Module 5 Gravitational Fields Flashcards
Define a gravitational field and gravitational field lines.
A region around a mass where other masses feel an attractive force towards the mass, is a gravitational field.
Gravitational field lines show the direction of the force of gravity.
Can there be a point between two bodies of large mass where no net force occurs?
Why?
Yup.
The gravitational fields of the two masses cancel each other out at specific points.
What quantity causes gravity?
Mass.
For a spherical mass, where do the gravitational field lines point?
Towards the centre of the circle.
What is the distance limit of gravitational force?
It has no limits, as gravitational force has an infinite range.
What is the relation between gravitational field strength and separation.
Give an example.
G.f.s is inversely proportional to the square of separation.
If d is increased by 3 times then the g.f.s is decreased by 9 times.
Why can gravitational field lines be considered parallel on the surface on Earth?
As the variant in g.f.s is minuscule, we assume that g.f.s is uniform over the surface.
Is gravitational field a vector?
Yup
Define gravitational field strength and state why it is a vector quantity?
Give equations and units too.
G.f.s is the force acting on a body divided by it’s mass at any point in gravitational field.
It is a vector since it is the product of a vector and a scalar(F x 1/m) hence it is a vector quantity.
g=F/m
g=Nkg^-1
Even though parallel lines can be drawn on the surface of the Earth to show g.f lines, in reality are there any fluctuations in g.f.s and why?
Yes there are tiny fluctuations as the matter across the surface of Earth is not uniform. The composition of Earth varies at different points and this affects the mass of Earth at that point, causing difference in g.fields.
What is the difference and similarities between acceleration g= 9.81 and gfs on the surface of the Earth.
“g” is the acceleration due to gravity and has units ms^-2, whereas gfs is has the units N/kg.
They both have equal magnitudes.
When you are stating that a 10 kg mass has a weight of 98.1N, are you multiplying mass with g or g.f.s?
G.f.s
State Newton’s law of gravitation and give equations.
Between two masses the force of attraction is directly proportional to the product of their masses and inversely proportional to the square of their separation.
F=-GMm/r^2 , where G is universal gravitational constant, M and m are masses of respective bodies and r is the separation between the CENTRE of the bodies
Why is there a negative sign in the equation for Newton’s law of gravitation.
This is to show that gravity is always attractive.
Relate the g.f.s of a point mass to Newton’s law of gravitation.
Since g = F/m
F=-GMm/r^2
g=-GMm/r^2 m
g=-GM/r^2
Describe the curve of an inverse square relationship between g and r.
If y axis is the quantity inversely proportional to square of another value, then the graph has increasing gradient but the increase in gradient becomes smaller.
(Makes the graph look like a boomerang with the outward tip pointed towards the origin)
Define gravitational potential. What is it’s sign?
At a point in a gravitational field, it is the work done to move a unit mass from infinity to that specific point.
Vg.
State equation and units for Vg.
Vg=-GM/r
Vg=Jkg^-1
How do you calculate change in Vg, when separation is changed?
Calculate initial vg and final vg and find the difference.
What is the magnitude of Vg at infinity?
How do you calculate change in Vg?
It is zero 0.
You first calculate the Vg at each point then find the difference between them.
Define the gradient of g.f.s against separation, for a distance from the centre of the sphere to the surface.
It is a straight line graph through the origin, meaning r and g are directly proportional within a spherical mass.
What is the gradient of a Vg against r graph equal to?
It is equal to -g
What is the area under a F against r graph?
It is equal to the work done in moving a body in a gravitational field.
Define gravitational potential energy.
Derive equations.
Gravitational potential energy for a defined mass ‘m’ of a body is the product of it’s mass and the gravitational potential.
E=m x Vg
Vg=-GM/r
E=-GMm/r
Derive equation to calculate the speed of an orbiting body.
F=-GMm/r^2 and F=-mv^2/r
-GMm/r^2= -mv^2/r
-GMm/r=-mv^2
v^2=-GMm/mxr
v^2=-GM/r
v=(-GM/r)^1/2
What is the change in Gravitational potential energy for a body travelling at escape velocity from the surface of the Earth?
It is increasing from E= -GMm/r to 0
Define escape velocity and Derive equation for escape velocity.
It is the velocity required to move a body from a point in a grav. field to infinity.
For a body travelling at escape v
K.E>= Gravitational potential energy
1/2xm v^2 = -GMm/r
v^2= -2 GMm/m r
v= (-2 x GM/r)^1/2
State Kepler’s 3 laws of planetary motion.
The planets have an elliptical orbit around the Sun.
A line joining the Sun and any planet will sweep equal amounts of area for the same time.
The square of the Time taken to orbit the Sun is directly proportional to the mean radius of the orbit cubed, for any planet in the Sun’s orbit.
Derive the equation for Time period for a planet.
v=d/t
t=T
T=d/v
T=2pi r/v
v=(GM/r)^1/2 (v for an orbiting body)
T=2 pi r/ (GM/r)^1/2
T^2= 4 pi^2 r^2/ GM/r
T^2= 4 pi^2 r^3/GM
T= (4 pi^2 r^3/GM)
Derive T for a body in orbit using v =2pi r/T
v=2 pi r/T, F=mv^2/r
F=m 4 pi^2 r^2/T^2 x r = m 4 pi^2 r/T^2
F=-GMm/r^2
m 4pi^2 r/T^2= -GMm/r^2
T^2=m 4 pi^2 r/ -GMm/r^2
T^2=-4 pi^2 r^3/GM
What causes the centripetal force in orbits?
The gravitational force as it is perpendicular to the direction of motion but acts towards the centre of the larger mass
Define a geostationary orbit.
An orbit that has the same rotational time period as the body it’s orbiting, 24 hrs for Earth is a geostationary orbit. The direction of orbit is also the same as the direction of rotation.
