Gravitational Fields Flashcards
Radial field
A field in which the field lines are straight and converge or diverge as if from a single point
Uniform field
A region where the field strength is the same in magnitude and direction at every point in the field
Field line
It’s direction indicates the direction of the force
It represents the direction of the gravitational force is acting on an object in that field
Strength of a gravitational field
The force per unit mass on a small test mass placed in the field - measures in Nkg -1 g=f/m
Also given as the negative of the potential gradient
g=-V/r
From newtons law of gravitation we get:
g=GM/r^2
Gravitational potential energy
The energy of an object due to its position in a gravitational field
The work done to move an object from infinity to that point
Gravitational potential
The work done per unit mass to move a small object from infinity to that point
V = W/m
Measured in J kg^-1
Also considering newtons law of gravitation: V = -GM/r
Gravitational potential is zero at infinity
Equipotentials
A line or surface in a field along which the gravitational potential is constant
Potential gradient
The change in potential per metre at that point
They are like contour lines on a map - the closer the equipotentials, the greater the potential gradient
Given by dV/dr
Gravitational field strength is the negative of the potential gradient -dV/dr
Kepler’s third law
For any planet, the cube of its mean radius of orbit r is directly proportional to the square of its time period T.
Using Newton’s law of gravitation it can be shown that:
r^3/T^2 = GM/4pi^2
Newton’s law of gravitation
Assumes that the gravitational force between any two point objects is:
Always an attractive force
Proportional to the mass of each object
Proportional to 1/r^2 where r is their distance apart
Universal attractive force acting between all matter
F = GMm/r^2
G is the universal constant of gravitational
M and m are the two masses involved
r is the distance between the centres of the two masses (m)
Low orbit satellites
Defined as a satellite which orbits between 180-2000km above the Earth’s surface
Cheaper to launch and require less powerful transmitters as they’re closer to the Earth
Useful for communications but their proximity to Earth and relatively high orbital speed means you need multiple satellites working together to maintain constant coverage
Close enough to see the Earth’s surface in a high level of detail
E.g. Imaging satellites for monitoring the weather
Usually lie in a plane including the North and South Pole
Each orbit is over a new part of the Earth’s surface as the Earth rotates underneath - so the whole Earth can be scanned
Geostationary satellites
Orbit the Earth once every 24 hours - always above the same point on Earth
Synchronous orbit - orbital period is the same as the rotational period of the orbited object
Must always be directly above the equator
Orbital radius ~ 42000km and 36000km above the Earth’s surface
Useful for sending TV and phone signals - you don’t have to alter the angle of the receiver
Energy of an orbiting satellite
Remains constant
Circular orbit - speed and distance above mass are constant so Ek and Ep are constant
Elliptical orbit - speed up as its height decreases and slow down as its height increases. Ek and Ep are exchanged but total energy remains constant
Force field
A region in which an object will experience a non-contact force
Gravitational potential difference
The energy needed to move a unit mass
2 points at different distances from a mass will have different gravitational potentials - therefore there is a potential difference
Given by: dW=m dV
dW - work done in J
m - mass in kg
dV - gravitational potential difference in Jkg^-1
