Gravitational fields

• Newton's law of universal gravitation states that every particle attracts every other particle with a force which is directly proportional to their masses and inversely proportional to the square of the distance between them.
• The formula for calculating the magnitude of the gravitational field strength at any point due to an object is given by F = G * m1 * m2 / r^2
• Newtons law of gravitation 


  Magnitude of gravitational force between 2 mass is directly proportional to product of masses

  inversely squared to distance between
• Newtons law of gravitation equation (force field exerts on object)

  F = Gm1m2/r^2
• gravitational field strength

  force per unit mass exerted by a gravitational field
• gravitational field strength equation for uniform fields

  g = F/m
• Gravitational field strength equation for radial fields 


  g = GM/r^2
• Value of G

  6.67x10-11
• Gravitational potential 


  Work done per unit mass when moving object to infinity from that point
• Gravitational potential equation

  V = -GM/r
• Why is gravitational potential always negative

  As infinity is equal to 0, any object will be seen as negative in light of infinity. Energy is released as potential is reduced
• Gravitational potential difference 


  Energy needed to move a unit mass between two points
• work done = m x change in potential
• Escape velocity 


  square root( 2 x G x M / r )
• Find escape velocity by equating GPE to KE.
• GPE

  gpe = GMM/ r
• Field lines only ever point towards the centre as it is an attractive force
• For radial fields, the further away you are the weaker the field - the more space between field lines
• For radial fields, gravitational field strength is proportional to mass
• For radial fields, gravitational field strength is inversely proportional to radius^2
• For radial fields, g is strongest at centre, if you were to dig towards the centre, g would decrease linearly
• Field strength is a vector
• To find point of where there is no force (no field strength) acting on an object between two fields, equate g1 to g2. (GM/r)1=(GM/r)2
• F = mg
• gravitational potential energy for UNIFORM fields = mgh
• Potential = -GM/r (Jkg-1)
• The potential is negative for gravitational as an attractive field must be created by a negative charge, has to be attracted to a positive charge (think positively)
• To escape gravitational field, must be given enough energy at surface to equal potential energy needed to get to infinity (V=0)
• To find escape velocity, equate kinetic energy equation to gravitational potential energy equation.
• anything on the equator has largest speed due to earths rotation.
• gravitational potential energy is negative.