Gravitational Fields (CIE A Level Physics)

• There is a force of attraction between all masses
• This force is known as the ‘force due to gravity’ or the weight
• The Earth’s gravitational field is responsible for the weight of all objects on Earth
• A gravitational field is defined as:

A region of space where a mass experiences a force due to the gravitational attraction of another mass

• The direction of the gravitational field is always towards the centre of the mass
  • Gravitational forces cannot be repulsive

• The strength of this gravitational field (g) at a point is the force (F_g) per unit mass (m) of an object at that point:

• Where:
  • g = gravitational field strength (N kg^-1)
  • F_g = force due to gravity, or weight (N)
  • m = mass (kg)

• This equations tells us:
  • On planets with a large value of g, the gravitational force per unit mass is greater than on planets with a smaller value of g

• On such planets such as Jupiter, an object's mass remains the same at all points in space. However, their weight will be a lot greater meaning for example, a human will be unable to fully stand up

A person’s weight on Jupiter would be so large a human would be unable to fully stand up

• The direction of a gravitational field is represented by gravitational field lines
• The gravitational field lines around a point mass are radially inwards
• The gravitational field lines of a uniform field, where the field strength is the same at all points, is represented by equally spaced parallel lines
  • For example, the fields lines on the Earth’s surface

Gravitational field lines for a point mass and a uniform gravitational field

• Radial fields are considered non-uniform fields
  • The gravitational field strength g is different depending on how far you are from the centre

• Parallel field lines on the Earth’s surface are considered a uniform field
  • The gravitational field strength g is the same throughout

• For a point outside a uniform sphere, the mass of the sphere may be considered to be a point mass at its centre
  • A uniform sphere is one where its mass is distributed evenly

• The gravitational field lines around a uniform sphere are therefore identical to those around a point mass
• An object can be regarded as point mass when:

A body covers a very large distance as compared to its size, so, to study its motion, its size or dimensions can be neglected

• An example of this is field lines around planets

Gravitational field lines around a uniform sphere are identical to those on a point mass

• Radial fields are considered non-uniform fields
  • So, the gravitational field strength g is different depending on how far you are from the centre of mass of the sphere