Gravitational Fields F01-05 Flashcards
Describe Newton’s law
of gravitation?
The force of attraction that is directly proportional to the product of the two masses, and inversely proportional to the distance between the two centres squared.
Define ‘gravitational field strength’
The force per unit mass felt by a small test object at any point within that field.
Is field strength a scalar or a vector?
Vector.
Units of field strength?
N kg^-1
Define ‘gravitational potential’
The work done PER UNIT MASS to bring an object from infinity to that point.
Is potential a scalar or vector?
Scalar.
Units of potential?
J kg^-1
Draw the field lines in a radial field.
Circular centre with arrows all going towards to the centre of the circle.
Draw the equipotentials in a radial field
A dotted circle around the circle centre in a circle shape.
Draw the field lines in a uniform field.
Parallel lines pointing towards the ground/downwards.
Draw the equipotentials in a uniform field.
Dotted lines perpendicular to the direction of the force field.
How do the field lines indicate field strength?
The closer the lines are together the stronger the field is.
What is the angle between equipotentials and field lines?
Perpendicular to the direction of the field lines so 90 degrees.
What is the graph of the field strength against distance?
A typical y = 1/x graph
What is the graph of the potential against distance?
r shaped curve starting in the bottom right quadrant away from the y axis, at the radius of sphere, ending at the surface of the next object or the total distance.
How can we find the work done moving between points from a g vs r graph?
Work done is the area under the graph
How can we find the field strength from a V vs r graph?
Finding the gradient = -(V/r)
Show that T² ∝R³ (Kepler’s law)?
F = Gm1m2/r^2
F = mv^2/r
GMm/r^2 = mv^2/r
From above derive… v = (GM/r)^1/2
v = 2pir/T
T = 2pir/v
T = 2pir/(GM/r)^1/2
T = (4pi^2r^3/GM)^1/2
Therefore T^2 = 4pi^2r^3/GM
Therefore T² ∝R³
Describe Newton’s law
of gravitation formula?
F = (Gm1m2)/(r^2)
What is the value of the gravitational potential at infinity?
As r tends to infinity, 0.
What are equipotential lines?
Definition: Join points of equal potential.
Orientation: at 90 degrees to the direction of the field lines.
Spacing: are closer in stronger in stronger fields.
Is there work done along equipotential lines?
No work done is moving along an equipotential lines.
What is a geostationary/geosynchronous satellite?
Time period is 24 hours.
Stays above the same point on the earth.
Cannot see the poles, (only up to 70 degrees above the equator).
What is a Low orbit (Polar) satellite?
Over the poles.
This way a satellite can cover the whole earth as the earth rotates.
Short time period, around 90 minutes.
How to calculate the total GFS?
g(T) = g(1) - g(2)
g(1) > g(2)
How to calculate the total Gravitational Potential?
V(T) = V(1) + V(2)
What is the equation relating work done, mass and gravitational potential?
W = mV
W = m(V(orbit) - V(surface))
What are the uses for geostationary/geosynchronous satellite?
Communications
What are the uses for Low orbit (Polar) satellite?
Military
Scientific
Weather
GPS
What are the energy considerations for an object in orbit?
Total energy = KE + GPE (negative)
If total < 0, then stays in orbit.
If total > 0, then will escape orbit.
(KE > GPE)
