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A Level Physics Paper 2 > Gravitational Fields > Flashcards

Gravitational Fields Flashcards

1
Q

Gravitational field

A

Region in which an object with mass experiences a force

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2
Q

Field lines

A

Arrows indicating the direction in which a small test mass would experience a force of attraction

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3
Q

Closer field lines

A

Stronger gravitational field

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4
Q

Equipotentials

A

Lines drawn to indicate points of equal potential

Cross so perpendicular to the field lines

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5
Q

How much work is done moving a test mass along an equipotential

A

None

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6
Q

Uniform field

A

Field lines are parallel to each other
Equipotentials are parallel to each other
Field lines and equipotentials are perpendicular to each other

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7
Q

Newton’s law of gravitation

A

The attractive force between two point masses is directly proportional to the product of their masses
And inversely proportional to the square of their separation

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8
Q

Mathematically express newtons law of gravitation

A

F∝Mm/r^2

F=GMm/r^2

G; Gravitational constant
M; Mass of one object
m; Mass of the other object
r; Distance between the centre of masses of each body

Technically should be negative

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9
Q

Units for G

A

Gravitational constant

Nm^2kg^-2

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10
Q

Assumptions when dealing with planets

A

Spherical

Uniform density so C.O.M is physical centre

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11
Q

Gravitational field strength

A

The force acting on a body per unit of mass

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12
Q

Equation for gravitational field strength

A

g=F/m

Where F is the force acting on the body
And m is the mass of the body in the field

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13
Q

Gravitating body

A

Any object/mass which creates a gravitational field

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14
Q

Test mass

A

Body with negligible size and mass

Which placed within the field will experience a force towards the gravitating body

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15
Q

Derive the equation for gravitational field strength and separation

A

F=gm
gm=GMm/r^2
g=GMm/r^2m
g=GM/r^2

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16
Q

How do you find the net gravitational field strength at a point if there are multiple gravitating bodies

A

Vector sum of the gravitational field strengths due to each of the gravitating bodies

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17
Q

Neutral point

A

Where the effective gravitational field strength is zero

Both gravitational field strengths have the same magnitude and are in opposite directions

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18
Q

Neutral point equation

A

m1/m2 = r1^2/r2^2

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19
Q

What happens when an object moves against the field

A

Moving away from the centre
Object does work against the field
Increasing its potential energy but decreasing its kinetic energy

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20
Q

What happens when an object moves along a field

A

Moves towards the centre
Field does work on the object
Attraction
Decreasing it potential energy but increases its kinetic energy

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21
Q

Absolute potential energy/potential energy

A

Work done in moving an object with mass from infinity to that point in the field

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22
Q

Equation for Potential energy in a uniform field

A

Ep=mgh

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23
Q

For a radial gravitational field where is the potential defined as zero

A

At infinity

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24
Q

Equation for potential energy in a radial field

A

Ep=-GMm/r

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25
Q

Is gravitational potential energy a scalar or vector

A

Scalar

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26
Q

How do you get the absolute potential energy for more than one pair of gravitating bodies

A

Add

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27
Q

Why is there a negative sign

A

Infinity defined as zero potential energy
When a body moves away from the gravitating body it gains potential energy
So it gets closer to zero
So it gets less negative

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28
Q

Absolute gravitational potential/potential

A

The work done per unit mass in moving a body from infinity to that point in the gravitational field

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29
Q

Is absolute potential a scalar or vector

A

Scalar

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30
Q

How do you convert absolute potential to potential energy

A

x mass

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31
Q

Explain V=-GM/r

A

The m is the mass of the object creating the gravitational field
Since it is the work done per unit mass to get the gravitational potential, the mass of the object cancel out on the top and on the bottom

V in Jkg^-1

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32
Q

How do you calculate the work done in moving an object (Ep)

A

mass x change in potential

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33
Q

How do you get the absolute potential at a point where two gravitational fields act

