12 gravitational fields Flashcards
Gravitational field
a region of space where a mass experiences an attractive force towards a second force.
What is Newton’s law of gravitation?
an inverse square law
Newton’s law of gravitation
F = GMm/r^2
Gravitational field strength equation
g = F/m = FM/r^2
Differences between electric fields and gravitational fields
electric fields are attractive and repulsive whereas gravitational is just attractive; objects can be shielded from electric fields but not gravitational; size of an electric field depends on the medium between the objects whereas gravitational does not; The force between (unit) charges at a given separation is much stronger than the force between (unit) masses at the same separation
Similarities between electric fields and gravitational fields
both are unit forces (gravitational - force per unit mass, electric - force per unit positive charge); both are inverse square laws; both have infinite range
When is energy transferred?
when a mass or charge moves in a field
Why do satellites stay in orbit?
Because they’re constantly in free fall along a curved path around the earth
What are the different types of orbit?
eccentric (altitude varies); polar orbit (passes over north/south poles); low earth orbit (orbit close to earth’s surface); geostationary orbit (takes a constant time to orbit earth)
What can orbits be presumed as?
circular
How is presuming orbits circular helpful?
F = GMm/r^2 = mv^2/r
What do field lines show?
The direction of the force a mass would feel
Properties of gravitational fields
always attractive; can’t be shielded; always the same no matter what’s placed in between; objects have to be large for the field to have any effects (i.e. planet size)
Gravitational field strength, g
force per unit mass
What happens to gravitational field strength below the surface of the earth?
g is proportional to the radius at that point. g increases the further you are from the center until you reach the surface.
Gravitational potential at a point alternative definition
the work done in moving a unit mass from infinity to that point
Why is gravitational potential negative?
you have to do work against the gravitational field to move an object out of it.
The further you are from the center of a radial field…
the smaller the gravitational field strength/ the gravitational potential
At an infinite distance from a point mass the gravitational potential will be…
0
If a mass is moved along equipotentials…
no work is done against gravity
g =
= F/m; = GM/r^2
Gravitational force of attraction =
= mass * centripetal acceleration; GMm/r^2 = m*v^2/r; g = v^2/r
Gravitational potential, V =
-GM/r
Why is gravitational potential negative?
because gravity pulls masses together
Gravitational potential at a point
the work done against gravity when a 1kg mass is brought from infinity to that point
Energy change when an object moves in a field =
change in gravitational potential * mass
Kepler’s third law
T^2 is proportional to r^3
Potential gradient
rate of increase of gravitational potential with distance r; g = dV/dr
Escape velocity
the speed needed to escape a gravitational orbit
Escape velocity =
v = √(2GM/R)
