Gravitational fields

Force field definition

A region in which a body experiences a non-contact force

Gravitational field definition

A region in which mass experiences a non-contact force

What is gravity

It is a universal attraction between two masses

It is quite a weak force so is only noticed in large objects like planets and stars

gravitational field strength definition

The force per unit mass on a small test mass placed in the field

the test mass must be small otherwise it will pull too much on the other object, making it change its position and alter the field

Gravitational field strength equation

g = grav field strength = 9.81 Nkg-1 on earth

F = gravitational force

m - mass

Newtons law of gravitation

he reasoned that the gravitational pull exerted on a body needs to be proportional to its mass, as 3rd law states these forces are equal, force between masses must be proportional to both

assumes that F is - always an attractive force, proportional to mass of each object, proportional to 1/r²

Newtons law of universal gravitation (Force between 2 masses) equation

F = Gravitational force

G = gravitational constant = 6.67×10^-11 Nm²kg^-2

m = mass

r = radius

Radial and uniform field patterns

Radial - Field lines directed towards centre of an object

this occurs on a large scale

Uniform - g is the same magnitude and direction, field lines equally spaced an parallel

occurs on small scale

Gravitational potential energy definition

Energy of an object due to its position in a gravitational field

infinity has 0 GPE as object is so far from gravitational force that it is negligible

GPE is negative at the surface so work needs to eb done to leave the surface

Gravitational potential definition

the work done per unit mass to move a small object from infinity to that point

Gravitational potential equation

V = gravitational potential = Jkg-1

W = work done

m = mass

Equipotential definition

surfaces on constant potential, so no work needs to be done to move along the surface as they are along the same potential gradient

horizontal movement at the same point on a field line when in a surface over a small region

Potential gradient definition

the change of potential energy per metre at that point

potential gradient = change in V/change in r

grav field strength is negative of potential gradient

how does g vary with distance from centre of planet

inverse square law relationship 1/r²

Gravitational potential of spherical object equation

V - gravitational potential

G - gravitational constant

M - mass of planet

r - distance from centre of planet (radius)

Escape velocity definition

minimum velocity an object must be given to escape from the planet when projected vertically from the surface

escape velocity equation

g - grav field strength

R - radius of planet

Derived from work done = mV = gmm/R

and Ek = 1/2mv² = Work done

v² = 2GM/R

Potential gradient near spherical planet of a graph

Its an inversely proportional relationship (1/r)

How does energy of a satellite work

Total energy is constant and is equal to GPE and KE

How do satellites act in orbit

They need to be travelling at the correct speed for the orbit

Their speed increases as they move close to the earth

Its period will decrease as it moves closer to the earth as its orbit is shorter

Measurement of distance of orbit should be from the centre of the earth

Eccentric orbit

orbits where the altitude varies

Polar orbits

Orbit that passes over north and south poles

as the earth spins on its axis this can scan the entire earth in a few revolutions

spy and weather satellites use this orbit

Low earth orbit satellites

these are easy to access and are used for space stations

Geostationary orbit satellites

These are 35,900km about the equator and take 24 hours to complete an orbit

The satellite is fixed but the earth spins round it to orbit

They are used for communication (INTELSAT) or weather monitoring (METEOSTAT)

Radius of orbit is calculated using the equation

Energy of an orbiting satellite equation