gravitation fields 1

Gravitational field

A region around a mass where other objects experience an acceleration towards the larger object.

Given by the equations : g = F/m

g = -GM/r²

Gravitational field strength

Gravitational field strength is defined as the force per unit of mass of an object.

g = F/m

The strength of a gravitational field is greater closer to the object.

Gravitational field line

The visualisation of the forces due to gravity.

At the surface of an object they are parallel, evenly spaced and perpendicular.

On an astral body they act round in a circle extending from all direction and get further from each other as distance from the body increases.

Point mass

An ideal object with mass but no size, used often in diagrams.

Newton’s law of gravitation

States that every 2 masses in the universe attract each other with a force directly proportional to the product of their masses and inversely proportional to the squat of the distance between their centres.

F=GMm/r²

Gravitations constant

G = 6.67×10^-11

Derivations for a satellite in circular orbit

GMm/r² = mv²/r

GM/r² = v²/r

GM/r = v²

v = square root GM/r

v= s/t = 2pi/T

T² = 4pi²r³/GM

T = 2pi square root r³/GM

v = 2pi/2pi square root r³/GM

r/square root r³/GM

v = square root GM/r

Satellite

Anything that orbits around a larger body due to gravity is a satellite.

Natural satellites are non man made

Artificial satellites are man made

Geostationary orbit

Orbits directly above the equator moving in the same direction as the earth rotates. And must have the same angular velocity/orbital period as the earth.

Gravitational potential Vg

Gravitational potential at a point in a gravitational field is the work done per unit of mass to bring a mass FROM infinity to that point without kinetic energy.

Equation in Vg=-GM/r

Gravitational potential energy

The energy stored by an object due to its position in a gravitational field. Represents the work done to move the object from a point to its current position.

E =-GMm/r

Total energy of a satellite

Made up of 2 parts : KE and GPE

KE = ½ mv² v = square root GM/r

KE = ½ m square root GM/r

GMm/2r

GPE = -GMm/r

E = KE + GPE

GMm/2r - GMm/r = -GMm/r

Escapee velocity

The minimum speed required for an object to completely escape the gravitational pull of a body without any additional propulsion. At this speed the object reaches infinity with no KE left.

Initial energy = Final energ

1/2mv² - GMm/r = 0

1/2mv² = GMm/r

1/2v² = GM/r

v² = 2GM/r

v = square root 2GM/r