Gravitational Fields CIE A-Level Physics

Gravitational field strength

the gravitational force per unit mass at that point

F = mg

Gravitational Field

A region of space where a mass will experience a force

Newton’s Law of Gravitation

any two masses attract each other with a force proportional ti

Attractive force (F)

F = GmM/r²

Gravitational Field of a point mass

g = GM/r²

Orbital Mechanics

The gravitational pull on a satellite provides the centripetal force to keep the satellite in orbit.

Formula of Orbital velocity

v² = GM/r

Formula of Orbital Period

T² = 4π²r³/GM

Features of Geostationary orbits

• A satellite orbits the Earth directly above the equator.

• If the satellite orbits in the same direction as the Earth spins and has an orbital period of 24 hours, it will remain over the same point above the Earth’s surface.

• Used for communication satellites.

Gravitational potential

Gravitational potential at a point is the work done per unit mass in bringing a unit mass from infinity to that point.

Formula for gravitational potential

Φ = -GM/r

Why is Gravitational Potential negative?

Because as a mass is brought closer to M its gravitational potential energy decreases. (GPE is defined as zero at infinity)

Formula for Gravitational Potential Energy of two isolated point masses

Ep = -GMm/r