Orbital Mechanics Notes

Describe the Law of Universal Gravitation.

Newtons Law of Universal Gravitation: The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to their seperation squared.

Solve problems involving the magnitude of the gravitational force between two masses using F=𝐺𝑀𝑚/𝑟2 .

Describe the concept of gravitational fields.

Gravitational Fields: The region in space surrounding an object in which another object would experience a gravitational force.

Solve problems involving the gravitational field strength at a distance from an object using g=𝐹/𝑚=𝐺𝑀/𝑟2 .

State the three laws of planetary motion.

Kepler’s First Law: All planets orbit the sun in elliptical paths with the sun at one foci.

Kepler’s Second Law: An imaginary line joining any planet to the sun sweeps out equal areas in equal time intervals.

Kepler’s Third Law: The square of the orbital (sidereal) period of any planet is proportioanl to the cube of its average orbital radius.

Describe the relationship between the Law of Universal Gravitation and uniform circular motion and recognise this as the third law of planetary motion.

Relationship Between Universal Gravitation and Uniform Circular Motion: Orbital motion occurs when the gravitational force provides the centripetal force needed for a planet’s circular (or nearly circular) path, which leads to Kepler’s third law: the square of a planet’s orbital period is proportional to the cube of its orbital radius.

Solve problems involving the third law of planetary motion using (𝑇𝑎²)/(ra³)=(Tb²)/(rb³)=(4pi²)/(GM)