gravitational fields

• a force field is a region where an object experiences a non contact force
• force fields cause interactions between objects or particles
• an object with mass will experience an attractive force if you put it in the gravitational field of another object
• rules for gravitational field lines:

  • the direction shows the direction of the force
  • the further apart the lines, the lower the force it experiences
• radial gravitational fields have field lines that meet at the centre of mass
• a uniform field has field lines that are parallel and equally spaced
• newton's law of gravitation:

  • formula is f=gm1m2/r^2
  • f is the magnitude of the gravitational force
  • G is the gravitational constant
  • r is the distance between the centre of masses
  • m1 and m2 are the masses of the objects

  this law is an inverse square law so F is inversely proportional to r^2
• formula for gravitational field strength:

  • g=F/m
  • g is the gravitational field strength
  • F is the magnitude of the gravitational force
  • m is the mass of the object
• point masses have radial gravitational fields. the magnitude of g is inversely proportional to r^2. this means that g is greatest at the surface, and rapidly decreases as r increases
• gravitational potential is negative on the surface of the mass and increases with distance from the mass. you can think of this negative energy as being caused by you having to do work against the gravitational field to move an object out of it. this means that the gravitational potential at an infinite distance from the mass will be zero
• formula for gravitational potential:

  • v=-GM/r
  • v is the gravitational potential
  • G is the gravitational constant
  • M is the mass of the object causing the gravitational field
  • r is the distance from the centre of the object
• formula for gravitational field strength relating to gravitational potential

  • g=-v/r
  • g is the gravitational field strength
  • v is the change in gravitational potential
  • r is the change in distance
• escape velocity is the velocity at which an object's kinetic energy is equal to minus its gravitational potential energy, meaning the total energy is zero. it is the minimum speed that is required for an object to escape the gravitational force exerted by a massive object.
• formula for escape velocity:

  • v=sqrt(2GM/r)
  • v is the escape velocity
  • G is the gravitational constant
  • M is the mass of the object creating the gravitational field
  • r is the distance

  the derivation of this formula involves putting the formula for kinetic energy and the formula for gravitational potential x mass and then you have to rearrange it

  • when we calculate escape velocity, we assume that there are no other gravitational fields interfering and that there is no air resistance
• gravitational potential difference is the energy needed to move a unit mass - you have to do work against the force of gravity.

  • a formula for this is W=mv
  • W is work done in joules
  • m is mass of the object
  • v is gravitational potential difference
• equipotentials are lines that join all of the points with the same potential - therefore as you travel along an equipotential, your potential doesn't change so you don't lose or gain energy. therefore for this journey, the gravitational potential difference is 0. as w=mv, the amount of work done is also zero.

  equipotentials are perpendicular to field lines
• • an object undergoing circular motion is kept in its path by a centripetal force.
  • for satellites, the centripetal force is the gravitational force.
  • T^2 is proportional to r^3
  • T^2 is the time period squared
  • r^3 is the radius cubed
• orbiting satellites have kinetic energy and potential energy - the total energy of an orbiting satellite is always constant

  • in a circular orbit, a satellite's speed and distance above the mass is always constant so kinetic energy and potential energy are also constant
  • in an elliptical orbit, the satellite will speed up as its height decreases, so its kinetic energy increases as its potential energy decreases, so the total energy remains constant
• geostationary orbit satellites:

  • always positioned above the same point on earth
  • directly above the equator
  • travels at the same angular speed as the earth turns below it - an orbit takes exactly 1 day
  • useful for sending TV and telephone signals, as the satellite is stationary relative to a certain point on earth, so you don't have to alter the angle of the receiver to keep up
• low orbit satellites:

  • orbit between 180 and 2000 km above earth
  • they cost less to launch and require less powerful transmitters as they're close to earth
  • they are useful for communications and imaging
  • close enough to see the earth in high levels of detail - imaging satellites are placed in this type of orbit
  • can be used to spy and to monitor the weather
  • orbits usually lie in a plane that includes the north and south pole
  • each orbit is over a new part of the earth's surface as the earth rotates, so the whole of earth can be scanned
• gravitational potential energy is the energy of an object at a particular position
• gravitational potential is the energy per unit mass at a position
• a gravitational field is a force per unit mass, relating to a position
• types of satellites are low orbiting satellites and geostationary satellites
• types of orbit are circular orbit and elliptical orbit