Gravitational Potential Energy (CIE A Level Physics)

• The gravitational potential energy (G.P.E) at point in a gravitational field is defined as:

 The work done in bringing a mass from infinity to that point

• The equation for G.P.E of two point masses m and M at a distance r is:

• The change in G.P.E is given by:

ΔG.P.E = mgΔh

• Where:
  • m = mass of the object (kg)
  • ɸ = gravitational potential at that point (J kg^-1)
  • Δh = change in height (m)

 

• Recall that at infinity, ɸ = 0 and therefore G.P.E = 0
• It is more useful to find the change in G.P.E e.g. a satellite lifted into space from the Earth’s surface
• The change in G.P.E from for an object of mass m at a distance r₁ from the centre of mass M, to a distance of r₂ further away is:

Change in gravitational potential energy between two points

• The change in potential Δɸ is the same, without the mass of the object m:

Change in gravitational potential between two points

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:            Difference in gravitational potential energy 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.)