gravitation

gravitation

1. field lines

   • If a small object is in freefall due to gravity the path that it will follow is called a “field line” or a “line of force”.
   • For a planet they are directed towards the centre at all points, we call this a radial field and the strength varies with distance.
   • g=f/m
     • F = force = weight (newtons)
     • M = mass (kg)
     • g = gravitational field strength 9.81 n/kg

2. newtons law of gravitation

   • the gravitational force F is related to the mass and radius of the planet
     • F∝ m/r²
       • when a constant of proportionality is added we get
         • F = Gm1m2/r²
           • f= gravitational force between the two objectives, force (newtons)
           • m1 and m2 = the masses of two objects (kg)
           • r= the separation between the centres of the masses (m)
           • G= gravitational constant

3. gravitation potential

   • • G gets weaker as you get further away from the planet
   • • G is zero at ∞
   • • Anything trying to escape g has to work against gravity
   • • As the object gets further away from the planet the GPE (gravitational potential energy) increases
   • GPE = mgh
   • The gravitational potential at a point is the work done per unit mass to move a small object from infinity to that point
   • V = work done/mass Units: Jkg-¹
   • if a small mass m is moved from a gravitational potential, V, to a gravitational potential, V2, then the change in GPE is given by
     • ΔEp = m(v2-v1) we can call (v2-v1) Δv
     • ΔEp = mΔv
     • The work done to move the mass from v1 to v2 is equal to change in GPE Δw = mΔv

4. gravitational field strength

   • The law of gravitation is an inverse square law
     • • As the distance between masses increases, the force decreases
       • • If the distance doubles, the force is a quarter of its original strength
   • Point masses have radial field lines g = GM/r² (m = point mass kg)
   • Ep = mgh – as something is moved higher the gpe increases Ep = -GMm r

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