• When a mass is moved against the force of gravity, work is done
• The work done in moving a mass?m?is given by:

?W = m?V

• Where:
  • ?W?= change in work done (J)
  • m?= mass (kg)
  • ?V?=?change in?gravitational potential?(J kg-1)

   

• This change in work done is equal to the change in?gravitational potential energy?(G.P.E)
  • When?V?= 0, then the G.P.E = 0

   

• The change in G.P.E, or work done, for an object of mass?m?at a distance?r1?from the centre of a larger mass?M, to a distance of?r2?further away can be written as:

• Where:
  • M?= mass that is producing the gravitational field (eg. a planet) (kg)
  • m?= mass that is moving in the gravitational field (eg. a satellite) (kg)
  • r1?=?first distance of?m?from the centre of?M?(m)
  • r2?= second distance of?m?from the centre of?M?(m)

   

• Work is done when an object in a planet's gravitational field moves?against?the gravitational field lines ie. away from the planet

Gravitational potential energy increases as a satellite leaves the surface of the Moon

Maths Tip

• Multiplying two negative numbers equals a positive number, for example:

Step 1:??????????? Write down the work done (or change in G.P.E) equation

Step 2:??????????? Determine values for r1?and r2

r1?is the radius of Mars = 3400 km = 3400 × 103?m

r2?is the radius + altitude = 3400 + 700 = 4100 km = 4100 × 103?m

Step 3: ?????????? Substitute in values

ΔG.P.E =? 643.076 × 106??=?640 MJ (2 s.f.)

• Equipotential lines (2D) and surfaces (3D) join together points that have the?same?gravitational potential
• These are always:
  • Perpendicular?to the gravitational field lines in both radial and uniform fields
  • Represented by?dotted?lines (unlike field lines, which are solid lines with arrows)

   

• In a radial field (eg. a planet), the equipotential lines:
  • Are concentric circles around the planet
  • Become further apart further away from the planet

   

• In a uniform field (eg. near the Earth's surface), the equipotential lines are:
  • Horizontal straight lines
  • Parallel
  • Equally spaced

   

• No work is done?when moving along an equipotential line or surface, only?between?equipotential lines or surfaces
  • This means that an object travelling along an equipotential doesn't lose or gain energy and ΔV?=? 0

   

Gravitational equipotential lines in a non-uniform and uniform gravitational field