A

The sum of the gravitational potential of the two gravitating bodies

34
Q

Gravitational field strength given change in potential and radius

35
Q

Force given the change in potential energy and the change in radius

36
Q

Force and separation equation

37
Q

Force and separation ratio

A

F1r1^2 = F2r2^2

38
Q

Field strength and separation ratio

A

g1r1^2 = g2r2^2

39
Q

Potential and separation ratio

A

V1r1 = V2r2

40
Q

Potential energy and separation ratio

A

Ep1r1 = Ep2r2

41
Q

How does the gravitational constant change when going from earth to the moon

A

It doesn’t

It is the same everywhere

42
Q

Area under a force separation graph

A

Work done moving between the two points

Change in Ep

43
Q

Area under a field strength and separation graph

A

Change in potential

Work done per unit mass

44
Q

Gradient of potential separation graph

A

Magnitude of gravitational field strength

45
Q

Gradient of potential energy separation graph

A

Gravitational force

46
Q

Gravitational field strength in a sphere of uniform density aka planet

A

g=4/3 x πpGr

Where p is density and r is radius

47
Q

Gravitational potential inside a sphere of uniform density aka planet

A

V=-2/3 x πpGr^2

Where p is density and r is radius

48
Q

Orbital time period equation

KEPLERS THIRD LAW

A

T^2 = 4π^2r^3/GM

49
Q

Proportionality for orbital time period

KEPLERS THIRD LAW

A

T^2 ∝ r^3

50
Q

Kepler’s Third Law

A

The orbital time period squared is directly proportional to the radius of orbit squared

51
Q

Ratio for Kepler’s third law

A

T1^2/r1^3 = T2^2/r2^3

52
Q

How do you derive the equation for orbital time period

A
  1. Equate gravitational force equation to centripetal force equation in terms of angular velocity
  2. Cancel m
  3. Convert w into time (w=2π/T)
  4. Cancel and rearrange to get an equation for T^2
53
Q

Orbital velocity equation

54
Q

Escape velocity equation

A

v=√2GM/r

55
Q

How do you derive the equation for orbital velocity

A

Equating gravitational force and centripetal force in terms of v

56
Q

How do you derive the escape velocity

A

Equate kinetic energy to gravitational potential energy

57
Q

What is escape velocity

A

For something to escape its orbit its kinetic energy must be greater than the increase in potential energy moving from position to infinity

58
Q

When is an orbit stable

A

Total energy is negative

Magnitude of KE

59
Q

Kinetic energy of orbit

60
Q

How is the kinetic energy of orbit derived

A

Subbing in the orbital velocity into the kinetic energy formula

61
Q

Total energy of orbit

A

Ke+Pe = -GMm/2r

62
Q

Potential energy of orbit

63
Q

Orbital velocity and separation ratio

A

v1√r1 = v2√r2

64
Q

Escape velocity equation

A

v1√r1 = v2√r2

65
Q

What doesn’t escape velocity apply to

A

Rockets or objects that have an engine to generate kinetic energy

66
Q

Why can’t light escape a black hole

A

A black holes escape velocity is greater than the speed of light

67
Q

Explain energy changes in an increasing orbit

A

Distance from the centre of the planet increases
Potential energy increases to get less negative and closer to zero
Kinetic energy decreases
Work done against field
Total energy increases so less negative
Velocity decreases

68
Q

Explain energy changes in a decreasing orbit

A

Distance from the centre of the planet decreases
Potential energy decreases to get more negative and further from zero
Kinetic energy increases
Work done on object by field
Total energy decreases so more negative
Velocity increases

69
Q

Polar orbit

A

A satellite moving from north to south pole and back

Typical orbit of 2 hours

70
Q

What uses do satellites with polar orbits have

A

Can be positioned above any point on the Earth’s surface

Meteorology, weather, espionage, spying

71
Q

Low earth orbit

A 
Used by ISS and hubble telescope 
Most man made objects
Orbital period of less than 128 minutes
Orbital radius of less than 8400km
Close to earth so goo for observation and spy satellites (detailed images)
72
Q

Middle earth orbit

A

Anything above LEO but below geostationary
Orbital period between 2 and 24 hour (12 hours most common)
Used for GPS and galileo navigation satellites and communication satellites for communication in high latitude regions (near poles using polar orbits)

73
Q

High earth orbit

A

Anything with an orbital radius greater than geostationary

74
Q

Geosynchronous

A

24 hours to complete a cycle in same direction as earth is rotating

75
Q

Geostationary

A

Takes 24 hours to complete a cycle in the same direction as earth
Fixed to a point on its equator

76
Q

Advantage of geostationary

A

Ground dishes
Antennae
Aerials don’t need repositioning

77
Q

Geostationary satellite uses

A

Communications of television l
Mobile phones
Sat nava

78
Q

Issue with putting more satellites in orbit

A

Increased risk of collision

79
Q

Orbital radius for geostationary

A

42200km

*all geostationary orbits are at the same height

80
Q

Derive the equation for gravitational field strength in a sphere of uniform density

A 
State density equation
Rearrange for m
Sub in volume of a sphere
Rearrange the gravitational field strength equation
Rearrange to get

g=4/3piGpr

A Level Physics Paper 2 (7 decks)

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