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10
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A small mass that is in the gravitational field will respond to the field by experiencing a force acting on it
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A gravitational field of a large planet is flat, because of its surface
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Topic 10 Page 2

Gravitational Potential Energy
Consider a mass placed somewhere in space, and a second mass that is a distance from
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This energy is the work done in bringing the two masses to their current postitions from an infinite position
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The energy belongs to both of the masses and not one of them
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The work (gravitational potential energy) of the two masses when their centres are separated by a distance
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Topic 10 Page 3

Gravitational Potential
The gravitational potential at a point P in a gravitational field is the work done per unit mass in bringing a small point mass
The gravitational potential is the ratio of the work done

The gravitational potential is a scalar quantity
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the potential a distance from a spherical mass

is:

This means that to get the potential at point P, you have to add all the gravitational potentials exerted by each mass
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The work done depends only on the mass and the change in potential, not the path taken
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The kinetic energy is negligible
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Topic 10 Page 4

Electric Fields
At a point distance away from a spherical charge , the magnitude of the electric field (electric field strength) is:
measured in N C-1 (Newtons per Coulomb)
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An example is a dipole, which has one equal
and one opposite charge separated by a distance

Topic 10 Page 5

Electric potential and energy
An electric charge creates electric potential
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Imagine two positive charges

and
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The electric potential at a point P is the amount of work done per unit charge as a small positive test charge q is moved from infinity to the point P:

The unit of potential is the volt (V)
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The work done is independent of the path followed
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The potential is represented by th e height from the flat surface
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But any point inside the sphere, the electric potential is constant and has the same value as the potential at the surface
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Equipotential lines are always perpendicular to the field lines
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If a mass is moved along a

is the magnitude of the gravitational field strength
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This applies
to both gravitational and electric fields
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Red lines are field lines and black lines are equipotential surfaces
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2 - Fields at work

Topic 10 Page 9

Orbital Motion
A satellite of mass orbits a planet of mass with speed
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The
total energy
of this system is the sum of the kinetic energy
and the gravitational
potential energy
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The satellite has an acceleration towards the centre of the circle of magnitude , because it
is orbiting in a circle
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This force is the gravitational attraction between from the planet and the satellite, that is
Newton's law of gravitation
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Escape Velocity
The total energy of a mass

launched from the surface of a planet of mass

and radius

with speed , is the sum of the kinetic and gravitational potential energies
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If we give the minimum energy at launch, then when the mass
have negligible kinetic energy
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This implies that:

This minimum velocity

that a mass must have in order to reach infinity and stop there is called the escape velocity
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Topic 10 Page 12

reaches infinity, it will stop there and so will

Weightlessness
Consider an astronaut of mass in a spacecraft in orbit around the Earth a distance from
the Earth's centre
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The forces on the astronaut are the reaction force
their weight
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, the astronaut experiences no reaction forces from the floor and

Topic 10 Page 13



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