Gravitational Fields Flashcards
Gravitational field
The field of force surrounding a body of finite mass in which another body would experience an attractive force.
Field line / Line of force
The path along which a test particle would follow in a force field.
Gravitational field strength, g
The force per unit mass on a small test mass placed in a field, g = F/m.
Gravitational field strength, g for a radial field
g = GM/r^2
Radial field
The field lines are like the spokes of a wheel, always directed towards the centre.
Uniform field
The gravitational field strength is the same in magnitude and direction throughout the field. Field lines are therefore parallel to one another and equally spaced.
Gravitational potetnial energy definition
The energy of an object due to its position in a gravitational field.
Gravitational potential, V
The work done per unit mass to move a small object from infinity to that point, V = W/m. Unit is J kg^-1.
Equipotentials
Surfaces of constant potential, because of this, no work needs to be done to move along an equipotential surface.
Potential gradient
The change of potential per metre at a point in a gravitational field = ΔV/Δr.
Gravitational field strength, g
g = - ΔV/Δr
Kepler’s third law
T^2 is proportional to r^3
Newton’s law of gravitation
F = G m1 m2 / r^2
Universal constant of gravitation, G
G = 6.67 x 10^-11 N m^2 kg^-2
Gravitational potential, V at distance r from the centre of a planet of mass M
V = - GM/r
Escape velocity
The minimum velocity an object must be given to escape from the planet when projected vertically from the surface = √2gr.
Geostationary satellite
Orbits the earth directly above the equator and has a time period of exactly 24h.
Radius of the earth
6400 km
Energy of an orbiting satellite
E = - GMm/2r
