Edexcel A Level Physics:复习笔记12.5 Gravitational Potential for a Radial Field

Near the Earth's Surface

• The gravitational potential energy (G.P.E) is the energy an object has when lifted off the ground given by the familiar equation:

G.P.E = mgΔh

• When using this equation, the G.P.E on the surface of the Earth is taken to be zero
  • This means work is done to lift the object

   

• This equation is only used for objects that are near the Earth's surface
  • This is because, near Earth's surface, the gravitational field is approximated to be uniform
  • Far away from the Earth's surface, the gravitational field is radial because the Earth is a sphere

In a Radial Field

• In a radial field, G.P.E is defined as:

The energy an object possesses due to its position in a gravitational field

• The gravitational potential at a point is the gravitational potential energy per unit mass at that point
• Gravity is always attractive, so work must be done on a mass to move it away to a point infinitely far away from every other mass
  • 'Infinity' is the point at which the gravitational potential is zero
  • Therefore, since the potential energy of all masses increases as work is done on them to move them infinitely far away, the value of the potential is always negative
• Gravitational potential energy is defined as:

The work done per unit mass in bringing a test mass from infinity to a defined point

• It is represented by the symbol, V and is measured in J kg–1
• Gravitational potential Vgrav can be calculated at a distance r from a mass M using the equation: