Gravitational Fields Flashcards
What are some properties of the gravitational force between 2 masses?
Always attractive, prop to product of masses, follows an inverse square law
What is a force field?
A region in space where objects experience non-contact forces
How do you find acceleration in a grav field?
Combine g = F/m and F = ma to get a = g
How do you find the field strength for a radial grav field?
Combine g = F/m and F = Gm1m2 / r^2 to get g = GM/r^2.
What is the grav field strength at the surface for a planet of radius R?
g = GM / R^2
What is the grav potential energy at a point in a grav field?
E(p) = Vm = -GMm / r, for a mass m in a field caused by a mass M
What are the units of grav potential?
Jkg^-1
Where is grav. potential zero?
At an infinite distance away from a mass.
Why is grav. potential always negative?
As work must be done to move objects apart, but Ep can only have a max of zero, so grav. potential must always be negative.
How do you find change in grav potential?
Area under the graph of g against r
Where is g (field strength) largest?
At the surface of a planet.
What is the work done moving along an equipotential?
0J
What is the potential gradient in a field?
Change in potential per metre, potential grad = change in V / change in r
How is grav field strength related to potential gradient?
g = -delta V / delta r. So g can be found from a gradient of a V against r graph.
What is the escape velocity?
The minimum energy an object must be given to escape a body’s grav field. So must be energy used to move from infinity to the surface.
What is the equation for escape velocity?
1/2 mv^2 = GMm / R; v(esc) = root (2GM/R)
Is escape velocity the same for all masses in a given grav field?
YES
What are some equations linking time period and radius of orbits?
T^2 / r^3 = c; T1^2 / r1^3 = T2^2 / r2^3
What is the derivation for T^2 / r^3 = c?
GMm / r^2 = mv^2 / r
GM/r = v^2
v = 2pi r / T,
GM / r = (2 pi r)^2 / T^2
so T^2 = 4 pi^2 r^3 / GM,
pi ^2 / GM is a constant so
T^2 directly prop to r^3
What is the total energy of a satellite?
Etotal = Ek + Ep = -Gmm / 2r
What are some features of geostationary orbits?
Remain at the same point above the equator
Orbits in the equatorial plane
Has a time period of 24 hours (!)
Moves in the same direction that the earth rotates
Orbits around 36,000km above earth, so orbital radius of about 42000km
Useful as communication satellites, receivers can point in a fixed direction
What are some features of low orbits?
Orbit less than 2000km above the Earth. Move at a right angle to the equatorial plane.
Will pass over every point on the Earth as it rotates beneath them
Useful for scanning the Earth for imaging, mapping, weather prediction.
