Gravitational Fields

Gravitational Fields

1. Equations

   • F = (Gm1m2)/r^2
     • F = Force between the two masses (N) G = Gravitational constant (Nm^2 Kg^-2) m1 = mass of the first object(Kg) m2 = mass of the second object(Kg) r = distance between the centres of the masses(m)
   • g = F/m
     • g = acceleration due to gravity (ms^-2) F = force due to gravity (N) m = Mass of an object (Kg)
   • g = GM/r^2
     • g = acceleration due to gravity in a radial field (ms^-2) G = Gravitational constant(Nm^2 Kg^-2) M = Mass of an object(Kg) r = Distance From centre of objects (m)
   • W = mV
     • W = Work done (J) m = mass of an object (Kg) V = gravitational potential (JKg^-1)
   • V = - GM/r
     • V = gravitational potential (jKg^-1) G = gravitational constant (Nm^2 Kg^-2) M = Mass of an object (Kg) r = Distance between the objects
   • g = -V/r
     • g = acceleration due to gravity (ms^-2) V = gravitational potential (JKg^-1) r = distance from object
   • r^3/T^2 = GM/4π^2
     • r = radius of orbit (m) T = Time period of orbit (s) G = gravitational constant(Nm^2Kg^-2) M = mass of planet
   • E = -GMm/2r
     • E = Total energy(J) G = gravitational constant (Nm^2Kg^-2) M = mass of planet(Kg) m = mass of satellite(Kg) r = radius of orbit (m)

2. Radial field

   • Field lines spread out form centre
   • Small masses are attracted to the centre
   • The magnitude of g decreases as distance increases

3. Uniform field

   • Gravitational field strength is the same magnitude and direction throughout the field
   • The field lines are parallel and equally spread

4. Definitions

   • The strength of a a gravitational field, g, is the force per unit mass on a small test mass placed in the field
   • Gravitational potential energy is the energy of an object due to it's position in a gravitational field
   • Gravitaitonal potential at a point in a gravitational field is the gpe per unit mass of a small test mass
   • Equipotentials are surfaces of constant potential
   • The potential gradient at a point in a gravitational field is the change of potential per metre at that point
   • Kepler's third law is that the value of r^3/T^2 is the same for all planets

5. Newton's law of gravitation assumes that 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 where r is their distance apart

6. Satellites

   • Geostationary satellites
     • Orbits directly above the equator
     • Time period of 24 h
     • Remains in fixed position above the equator

7. Graphs

   • • Area under graph from a point of distance 1 to distance 2 is the workdone to get from r1 to r2

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