5.4.1 Point and spherical masses

• Gravitational field: a field created around any object with mass, extending all the way to infinity, but diminishing as the distance from the centre of mass of the object increases.
• Gravitational field lines (also known as lines of forces): lines of force used to map the gravitational field pattern around an object having mass.
• Gravitational field strength, $g$: the gravitational force exerted per unit mass at a point within a gravitational field. Nkg^-1
• What can field lines tell you about a field?

  The direction of the field and the strength of the field depending on the density of the field lines.
• In a radial field the magnitude of $g$ is the proportionality constant at that point between force and mass. ie g = GM/r^2
• • All objects with mass create a gravitational field around them. That includes you.
  • Any other object with mass placed in a gravitational field will experience an attractive force towards the centre of mass of the object creating the field. For objects on Earth, we call this gravitational attraction the object's 'weight'.
• Derive SI base unit of $g$


  F = mg <=> F = ma

  Thus, g = a

  g = F/m

  => N/kg, since F =ma => kgms^-2

  => kgms^-2/kg

  => ms^-2
• On the surface of the Earth the gravitational field stregnth is approximately 9.81 Nkg^-1
• Is gravitational field strength $g$ a vector or scalar quantity?


  It is a vector quantity as it always points to the centre of mass of the object creating the gravitational field.
• Describe how you can use a newton-metre and a known mass to determine he gravitational field strength on the top of a mountain. (2)

  Hold the newton-metre vertically in a fixed position and suspend the known mass from it.

  Measure the value of force shown in the newton-metre and us this, along with the known mass $m$ , to find $g$ using $g =$$F/m$
• Explain why the direction of the gravitational field strength at any point around a planet is always towards the centre of the planet (1)

  Gravitational field strength is always attractive and points towards the centre of mass of the object causing the gravitational field.
• Can you describe gravitational field lines to map gravitational fields?

  We can map the gravitational field pattern around an object with gravitational field lines (also known as lines of force):

  • These lines do not cross, and the arrows on the line show the direction of the field, which is the direction of the force on a mass at that point in the field.
• Can you state the mass of a spherical object modelled as a point mass at its centre?

  The radial fields for a spherical mass and a single point are very similar. This means that we can model even a large planet or a star as a point mass, with field lines converging at the centre of mass of the object.