Gravitational fields Flashcards
Define a gravitational field
A force field which causes objects with mass that are placed in the field to experience an attractive force as the field produced by the mass interacts with the field it is placed in
Define a force field
A region where an object experiences a non-contact force
Describe Earth’s gravitational field lines
- Radial meaning they meet at the centre of Earth and spread out as distance increases
- Close to the Earth’s surface field lines are almost uniform, meaning they are parallel and equally spaced
What is Newton’s Law of Gravitation
F = GM1M2/ r^2
How does Newton’s Law of Gravitation show an inverse square law
F ∝ 1/ r^2
e.g. as distance between centres doubles, F between them decreases by 4 x
Define gravitational field strength
Gravitational force experienced by a 1 kg mass
i.e. g = F/m
How can you calculate gravitational field strength at a point in a radial field
g = GM / r^2
How does the formula for g in a radial field show an inverse square law
g ∝ 1/ r^2 (inverse square law)
e.g. as distance from centre doubles, field strength decreases by 4x
This is shown by how field lines get further apart as distance increases
How does field strength change in a uniform field
It is constant
Shown by how field lines are equally spaced
Define gravitational potential at a point in the field
The GPE that a 1 kg mass has at that point in the field
Why is V negative
Because you need to do work against the field to move an object out of it
Why does V = 0 at infinity
0 work done required to remove the object from the field
(Therefore as distance from centre increases, V becomes less negative and closer to 0)
What is the formula for V in terms of M and r
V = -GM / r
Describe the graph of g against r
g = ΔV/Δr
so V is the area under a g against r graph
- Graph is in the form k/x^2 where x>0 as g ∝ 1/r^2
Describe the graph of V against r
g = ΔV /Δr so g is the gradient of a V against r Graph is in the form k/x where x>0 as V ∝ 1/r
Derive the relationship that T^2 ∝ r^3
in circular motion:
1. mv^2 /r = GMm /r^2
so v = sqrt (GM/r)
2. since v = 2πr/T
T = 2πr / sqrt(GM/r)
3. T^2 = (4π^2 r^3) / GM
so T^2 ∝ r^3
4. Use T1^2 / r1^3 = T2^2 / r2^3 in calculations a lot
Define escape velocity
Velocity required to escape the gravitational field
Derive the formula for escape velocity
Escape velocity where the objects kinetic energy = energy due to gravitational field (F x d)
1/2 m v^2 = (GMm/r^2) x r
Gives the equation
v = sqrt(2GM/r)
Define gravitational potential difference
Difference in V between 2 points in the field
How can you calculate the work done required to move between 2 points in the field
- Work done to move across the gravitational potential difference
W = mΔV
Define an equipotential
Lines or surfaces perpendicular to the field lines that join points with equal potential, meaning ΔV = 0 so work done in moving across = 0
Describe the equipotential line for a radial field
Circular as every point has equal distance from centre so equal potential
Equipotential lines with equal potential apart e.g. 10 MJ/Kg apart would get further apart as distance from centre increases as v ∝ 1/r so as as V gets closer to 0, less Δpd required to increase distance
Explain the difference in energy changes for a circular and elliptical orbit
For circular orbit, distance from the planet is the same so Ek and Ep are constant
For an elliptical orbit, speed increases as height decreases (Ep is falling and Ek is rising while Et remains constant)
Define a synchronous orbit
Where orbital period of
orbiting object = rotational period of the object being orbited around so same angular speed
e.g. A satellite which orbits around Earth in 24 hours (this is known as a geostationary orbit)
