1. Who Was Kepler?
Johannes Kepler was a German astronomer who studied the motion of planets using accurate observational data collected by Tycho Brahe. After years of analysis, he discovered three simple laws that beautifully describe how planets move around the Sun.
These laws apply not just to planets but to moons, satellites, and even artificial spacecraft.
1.1. Why Kepler’s Laws Matter
Before Kepler, people believed planets moved in perfect circles. Kepler’s work showed that their paths are slightly stretched and follow predictable mathematical patterns. His laws formed the foundation on which Newton later built the law of gravitation.
2. Kepler’s First Law: Law of Orbits
Each planet moves around the Sun in an elliptical orbit, with the Sun at one of the two foci.
An ellipse looks like a stretched circle. It has two special points called foci. The Sun occupies one of these foci, not the centre.
2.1. Shape of an Elliptical Orbit
- Planets are closer to the Sun at some points and farther at others.
- The closest point is called perihelion.
- The farthest point is called aphelion.
2.2. Orbit Diagram
Even though orbits are elliptical, for many planets (like Earth) the ellipse is very close to a circle, which is why the orbit appears nearly circular.
3. Kepler’s Second Law: Law of Areas
A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.
This means the speed of a planet changes as it moves around the Sun. It moves faster when it is closer to the Sun and slower when it is farther away.
3.1. Why This Happens
The gravitational force is stronger when a planet is near the Sun. So it speeds up. When farther, gravity weakens, making the planet slow down.
3.2. Area Concept Explained Simply
Imagine drawing a triangle from the Sun to the planet’s position every 30 days. No matter where the planet is in its orbit, the area of these triangles will always be the same.
4. Kepler’s Third Law: Law of Periods
The square of the time a planet takes to complete one orbit (T²) is proportional to the cube of the average distance from the Sun (R³).
4.1. Mathematical Form
\( T^2 \propto R^3 \)
This means:
- Planets that are far from the Sun take much longer to complete an orbit.
- Planets closer to the Sun move faster and complete an orbit in less time.
4.2. Examples
- Mercury (closest to Sun) → completes an orbit in about 88 days.
- Neptune (very far) → takes about 165 years to orbit once.
5. Connection Between Kepler’s Laws and Newton’s Law of Gravitation
Kepler discovered the patterns of planetary motion, but he did not know why they occurred. Later, Newton showed that all three laws follow naturally from the universal law of gravitation.
5.1. Gravity as the Cause
Newton proved that the Sun’s gravitational pull provides the exact centripetal force needed to keep planets in elliptical orbits.
5.2. Mathematical Harmony
Kepler’s third law can be derived directly from Newton’s inverse-square law of gravity, showing the deep connection between forces and motion.
6. Why Kepler’s Laws Are Important
Kepler’s laws help us understand:
- Planetary orbits
- Satellite motion
- Comet paths
- Space mission trajectories
- The structure of the solar system
They remain one of the most elegant and accurate descriptions of celestial motion.
Next, we study the concept of weightlessness and why astronauts feel weightless in space even though gravity is still acting.