Evolution of Planetary Models: From Ptolemy to Newton
Evolution of Planetary Models
Models Planted.
1. Ptolemy (2nd Century)
- Geocentric Model: The Earth is at the center of the universe.
- All stars and planets revolve around the Earth in circular orbits.
- To explain the movement of planets against the background of fixed stars (retrograde motion), Ptolemy introduced epicycles and deferents.
- The model is mathematically complex but fits observations well and can be applied in practice (navigation, eclipse prediction, etc.).
2. Copernicus (16th Century)
- Heliocentric Model: The Sun is at the center of the universe.
- All stars and planets revolve around the Sun, except for the Moon, which revolves around the Earth.
- The stars’ orbits are circular, requiring epicycles and deferents to adjust the model to observations.
- The model is much simpler than Ptolemy’s but clashes with the dominant thinking of the era and is rejected by the Church.
3. Galileo (17th Century)
- Uses a telescope for the first time to observe stars.
- His discoveries support the heliocentric model and contradict the prevailing view of the universe throughout the Middle Ages.
- He discovers sunspots and mountains on the Moon (imperfect celestial bodies similar to the Earth), and observes 4 satellites revolving around Jupiter (celestial bodies that do not revolve around the Earth).
4. Kepler (17th Century)
- After analyzing Tycho Brahe’s experimental data, Kepler proposes a planetary model based on 3 fundamental laws.
- 1st Law: Planets revolve around the Sun in elliptical orbits, with the Sun at one of the foci.
- 2nd Law: The radius vector sweeps out equal areas in equal times. This implies that a planet’s velocity increases as it approaches the Sun and decreases as it moves away.
- The maximum velocity is reached at the perihelion and the minimum at the aphelion.
- 3rd Law: There is a relationship between a planet’s orbital period and its average distance to the Sun:
where k is a constant that has the same value for all planets in the solar system. Kepler’s model describes the movement of planets with great precision but does not explain why the planets move in this way.
Newton’s Law of Universal Gravitation
Newton (17th Century) explains why planets move according to Kepler’s 3 laws. It is caused by the gravitational interaction between the planets and the Sun.
Newton’s law explains planetary movement and states that the same force that makes planets move around the Sun is responsible for bodies falling on the Earth’s surface.
- Law of Universal 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:
where G is the universal constant with the value:
G = 6.67 · 10-11 N m2 kg-2
Relationship between Gravitational Force and Weight
- The force we usually call weight is the gravitational force with which the Earth attracts us.
- If a body of mass m is on the Earth’s surface, the gravitational force exerted by the Earth on it, according to the law of universal gravitation, is:
Where:
- Earth’s mass: Mt = 6.1024 kg
- Earth’s radius: Rt = 6.4 × 106 m
If we compare this expression with the one usually used for weight:
We obtain the value of gravitational acceleration on the Earth’s surface.
If instead of the Earth, we are on another planet P, the gravitational acceleration on the surface would be:
where Mp = mass of the planet
Rp = radius of the planet