Gravitational Fields Flashcards
What is Gravity
Universal attractive force that acts between all matter
What can field lines tell you about a field?
The direction of a field and the strength of a field depending on the amount of field lines per unit area
What is gravitational potential
What is its convention
Work done per unit mass to move a small test mass from a position in a field to infinity
0 Potential is defined at infinite radius away from centre of mass. Work is done against gravity to move an object away hence always a a negative value
Why is gravitational potential negative (2)
0 Potential is defined at infinite radius away from centre of mass,
as work is done against gravity so energy needs to be put in to move an object towards infinity. hence negative values
What is the work done from moving a mass in a gravitational field.
Mass * Change in Potential
What is an equipotential
A surface on the gravitational field in which every point on the surface has the same gravitational potential
How is the orbital period related to the radius of a circular orbit
T^2 is proportional to R^3
What is Geosynchronous orbit?
orbit with a 24 Hour time period
What is the potential gradient?
The change of gravitational potential per meter in a gravitational field
What is escape velocity
Minimum velocity an object must be travelling in order to escape a planets/objects gravitational field if projected perpendicularly to the surface of the planet.
The strength of a gravitational field ______________________
is the force per unit mass on a small test mass placed in a gravitaitonal field
Explain a uniform field
Gravitational field strength is at the same magnitude and direction throughout the field
field lines Always directed towards the centre and are parallel and equally spaced
Explain a radial field
magnitude of gravitational field strength decreases with increasing distances from the centre of mass of the larger object
Field lines are like spokes on a wheel, equally spaced and always directed towards the centre
Produced from a point charge
What does the test mass have to be sufficiently small when measuring the strength of a granola field
has to be small to prevent altering the larger masses field by exerting a larger enough pull.
otherwise the data will be unreliable
Define Newtons laws of gravitation (3)
That any particle in the universe attracts any other particle
With an attractive force proportional to the product of the masses
and inversely proportional to the square of the distances between them
What assumptions do you make when using newtons laws of gravitation
. Always and attractive force
. Proportional to the product of the masses of the object objects
. Proportional to 1/r^2
Write out the proof that T^2 is proportional to R^3
equate Circular motion force to force between two masses
What is the equation for the gravitational field strength at any point on a planet using the grav field strength at the surface
Describe the graph for gravitational field strength as radius increases
Gravitational fields strength peaks at surface
Before the surface As radius from COM increases your field strength increases with direct proportion as the mass causing the gravitational force increases
g = 4/3(density)GPi(radius)^3
After the surface as g = GM/r^2 as radius increases, g decreases in inverse proportion
What is the formula for the gravitational field strength below the planets surface
Explain from which point from earth is it best to launch satellites
Equator
Launching from here the satellite has the largest kinetic energy and linear speed from the earths rotation compared with any other point
Minimising the fuel needed for outer space fuel burns
A satellite is in a higher orbit then another
Explain how the linear speeds of the two differ
What equations links linear velocity of a satellite to the mass and radius of a planet its orbiting
Velocity^2 = G(Mass of planet) / Radius of orbit
Equating circular motion to gravitational force
Write out the derivation for escape velocity
Change in KE = M*Change in Potential
both = work done
1 of 2 answers:
The potential differences between the lines are constant but the distances or not . (changing potential gradient) meaning different magnitudes of grav field strength
The equipotential surfaces are not straight, and are curved
Explain how you would work out the escape velocity from a planet using equipotentials
Explain Why using the potential gradient averaged over multiple equipotentials & field strength won’t work
1) work out the mass of the object :
use the equation V= -GM/r
using any equipotential but it must be the same
2) use escape velocity equation
V esc = root(2GM/radius of planet)
using root(2GR) won’t work unless you have the value of g at the surface.
using the distance between equipotentials for g means the value of g is the average between those equipotentials not g at the surface
D
Use GPE of a Satellite
-5.31x10^14 - -1.21x15 = 6.69 X10^14 J
B
Use volume of. sphere to work out the volume of M in comparison to N
(2^3 = 8) so if density is the same then the mass would be 8x as larger
as density is doubled
mass = 16x large
as V = -GM/r
-16/2 = 8
What is the formula for the Kinetic Energy of a Satellite
When Net Grav field is 0
Then there is no resultant force acting on the object
What is the “Rocket Equation”
Change in Velocity = Exhaust Velocity * ln(initial mass/final mass)
