal times. This implies that the speed of the planet increases as it approaches the Sun and decreases as it moves away from it.

   The maximum speed is reached at perihelion and the minimum speed is reached at aphelion.

3. Third Law (Law of Harmonies)

   Between the period (T) of the planet and its average distance (R) from the Sun, there is the following relationship:

   T² = k R³

   Where k is a constant that has the same value for all planets in the Solar System.

Kepler’s model describes the motion of the planets very precisely, but it did not indicate the underlying cause of this movement.

5. Newton’s Law of Universal Gravitation (17th Century)

Isaac Newton explained why the planets move in obedience to Kepler’s three Laws. The cause is the gravitational interaction between the Sun and the planets.

Newton went beyond planetary motion, stating that the same force that makes the planets move around the Sun is responsible for bodies falling on the surface of the Earth.

The Law of Gravitation

• Any two bodies in the universe attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
• The mathematical expression of the Law of Universal Gravitation is:

  F = G (M m / r²)

• Where G is the universal gravitational constant, which has the following value:

  G = 6.67 × 10^-11 N m² kg^-2

Relationship Between Weight and Gravity

• The force we commonly call weight is simply the force of gravity with which the Earth attracts us.
• If a body of mass m is on the surface of the Earth, the gravitational force (F_g) that Earth exerts on it, according to the Law of Universal Gravitation, is:

  F_g = G (M_T m / r_T²)

  Where: Earth’s mass: M_T ≈ 6 × 10²⁴ kg; Earth radius: r_T ≈ 6.4 × 10⁶ m.

• If we compare this expression with the routine formula for weight:

  W = m g

• We derive the value of gravity at the Earth’s surface (g):

  g = G M_T / r_T²

• If we are instead on planet P, the gravity at its surface (g_P) will be:

  g_P = G M_P / r_P²

  Where: M_P = mass of the planet; r_P = radius of the planet.