Gravitational fields

• A gravitational field acts between any objects which have mass and is always attractive.
• Newtons law of gravitation shows that the magnitude of the gravitational force between two masses is directly proportional to the product of the masses and is inversely proportional to the square of the distance between them.
• Mass can be assumed to act in the centre of an object and so r is the distance between the centres of the masses.
• The equation for gravitational force (F) between two masses is F=GMm/r^2.
• G is the gravitational constant, 6.67 x 10^-11.
• Gravitational field strength (g) is the force per unit mass that a gravitational field exerts on an object.
• The general equation for gravitational field strength is g=F/m.
• The equation for gravitational field strength for a radial field is g=GM/r^2.
• Gravitational fields cannot be uniform, and can only be approximated as uniform near the surface of a large mass.
• Gravitational potential (V) at a point is the work done per unit mass when moving an object from infinity to that point. Potential at infinity is zero, and so gravitational potential is always negative.
• The equation for gravitational potential (for a radial field) is V=-GM/r.
• The gravitational potential difference is the energy needed to move a unit mass between two points.
• The work done when moving an object between two points in a gravitational field equals the mass multiplied by the change in potential.
• The equation for gravitational field strength using the potential is g=- delta V/delta r.
• Kepler's third law states that the square of the orbital period (T) is directly proportional to the cube of the radius (r).
• The total energy of a satellite is constant and equals kinetic energy plus potential energy.
• The escape velocity of an object is the minimum velocity it must travel at in order to escape the gravitational field at the surface of a mass. This is the velocity at which the objects kinetic energy equals the magnitude of the gravitational energy.
• The equation for the escape velocity of an object is v=root( 2GM/r ).
• Escape velocity is independent of the mass of the escaping object, and only relies on the mass of the larger object.
• M is the larger mass, m is the smaller mass.
• The equation for orbital radius of a satellite with a synchronous orbit is r=cube root(GMT^2/4pi^2).
• A synchronous orbit is one where the orbital period of the satellite is equal to the rotational period of the object that it is orbiting.
• Geostationary satellites follow a geosynchronous orbit, meaning their orbital period is 24 hours and they always stay above the same point on earth. They are used for TV and telephone signals and GPS.
• Low-orbit satellites have lower orbits to geostationary satellites and so travel much faster and their orbital periods are smaller. This means they require less powerful transmitters and can orbit across the whole of the earths surface, so they are used for weather and communication.