Gravitational fields Flashcards
What is Newton’s law of gravitation? (Quantative)
F = G.M.m/r²
What is Newton’s law of gravitation? (Define it)
The attractive force felt between masses due to their gravitational field is proportional to the product of the masses and inversely proportional to the square of the distances between them.
What equation links gravitational field strength (g), force (F) and mass (m)?
g = F/m
What is the magnitude of gravitational field strength (g) of a radial field?
g = GM/r²
What direction to gravitational field lines point?
Towards the centre of the mass
What do uniform field lines look like?
Parallel and evenly spaced so that a mass placed at any position withi the field experiences the same force?
What is a gravitational field?
A region of space in which a test mass placed within it experiences a force of strength determined by g.
What is the gravitational potential?
The gravitational potential of a point in space is the work done per unit charge of moving a mass from infinity too that point.
What is the gravitational potential at infinity?
0
Why is the gravitational potential always negative?
As an object moves from infinity to that ‘point’, energy is released and the potential energy of the mass decreases. (work must be done to move the mass from a point to infinity as the gravitational force is attractive).
What is the work done in moving a mass (m) through a field?
Δw= m. ΔVe
What is the equation for the gravitational potential of a point in a radial field?
Ve = - G.M/r (j/kg or volts)
What is the equation for the gravitational potential of a point in any field?
Ve = Δh. g (j/kg or volts)
What is an equipotential surface?
A surface in which the potential is constant, the is no change in potential and therefore there is no work done in moving a mass along its surface.
How can you find the gravitational field strength (g) from a grav potential (Ve) against distance (r) graph?
-ive gradient
What is the relationship between a g/r graph and a Vg/r graph?
The grav field strength/ distance graph (g/r) is the negative gradient function of the grav potential/ distance graph (Vg/r)
How can you find the grav potential (Ve) between two points from a gravitational field strength (g) against distance (r) graph?
The area under the g/r curve between the points r1 and r2
What is Kepler’s third law?
The square of the Time period of an orbit is directly proportional to its radius cubed.
How do you derive Kepler’s third law relationship?
Let the centripetal force = the gravitational force of attraction
mω²r = GMm/r²
rearrange for T, use ω = 2π/ T
What is the total energy of an orbiting satellite?
Constant, kinetic energy + potential energy
(so if ek increases, potential energy decreases and so on…)
What is the escape velocity of an object?
The minimum velocity an object must travel at too escape the gravitational field at the surface of an object (like a planet).
Velocity when Ek = Ep
What is the equation for escape velocity?
v = √(2GM/r)
What is a synchronous orbit?
The orbital period of the object is equal to the rotational period of the object it is orbiting. Eg. satellite around earth, T=24hrs
What is a geostationary satellite?
It has a synchronous orbit so stays over the same geographical point, as usually placed over the equator.
What are geostationary satellites useful for?
TV and telephone, stays over the same point so there is no need to adjust any aerials/ masts
What is Kepler’s third law equation?
T² = 4π²/GM x r³
What are low orbit satellites useful for, and why?
Weather monitoring, scientific observations of unreachable areas and military applications.
Low orbits mean that they satellites travel much faster with lower periods, requiring less powerful transmitters and can potentially cover the earth’s surface.
