AS and A2 lesson plans

Gravitational Fields

Section headings from the AS/A2 specifications are shown as titles. Since there is more than one specification all topics may not be part of all specifications.

All teachers may not wish to use all the ideas suggested. It is up to you to fit them to your own pupils' needs and to the school's facilities.

Recommended prior knowledge
Newton's laws of motion

Gravitational fields

Revise work done at GCSE and remind the students that gravitational fields are force fields with a strength (g) of F/m.
Discuss the idea of a gravitational field and the use of field lines to represent the field. The closer the field lines the stronger the field.
Discuss the development of the idea of gravitation leading to a statement of Newton's Law of Gravitation.
See: Newton's law of gravitation


Teaching note
Relate gravitational field to the value of g and remind them that this value is more or less the same over the Earth's surface but not exactly constant. Talk about the change of g up a mountain and between the poles and the equator.

The Earth is not quite spherical – its shape being rather like a sphere that someone has sat on – with a slightly greater radius at the equator than at the poles. (Polar radius 6356.8 km, equatorial radius 6378.2 km – a difference of 21.4 km). It is interesting to estimate the change in athletic records such as the high jump, pole vault, javelin and shot if they were performed at the equator and then the poles.
See: Gravitational field intensity


Extension topic
The measurement of G. Consider the historical measurement of G and the development of the Cavendish and Boys' experiment.
See: Gravitational constant measurement

Gravitational potential

Discuss the idea of gravitational potential.
See: Gravitational potential

Teaching note
It may seem strange that the gravitational potential for an object outside the Earth is negative. However point out that the potential is taken to be zero at infinity and that energy has to be given to an object to move it away from the Earth (or indeed any other body). The net result of this is that gravitational forces are attractive – two objects left isolated far out in space will attract each other and move together.

Extend to gravitational potential energy.
Point out that gravitational potential refers to unit mass while gravitational potential energy refers to a mass m.

Close to the Earth the gravitational field is sensibly constant and so the gravitational potential energy increases in direct proportion to the height above the ground. We are used to talking about a body above the ground having a positive amount of gravitational potential energy and this seems to contradict the statement above. However what we really mean is that DIFFERENCE in gravitational energy between a body at a height h above the ground and one on the surface of the Earth. The actual value of the potential energy at height h is less negative than on the Earth's surface.

Demonstration experiment
Gravitational field simulation using a stretched rubber sheet. A thin rubber sheet should be stretched over a wooden hoop or better still a bicycle wheel rim (no spokes). It can be tied securely in place with a length of string around the rim. A set of slotted masses can then be hung by a thread from the centre – attach the upper end of the thread to a circle of card before it passes through the sheet to avoid tearing the rubber. Roll marbles across the sheet to demonstrate the motion of masses in a radial gravitational field. Adding more slotting masses effectively increases the 'attraction' of the central mass.
See: Photographic images/Gravitational field simulation
See: Creative teaching ideas/Mechanics – experiment 29

Motion of masses in a gravitational field

Circular motion of planets and parabolic motion of projectiles.
Mention the highly elliptical orbits of comets.
See: Kepler's laws
See: Cannons and satellite orbits
See: Comets (14-16)

Escape velocity (extension topic)

Calculate the escape velocity from a series of different bodies – the Earth, Moon, and asteroid etc.
See: Escape velocity

Satellite orbits

The orbits of satellites must be centred on the centre of the planet.
Talk about geostationary satellites (synchronous satellites) which 'hang' above one point on the Earth's surface and weather and also resource satellites that orbit the Earth, moving above its surface.

Consider in detail the orbit radius for a geostationary satellite and discuss the properties of such an orbit.
See: Geostationary satellites

Teaching note
It is important to remember that a satellite must not only be lifted into orbit but must also be given the correct tangential velocity for that orbit.

See: 16-19/Mechanics/Gravitation/Problems/Gravitational and electric fields
See: 16-19/Mechanics/Gravitation/Problems/Gravitational fields 1
See: 16-19/Mechanics/Gravitation/Problems/Gravitational fields 2
See: 16-19/Mechanics/Gravitation/Problems/Gravitational fields 3