Gravitational fields Flashcards

1
Q

Define a gravitational field

A

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

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2
Q

Define a force field

A

A region where an object experiences a non-contact force

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3
Q

Describe Earth’s gravitational field lines

A
  • 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
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4
Q

What is Newton’s Law of Gravitation

A

F = GM1M2/ r^2

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5
Q

How does Newton’s Law of Gravitation show an inverse square law

A

F ∝ 1/ r^2

e.g. as distance between centres doubles, F between them decreases by 4 x

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6
Q

Define gravitational field strength

A

Gravitational force experienced by a 1 kg mass

i.e. g = F/m

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7
Q

How can you calculate gravitational field strength at a point in a radial field

A

g = GM / r^2

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8
Q

How does the formula for g in a radial field show an inverse square law

A

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

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9
Q

How does field strength change in a uniform field

A

It is constant
Shown by how field lines are equally spaced

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10
Q

Define gravitational potential at a point in the field

A

The GPE that a 1 kg mass has at that point in the field

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11
Q

Why is V negative

A

Because you need to do work against the field to move an object out of it

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12
Q

Why does V = 0 at infinity

A

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)

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13
Q

What is the formula for V in terms of M and r

A

V = -GM / r

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14
Q

Describe the graph of g against r

A

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

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15
Q

Describe the graph of V against r

A

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

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16
Q

Derive the relationship that T^2 ∝ r^3

A

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

17
Q

Define escape velocity

A

Velocity required to escape the gravitational field

18
Q

Derive the formula for escape velocity

A

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)

18
Q

Define gravitational potential difference

A

Difference in V between 2 points in the field

19
Q

How can you calculate the work done required to move between 2 points in the field

A
  • Work done to move across the gravitational potential difference
    W = mΔV
20
Q

Define an equipotential

A

Lines or surfaces perpendicular to the field lines that join points with equal potential, meaning ΔV = 0 so work done in moving across = 0

21
Q

Describe the equipotential line for a radial field

A

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

22
Q

Explain the difference in energy changes for a circular and elliptical orbit

A

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)

23
Q

Define a synchronous orbit

A

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)

24
Q

What is the orbital radius of a synchronous orbit

A

42000 km and they always lie above the equator

25
Q

What are the uses of synchronous orbit satellite

A

Sending TV and radio signals as the satellite is stationary relative to Earth so don’t need to constantly change angle of receiver

26
Q

What is the orbital radius of a low orbiting satelite

A

Between 180 and 2000 km above Earth

27
Q

What are the advantages of a low orbiting satellite

A
  • Cheaper
  • Close distance makes them useful for communications and weather
  • Each orbit covers a new part of Earth so can scan the whole of Earth more easily
28
Q

What is the disadvantage of a low orbiting satellite

A

There is a high orbital speed so will need multiple satellites working to maintain constant coverage