Chapter 21 - Gravitational fields Flashcards
What is a force field?
Region in which a body experiences a non-contact force
What is a gravitational field?
Force field around a mass
What is a (gravitational) field line?
Path a smaller mass would follow if pulled towards a larger mass.
Define the strength of a gravitational field(g)
Force per unit mass on a smaller test mass placed in the field
Give the equation for gravitational field strength (g)
g = F/m (NKg^-1)
Give the equation for acceleration of free fall in a gravitational field.
a = force/ mass = mg/m = g
What’s a radial field?
Where field lines are like spokes of a wheel. Towards the centre
What happens to g in a radial field?
Decreases with increasing distance from the massive body.
What is a uniform field?
Field lines are parallel and equally spaced.
What happens to g in a uniform field?
Magnitude + direction of g is constant throughout the field
Is earth’s gravitational field uniform or radial?
- Radial (Uniform over a very small distance)
- g decreases with distance from the earth increasing
Define gravitational potential energy
Energy of an object due to its position in a gravitational field
Define gravitational potential (V)? Give the equation
The gravitational potential at a point is the work done per unit mass to move a small object from infinity to that point. (As gravitational potential is zero at infinity)
V = W/m (unit: JKg^-1)
What’s the equation for change in gpe (Ep) if a small object of mass m is moved from gravitational potential V1 to gravitational potential V2?
Change in Ep = m(V2-V1)
What are equipotentials?
- Surfaces of constant potential. So no work needs to be done to move along an equipotential surface.
Define potential gradient (gravitational)
Potential gradient at a point in a gravitational field is the change of potential per metre at that point
Draw the equipotentials on a diagram of a planet
Why do the equipotential get further apart as the distance increases from the planet?
gravitational fields become weaker so gain of gravitational potential energy per metre of height gain becomes less.
Give the equation for potential gradient for change in V and change in r (small distance
potential gradient = change in V/ change in r
Give the equation for g (gravitational field strength) using potential gradient
g = - change in V/ change in r = - potential gradient
What is Kepler’s third law?
- The value of r^3/T^2 was the same for all planets.
where r = average radius of it’s orbit and T = time period
What are the assumptions in Newton’s laws of gravitation?
Gravitational force between any 2 point objects (planets were taken to be point masses) is:
- always an attractive force
- Proportional to the product of the masses of each object
- Proportional to 1/r^2 where r is their distance apart
What is G and give a value and units
Universal constant of gravitation, G
6.67x10^-11 Nm^2Kg^-2
Give the equation for gravitational force, F, using Newton’s laws of gravitation.
Gravitational force F = Gm1m2/r^2
What is the equation for magnitude of the gravitational field strength (g) at distance r from a point object or from the centre of a sphere of mass M?
g = GM/r^2
as f = F/m:
F = Gm1m2/r^2
F/m = GM/r^2
How do you calculate the gravitational potential near a spherical planet (at or beyond the surface)?
V = -GM/r
Define escape velocity
Minimum velocity an object must be given to escape from a planet when projected vertically from the surface.
What is the formula for escape velocity?
v(esc) = (2gR)^1/2 where R = radius of planet or = (2GM/R)^1/2
What does the area under a g-r graph represent? where r is the distance from surface
Gravitational potential (V) at the surface
What’s the relationship between gravitational potential, V, and distance r from the centre of the planet?
V is inversely proportional to r
What’s a geostationary satellite?
- Satellite that orbits the earth directly above the equator and has a time period of exactly 24 hours.
- Remains in fixed position above the equator
What advantage does a geostationary satellite offer when used for communications?
Maintains fixed position relative to earth’s surface, so offers uninterrupted communication between transmitter and reciever
steerable dish not necessary
What’s the height of a geostationary wave above the earth?
36000 Km
For a satellite in circular orbit of radius r, how do you calculate it’s total energy?
E = -GMm/2r
What’s the equation for radius of the orbit of a geostationary satellite?
r3 / T2 = GM/4π2
as F = GMm/r2 : v2/r = GM/r2
therefore speed, v2 = GM/r
v = 2πr/T so: (2πr)2 / T2 = GM/r
so: r3/T2 = GM/4π2
What happens to the speed of a satellite when it moves to an orbit that’s closer to earth?
Speed increases as:
- as GMm/r2 = mv2/r:
v = (GM/r)1/2 so as r decreases, velocity increases. V proportional to 1/r
- Loses potential energy, so gains kinetic
Whats the equation for increase in potential energy, when a satellite is raised from planets surface to a height
change in Ep = m x change in V
= GMm(1/R - 1/r)
where R = radius of planet and r = radius of orbit
