Gravitational fields Flashcards
What are the two types of gravitational fields?
Uniform and radial
What does gravity act on?
Any objects which have mass.
What is F in Newton’s law of gravitation?
The gravitational force between two masses
What is the symbol for gravitational field strength and what is it?
g
The force per unit mass exerted by a gravitational field on an object.
What is gravitational potential (V) at a point?
The work done required to bring one unit mass from infinity to the point.
What is the gravitational potential at infinity?
Zero, so it is always negative
What is gravitational potential difference?
The energy needed to move a unit mass between two points.
What are equipotentials?
Equipotentials are surfaces which are created by joining points of equal potential together, therefore the potential on an equipotential surface is constant everywhere.
What is the gravitational potential difference when moving along an equipotential?
Zero, so no work is done.
How are equipotentials situated?
Perpendicular to field lines
What does the graph for V against R look like?
Negative inverse proportion graph
How can you get g (gravitational field strength) from a V/r graph?
Drawing a tangent to the curve at the necessary distance and then multiplying by -1.
What does a g/r graph look like?
Inverse proportion
How can you get gravitational potential difference from a g/r graph?
Area under the curve.
What is Kepler’s third law?
The square of the orbital period (T) is directly proportional to the cube of the radius (r):
T^2 is proportional to r^3
Derive Kepler’s third law
1 - set centripetal force equal to gravitational force
2 - rearrange to make v^2 the subject
3 - set that equal to the circular motion v equation ( v = 2 pi r / T)
4 - rearrange to make T^2 the subject
What is the equation for the total energy of a satellite?
kinetic energy + potential energy
What happens if the height of a satellite is decreased?
Its gravitational potential energy decreases, however it will travel at a higher speed meaning kinetic energy increases - therefore total energy is always kept constant.
What is escape velocity?
The minimum velocity an object needs to travel at in order to escape the gravitational field at the surface of a mass. It is the velocity at which the object’s kinetic energy is equal to the magnitude of its gravitational potential energy.
What is the formula for escape velocity?
the square root of 2GM/r
Independent of the mass of the object.
What is a synchronous orbit?
Where the orbital period of the satellite is equal to the rotational period of the object that it is orbiting.
What is the orbital period of geostationary satellites?
Geostationary satellites follow a geosynchronous orbit, meaning that their orbital period is 24 hours.
Why do geostationary satellites always stay above the same point on the Earth?
Because they orbit directly above the equator.
What are geostationary satellites useful for?
Communications (sending TV and telephone signals) because they are always above the same point on the Earth so you don’t have to alter the plane of an aerial or transmitter.
