Gravitational fields

• Uniform field


  same gravitational force on a mass everywhere in the field
• Newton's law of gravitation

  • force is directly proportional to the product of the masses
  • force is inversely proportional to the square of the distance between them
• Radial Field


  • force exerted depends on the position of the object in the field
  • e.g. Earth, however close to surface it is almost completely uniform
• Gravitational field strength


  • force per unit mass exerted by a gravitational field on an object
  • this value is constant in a uniform field but varies in a radial field
• Gravitational potential


  the work done per unit mass against gravitational force to move an object from infinity to a given point

  • gravitational potential at infinty is zero and as an object moves from infinity to a point, energy is released as the GPE is reduced, therefore gravitational potential is always negative
• Gravitational potential difference


  the energy needed to move a unit mass between two points
• Equipotential surface


  • created through joining points of equal potential together, therefore the potential on an equipotential surface is constant everywhere
  • no work is done when moving along an equipotential surface
• relationships


  gravitational potential is inversely proprtional to the distance between the centres of the two objects

  the gradient of this graph will be the gravitational field strength
• Keplers third law

  square of orbital period is directly proportional to the cube of the radius

  
• Total energy of a satellite

  • made of its kinetic and potential energy
  • constant
• Escape velocity


  • minimum velocity it must travel at in order to escape the gravitational field at the surface of a mass
  • Ek = Ep

  
• Synchronous orbit


  an orbit where the orbital period is equal to the rotational period of the object that it is orbiting
• Geostationary satellites


  • their orbital period is 24 hours and they always stay above the same point on the Earth because they orbit directly above the equator
• Low orbit satellites


  • lower orbits so they travel much faster which means orbital periods are smaller
  • they are useful for monitoring weather and making scientific observations about places that are unreachable