Kepler's Laws of Planetary Motion
This page delves into Kepler's three laws of planetary motion, providing a comprehensive overview of each law and its implications for celestial mechanics.
Highlight: Kepler's laws describe the motion of planets around the Sun and are crucial for understanding orbital dynamics.
First Law of Kepler (Law of Ellipses):
Definition: In the heliocentric reference frame, the trajectory of a planet's or satellite's center around a celestial body is an ellipse with the Sun at one of its foci.
Second Law of Kepler (Law of Equal Areas):
Definition: The line segment connecting the Sun to a planet sweeps out equal areas during equal intervals of time.
This law implies that planets move faster when they are closer to the Sun (perihelion) and slower when they are farther away (aphelion).
Third Law of Kepler (Law of Periods):
Definition: The ratio of the square of the orbital period to the cube of the semi-major axis is constant for all planets.
The page provides the mathematical formulation of the third law:
T² / a³ = 4π² / (G · Ms)
Where:
- T is the orbital period
- a is the semi-major axis
- G is the gravitational constant
- Ms is the mass of the Sun