Chapter 21 Gravitational Fields Flashcards
What is a gravitational field?
A force field surrounding an object which attracts other objects towards it/
What is a field line.
Field lines line of force through which path the mass pulled by the gravitational field would follow.
What is the strength of the gravitational field.
Strength of gravitational field, g is the force per unit mass on a small test mass placed in the field
g = F/m the unit is Nkg-1
How can free-fall in a gravitational field be calculated?
if object of mass, m is in a gravitational field, the gravitational force on the object is F = mg
where g is gravitational field strength
If the object is not acted on by anything else its acceleration a = f/m =mg/m = g
There fore acceleration during free-fall is g measured in ms-2
what is a radial field?
A radial field is where the field lines are like the spokes of a wheel and are always directed towards the centre.
The magnitude of g decreases with increasing distance from a body
What is a uniform field?
The gravitational field strength is the sam in magnitude and direction throughout the field. The field lines are therefore parallel to one another and equally spaced
Is the gravitational field of earth uniform or radial?
Radial but it can be considered uniform since the gravitational field strength differences between places are too small to be noticed.
What is gravitational potential energy?
The energy of an object due to its position in a gravitational potential field? At the surface of the planet, the gpe is negative, to reach a zero gpe you would need to escape the gravitational field completely such that its effects is negligible. Due to this a zero gpe can be said to be at infinity
How is gravitational potential calculated?
Gravitational potential v, is the workdone per unit mass to move a small object from infinity to that point.
V = W/m measured in Jkg-1
since work done is equal to change in gravitational potential energy then ΔW =m ΔV
What are equipotentials?
Surfaces of constant potential.
What is the relationship between distance from the surface and equipotential?
At a distance from the surface gravitational field becomes weaker, so the gain in gravitational potential energy per meter of height becomes less. The equipotential for equal increases of potential are spaced further when away from earth’s surface.
Near the surface, equipotential are horizontal (parallel to the ground) due to the uniform gravitational field over a small area
What is potential gradient?
the potential gradient at A point in the gravitational field is the change of potential per meter at that point.
It becomes less and less the further from earth’s surface.
potential gradient = ΔV(change in potential)/ Δr
What is the condition to move a mass m a small distance Δr in the opposite direction to the gravitational force Fgrav?
The gravitation potential energy must be increased by
- an equal and opposite force acting through the distance Δr
-an amount of energy equal to the work done by F, ΔW = FΔr
g = - ΔV/Δr
What is the equation for gravitational field strength?
g = -ΔV/r
It is the negative of the potential gradient since it acts in the opposite direction
What is Kepler’s Third Law? It’s equation?
The squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits (orbital distance).
r^3/T^2
What does Newton’s Law of Gravitation Assume?
The gravitational force between any two point objects is
- always an attractive force
- proportional to the mass of each object
- proportional to 1/r^2 where r is distance apart
F = Gm1m2/r^2
where m1 and m2 are masses of two objects
What is the universal constant of gravitation?
The constant of proportionality is gravitational force acting between two bodies of unit mass, kept at a unit distance from each other.
The unit G can be worked out from F = Gm1m2/r^2
G = Fr^2/m1m2
G can be given in Nm^2kg-2
The value of G is 6.67 x 10^-11
How can gravitational field strength be calculated using Newtons law?
g = F/m = Gm/r^2 because the distance from the center r is equal to R at the surface.
What is escape velocity?
The minimum velocity an object must be given to escape the planer when projected vertically from the surface.
Vesc = √2gr
How is the gravitational potential at or beyond the surface of a spherical planet calculated?
V = -Gm/r
How is the equation for escape velocity derived?
Check textbook page 348 or notes.
How is surface gravitational field strength calculated?
g = gsR^2/r^2
What is the gradient of a force - distance time? Area under the curve?
Work done is area under the curve while the gradient is g = gsR^2/r^2
How is workdone in gravitational field calculated?
ΔW = F Δr = (Δr)Gm1m2/r^2
How does the gravitational potential of Earth vary with distance?
V = -GM/r
Gravitational potential is inversely proportional to the distance r from the center of the planet
at distance 2r the center is 1/2 x the potential at distance r from center
at distance 3r the center is 1/3 x the potential distance
at distance 4r the center is 1/4 x the potential distance
etc
How can speed of the planet be calculated?
v^2 =GM/r or (2πr^2)/T^2
if rearranged with Kepler’s law r3/T2
then v = GM/4π^2 which will be the same for all planets since keplers law is the same for all planets
How can energy of an orbiting satellite be calculated?
Ek = 1/2mv^2 = 1/2m(Gm/r) = GMm/2r
Ep =mV = -GMm/r
Et = Ep +Ek
Et =GMm/r + GMm/2r = -GMm/2r
What are the defining characteristics of geostationary orbits?
- orbital period of 24 hours
- equatorial orbit
- remain in a fixed position in the sky to viewers on earth
How can you calculate the height of a geostationary orbit?
T^2 = 4π^2/Gm x r^3
