Mass & Weight

Mass and weight are different quantities. Mass is defined as the amount of matter in a body, it is measured in kilograms. Weight is the force of gravity on an object. The acceleration due to gravity is 'g', so the weight of a mass 'm' is given by F = mg (newtons). The amount of matter in an object does not change, hence the mass of an object is always the same. However, 'g' varies from place to place on the Earth's surface depending on the distance from the centre of the Earth, so weight does change.

Newton's law of universal gravitation

Gravity is a force that exists throughout the Universe. It makes things fall down when you drop them, it keeps satellites in the orbits, it leads to tides on Earth, it causes stars and black holes to form and it will ultimately determine the fate of the Universe.

Newton determined that gravity is a force of attraction that exists between any two bodies. In fact, any two objects that have mass will exert a gravitational force of attraction. Gravitational forces are very weak and only become noticeable when at least one of the objects is extremely massive. The gravitational force can be calculated using the formula below.

Gravitational fields

For a body on, or above, the surface of the Earth, the mass of the Earth may be considered to be concentrated at its centre. The formula for the gravitational field is found by dividing the gravitational force by the mass of the smaller object.

Gravitational field of Earth

Field strength is weaker as the field lines spread out.

The force between the two bodies = weight of small body = mg g =

Thus the acceleration due to gravity at the surface of the earth, g, is determined by the mass of the earth and the radius of the earth, not the size of the mass in the field.

To calculate the value of 'g' at the Earth's surface:

G = 6.67 10-11 N m2 kg-2 , M = 6.0 1024 kg, r = 6.4 106 m. g = 9.8 N kg-1.

Any object that is falling freely through a gravitational field will fall with an acceleration equal to the gravitational field strength at the point. At the surface of the Earth, the gravitational field strength, g, is 9.8 Nkg-1, it becomes weaker further from the Earth.

Satellites in orbit

A satellite is any object that is in a stable orbit around another object. The Earth and all the other planets are natural satellites of the Sun. The moon is the Earth's only natural satellite but there are thousands of artificial satellites orbiting. These are used for communication, weather forecasting, geological surveying and espionage.

For a satellite in a stable circular orbit, the only force acting on a satellite is the gravitational attraction between it and the central body. This force acting on it is always perpendicular to its motion. Therefore the energy of the satellite is unchanged as it orbits. The kinetic energy and gravitational potential energy both stay the same.

The force of gravity holds the satellites in their orbits and causes them to have an acceleration towards the central mass. If the force of gravity could be 'turned off' then the satellites would fly off at a tangent. The satellites are continually falling towards the earth at the same rate that the curved surface of the earth is falling away from the satellites.

Notice that the acceleration of the satellite is independent of the mass of the satellite. If a satellite is in a geo-stationary orbit, the satellite orbits the Earth every 24 hours. This is a 'synchronous' orbit and keeps the satellite above the same place all the time.

Gravitational Potential Energy

As a body gets further from the earth, 'g' decreases and the expression Ug = mgh is no longer adequate. The force at different distances from the earth is given by the formula F = .