Gravitational fields

Gravitational fields

1. Satellites

   • Any small mass that orbits a larger mass
   • Geostationary
     • Orbits the Earth directly above the Equator. Has a time period of 24 hours and is used for communications and tv signals as it stays in the same place

2. Planetary fields

   • Law of Gravitation
     • F = (GMm)/r^2
   • Magnitude of the gravitational field strength
     • g = (GM)/r^2
   • V = (-GM)/r
     • V is proportional to 1/r

3. Gravitational Potential

   • Gravitational potential ENERGY is the energy of an object due to its position in a gravitational field
   • The GP at a point is the work done per unit mass to move a small object from infinity to that point
     • 0 at an infinite distance
     • Negative at distances closer than infinity
   • Equipotentials
     • Lines of constant potential
     • As you get higher these are spaced further apart
   • Potential Gradient
     • The PG at a point in a gravitational field is the change of potential per metre at that point
     • Becomes smaller the further from the Earth you get
     • ▲V/ ▲r

4. Newton and Kepler's laws

   • Kepler
     • r^3/T^2
       • = (GM)/4pi^2
   • Newton
     • Assumptions about the gravitational force between any two point objects is
       • Always an attractive force
       • proportional to the mass of each object
       • Proportional to 1/r^2

5. Gravitational field strength

   • The force field around a mass
     • A region in which a body experiences a force
   • The mass of an object creates a force field around itself
   • Measured in Nkg^-1
   • Weightlessness
     • When only gravity is acting and so the object is unsupported and goes into free fall
   • The strength is the force per unit mass on a small test mass placed in the field
     • This mass needs to be small otherwise it could pull the other object's position and alter the field
   • Radial field is like the spokes of a wheel and is directed to the centre of a large mass eg planet
   • Uniform field is where the GFS is the same magnitude and direction throughout the field
     • The Earth has a radial field, however it can be considered uniform over small distances
   • g is the negative of the potential gradient