Johannes Kepler, a German mathematician and astronomer, significantly advanced our understanding of the solar system in the early 17th century. He formulated three fundamental laws describing planetary motion, moving astronomy beyond earlier models. These laws revolutionized the prevailing view of the cosmos, providing a new framework for how planets orbit the Sun.
The Law’s Core Principle
Kepler’s Second Law, also known as the Law of Equal Areas, describes how a planet moves through its orbit around the Sun. This law states that an imaginary line connecting a planet to the Sun sweeps out equal areas during equal intervals of time. The “line segment” refers to this imaginary connection between the planet and the Sun.
What the Law Means for Orbital Speed
The Law of Equal Areas has a direct implication for a planet’s speed as it orbits the Sun. Since planets travel in elliptical paths, their distance from the Sun changes. For the line segment to sweep out equal areas in equal times, the planet must adjust its speed.
When a planet is closer to the Sun, it moves faster. This point in its orbit is called perihelion. Conversely, when a planet is farther from the Sun, it moves slower. This farthest point is known as aphelion. For example, Earth moves fastest in early January when it is closest to the Sun, traveling at about 30.3 kilometers per second.
The Underlying Scientific Reason
Kepler’s Second Law is a direct consequence of the conservation of angular momentum. Angular momentum measures an object’s tendency to rotate, considering its mass, speed, and distance from the center. For a planet orbiting the Sun, the gravitational force acts along the line connecting the two bodies, creating no rotational force or torque. This means the total angular momentum of the orbiting planet remains constant.
As a planet’s distance from the Sun changes, its speed must compensate to maintain this constant angular momentum. When closer to the Sun, its distance (radius) is smaller, so its velocity must increase to keep angular momentum constant. This explains why planets speed up at perihelion and slow down at aphelion.
Historical Context and Importance
Kepler’s laws, including the Second Law, marked a significant shift in astronomical thought. Before Kepler, models like Copernicus’s heliocentric view often assumed planets moved in perfect circles at constant speeds. Kepler’s meticulous analysis of observational data, particularly from Tycho Brahe, demonstrated that planetary orbits are elliptical and that their speeds vary. This provided empirical evidence that solidified the heliocentric view of the solar system.
Kepler’s work laid the groundwork for later scientific breakthroughs. Isaac Newton, in the late 17th century, used Kepler’s empirical laws as a foundation for his universal law of gravitation. Newton’s theory provided the physical explanation for why planets move according to Kepler’s descriptions, showing that gravity causes the observed elliptical orbits and varying speeds. This integration of observational data with a unified physical theory influenced the development of modern physics and astronomy.