المechanics of the Solar System

Motion of Planets and Gravity

Kepler's Laws of Planetary Motion

• Law of Elliptical Orbits: Planets orbit the sun in elliptical paths, with the sun at one of the focal points.
• Law of Equal Areas: The line connecting the planet to the sun sweeps out equal areas in equal times.
• Law of Harmonies: The square of a planet's orbital period is proportional to the cube of its semi-major axis.

Newton's Law of Universal Gravitation

• Gravity: A force of attraction between two objects, proportional to the product of their masses and inversely proportional to the square of the distance between them.
• Universal Gravitation: Gravity is a universal force, affecting all objects with mass, from the falling of objects on Earth to the motion of planets in our solar system.

Gravitational Force

• Gravitational Force Equation: F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them.
• Gravity and Orbital Motion: Gravity is the force that keeps planets in orbit around the sun, and moons in orbit around their parent planets.

Gravitational Fields

• Gravitational Field: A region around a massive object where the gravitational force can be detected.
• Gravitational Field Strength: The strength of the gravitational field depends on the mass of the object and the distance from the object.

Escape Velocity

• Escape Velocity: The minimum speed an object needs to escape the gravitational pull of a planet or moon.
• Escape Velocity Equation: v = √(2 * G * M / r), where G is the gravitational constant, M is the mass of the planet or moon, and r is the radius of the planet or moon.