gravitational fields

• a force field is a region in which a body experiences a non-contact force
• a force field can be represented as a vector, the direction of which must be determined by inspection
• force fields arise from the interaction of mass, of static charge, and between moving charges
• both gravitational and electrostatic forces have inverse-square force laws that have many characteristics in common. this includes the use of field lines, use of the concept of potential and equipotential surfaces
• a difference between gravitational and electrostatic forces is that masses always attract, but charges may attract or repel
• gravity is a universal attractive force acting between all matter
• Newton's law of gravitation states that the force of attraction between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them
• Newton's law of gravitation is an example of an inverse-square law
• in the equation for Newton's law of gravitation, the symbol r stands for the distance between the centres of the two masses
• the constant G is known as the universal gravitational constant
• a gravitational field can be represented by gravitational field lines
• gravitational field lines show the direction and relative magnitude of a force on a mass placed in the force field
• the direction of a gravitational field line at a point gives the direction of the force of attraction that would be felt by a small mass placed there
• gravitational field strength is a vector quantity
• the gravitational field to the Earth is an example of a radial field
• a uniform gravitational field exerts the same force per unit mass everywhere in the field. this is shown by the field lines being parallel and evenly spaced
• gravitational field strength, g, is the force exerted on an object (at a point) per unit mass

  measured in newtons per kilogram
• the gravitational field strength at a point in a field is independent of the mass places there - it is a property of the field
• two objects of different masses placed at the same point in a gravitational field will experience the same field strength, but will feel different gravitational forces
• the gravitational field strength of an object is greatest at its surface
• the gravitational potential at a point in a gravitational field is the work done per unit mass in bringing an object from infinity to that point
• the value of gravitational potential is zero at infinity
• gravitational potential is a scalar quantity
• the gravitational potential difference between two points is the work done in moving a unit mass from one point to the other
• equipotentials are surfaces of constant potential
• equipotentials are always perpendicular to field lines
• if the equipotentials are close together, a lot of work must be done over a relatively short distance to move a mass from one point to another against the field - i.e. the field is very strong
• no work is done when moving along an equipotential surface
• gravitational potential values are always negative as it is defined as zero as infinity. gravitational forces are attractive, so work must be done on a mass in order to reach infinity
• the potential gradient at a point in a gravitational field is the change of gravitational potential per unit distance
• the quantity Δv/Δr is known as the potential gradient
• the area under a g-r graph is equal to the change in gravitational potential
• the area under a non-linear graph can be found using the 'counting the squares' method
• the gradient of a V-r graph at any point is equal to the gravitational field strength at that point
• the gradient at any point of a non-linear graph can be found using the 'tangent' method
• the gravitational potential in a radial field is given by:

  V=$-GM/r$
• gravitational field strength is the negative of the potential gradient:

  g=$-ΔV/Δr$
• the square of the orbital period of a circular orbit is directly proportional to the cube of its radius of orbit
• the time taken for a satellite to complete one full orbit is known as its orbital period
• a synchronous orbit is one in which an orbiting object has an orbital period equal to the rotational period of the object its orbiting