Johannes Kepler, a German astronomer and mathematician, made profound contributions to our understanding of the cosmos during the 17th-century Scientific Revolution. His meticulous analysis of planetary observations led to the formulation of three fundamental laws describing how planets move around the Sun. These laws transformed the prevailing view of the solar system, laying important groundwork for later scientific advancements, including Isaac Newton’s theory of universal gravitation.
The Law’s Statement
Kepler’s Second Law of Planetary Motion provides a precise description of how a planet’s speed changes as it orbits the Sun. This law states that “a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.” This means the imaginary line connecting a planet to the Sun covers the same area in the same amount of time, regardless of its position in orbit.
What “Equal Areas” Means
This concept implies that a planet’s orbital speed is not constant. When a planet is closer to the Sun, the imaginary line connecting them is shorter, so the planet must move faster along its orbit to sweep out the same area in a given time. Conversely, when the planet is farther from the Sun, this line is longer, and the planet moves slower to cover an equivalent area. For example, imagine a pie slice from the orbit: a thin, long slice (planet far) means a short arc, while a wide, short slice (planet close) requires a longer arc in the same time to equalize areas. This variation in speed is a direct consequence of the law.
The Physics Behind the Law
The underlying physical principle explaining Kepler’s Second Law is the conservation of angular momentum. Angular momentum is a measure of an object’s tendency to continue rotating or revolving, and for a planet orbiting the Sun, it remains constant. This is because the gravitational force exerted by the Sun acts directly towards its center, creating no “torque” or rotational force on the planet. As a planet moves closer to the Sun, its distance from the central point decreases, so its orbital speed must increase to maintain this constant angular momentum.
Observing the Law in Space
Kepler’s Second Law is evident in the orbits of all celestial bodies in our solar system, including Earth. Our planet moves faster when it is closest to the Sun, a point known as perihelion, which occurs around early January each year. Conversely, Earth moves slower when it is farthest from the Sun, at a point called aphelion, typically in early July. This difference in speed is noticeable. Comets, with their highly elliptical orbits, provide a clear illustration, significantly speeding up as they swing close to the Sun and moving very slowly when far away.