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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
Is gravitational potential energy a scalar or vector
Scalar
26
How do you get the absolute potential energy for more than one pair of gravitating bodies
Add
27
Why is there a negative sign
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
28
Absolute gravitational potential/potential
The work done per unit mass in moving a body from infinity to that point in the gravitational field
29
Is absolute potential a scalar or vector
Scalar
30
How do you convert absolute potential to potential energy
x mass
31
Explain V=-GM/r
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
32
How do you calculate the work done in moving an object (Ep)
mass x change in potential
33
How do you get the absolute potential at a point where two gravitational fields act
The sum of the gravitational potential of the two gravitating bodies
34
Gravitational field strength given change in potential and radius
g=-V/r
35
Force given the change in potential energy and the change in radius
F=-E/r
36
Force and separation equation
F=GMm/r^2
37
Force and separation ratio
F1r1^2 = F2r2^2
38
Field strength and separation ratio
g1r1^2 = g2r2^2
39
Potential and separation ratio
V1r1 = V2r2
40
Potential energy and separation ratio
Ep1r1 = Ep2r2
41
How does the gravitational constant change when going from earth to the moon
It doesn't | It is the same everywhere
42
Area under a force separation graph
Work done moving between the two points | Change in Ep
43
Area under a field strength and separation graph
Change in potential | Work done per unit mass
44
Gradient of potential separation graph
Magnitude of gravitational field strength
45
Gradient of potential energy separation graph
Gravitational force
46
Gravitational field strength in a sphere of uniform density aka planet
g=4/3 x πpGr Where p is density and r is radius
47
Gravitational potential inside a sphere of uniform density aka planet
V=-2/3 x πpGr^2 Where p is density and r is radius
48
Orbital time period equation KEPLERS THIRD LAW
T^2 = 4π^2r^3/GM
49
Proportionality for orbital time period KEPLERS THIRD LAW
T^2 ∝ r^3
50
Kepler's Third Law
The orbital time period squared is directly proportional to the radius of orbit squared
51
Ratio for Kepler's third law
T1^2/r1^3 = T2^2/r2^3
52
How do you derive the equation for orbital time period
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
Orbital velocity equation
v=√GM/r
54
Escape velocity equation
v=√2GM/r
55
How do you derive the equation for orbital velocity
Equating gravitational force and centripetal force in terms of v
56
How do you derive the escape velocity
Equate kinetic energy to gravitational potential energy
57
What is escape velocity
For something to escape its orbit its kinetic energy must be greater than the increase in potential energy moving from position to infinity
58
When is an orbit stable
Total energy is negative | Magnitude of KE
59
Kinetic energy of orbit
GMm/2r
60
How is the kinetic energy of orbit derived
Subbing in the orbital velocity into the kinetic energy formula
61
Total energy of orbit
Ke+Pe = -GMm/2r
62
Potential energy of orbit
-GMm/r
63
Orbital velocity and separation ratio
v1√r1 = v2√r2
64
Escape velocity equation
v1√r1 = v2√r2
65
What doesn't escape velocity apply to
Rockets or objects that have an engine to generate kinetic energy
66
Why can't light escape a black hole
A black holes escape velocity is greater than the speed of light
67
Explain energy changes in an increasing orbit
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
Explain energy changes in a decreasing orbit
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
Polar orbit
A satellite moving from north to south pole and back | Typical orbit of 2 hours
70
What uses do satellites with polar orbits have
Can be positioned above any point on the Earth's surface | Meteorology, weather, espionage, spying
71
Low earth orbit
``` 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
Middle earth orbit
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
High earth orbit
Anything with an orbital radius greater than geostationary
74
Geosynchronous
24 hours to complete a cycle in same direction as earth is rotating
75
Geostationary
Takes 24 hours to complete a cycle in the same direction as earth Fixed to a point on its equator
76
Advantage of geostationary
Ground dishes Antennae Aerials don't need repositioning
77
Geostationary satellite uses
Communications of television l Mobile phones Sat nava
78
Issue with putting more satellites in orbit
Increased risk of collision
79
Orbital radius for geostationary
42200km *all geostationary orbits are at the same height
80
Derive the equation for gravitational field strength in a sphere of uniform density
``` 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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