(a) gravitational fields are due to objects having mass

The idea

Any object with mass produces a gravitational field, a region in which another mass experiences an attractive gravitational force. The field is represented by field lines pointing towards the mass, and its strength at a point is the gravitational force per unit mass on a small test mass placed there. For a point mass or a uniform sphere, the field strength at distance r from the centre is g = GM/r², where G is the gravitational constant and M is the mass producing the field. Doubling the mass doubles the field strength at the same distance; doubling the distance reduces it to one quarter.

What earns the marks

• Mass is the source of a gravitational field; every object with mass has one.
• The gravitational force between two masses is always attractive.
• Gravitational field strength is defined as force per unit mass, g = F/m, measured in N kg⁻¹.
• For a point mass or uniform sphere, g = GM/r² at distance r from the centre.
• Field strength follows an inverse-square dependence on distance from a point mass.

Common mistakes and how to put them right

• Believing a gravitational field requires a second mass to exist.

  Put it right: The field belongs to the mass that produces it.

• Treating gravitational force as repulsive or as sometimes attractive and sometimes repulsive.

  Put it right: It is always attractive.

• Using g = GM/r instead of g = GM/r² for a point mass.

• Forgetting that r is measured from the centre of the spherical mass, not from its surface.

Exam tips

• Quote the definition of gravitational field strength as force per unit mass.
• Use g = GM/r² and substitute distances from the centre of the mass.
• Check units: N kg⁻¹ is equivalent to m s⁻².
• When comparing field strengths, compare the ratio of masses and the inverse ratio of distances squared.