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Physics paper 2 > Gravitational fields > Flashcards

Gravitational fields Flashcards

1
Q

What is the equation for the gravitational force between two point masses?

A

F = Gm₁m₂ / r²

Where:
* F = Force (N)
* G = Gravitational constant = 6.67 x 10^-11 Nm²/kg²
* m = Mass (kg)
* r = Distance between centres of two point masses (m)

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2
Q

What is the equation for the speed of an object orbiting a larger object (e.g. a planet)?

A

GMm/r² = mv² /r.

equating centripetal force equation to gravity equation

The smalls m’s cancel and one of the r’s cancel.

V = √GM/r
(Not given on formula sheet)

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3
Q

What is the equation of the time period of earths orbit?

A

Time = distance/speed.

T = 2πr/v
(Not given on formula sheet)

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4
Q

What type of law is Newton’s Law of Gravitation and how can this be symbolised?

A

Inverse square law
* F ∝ 1 / r²

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5
Q

What is gravitational field strength?

A
  • The force per unit mass exerted at a given position in a gravitational field.
    OR
  • The acceleration of a mass in a gravitational field.
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6
Q

What is the symbol for gravitational field strength?

A

g

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7
Q

What are the units for gravitational field strength?

A

N/kg or m/s²

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8
Q

What is the equation that defines gravitational field strength?

A

g = F / m

Where:
* g = Gravitational field strength (N/kg)
* F = Force (N)
* m = Mass (kg)

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9
Q

Is the value of g constant throughout a field?

A

No, its value depends on the where you are in the field.

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10
Q

What is the value of g at the Earth’s surface?

A

9.81 N/kg (or m/s²)

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11
Q

In a radial field, how does g vary with the radius from the centre of the mass?

A

g is inversely proportional to r²

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12
Q

Give the equation for g around a point mass.

A

g = GM / r²

OR

g = -ΔV / Δr

Where:
* g = Gravitational field strength (N/kg)
* G = Gravitational constant (Nm²/kg²)
* M = Point mass (kg)
* r = Distance from centre (m)
* V = Gravitational potential (J/kg)

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13
Q

What is gravitational potential?

A

The gravitational potential at a point is defined as the work done per unit mass in bringing a test mass from infinity to a defined point.

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14
Q

What is the symbol for gravitational potential?

A

V

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15
Q

What are the units for gravitational potential?

A

J/kg

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16
Q

What is the difference between gravitational potential energy and gravitational potential?

A

-Gravitational potential -> GPE that a unit mass would have at a given point in a gravitational field
-Gravitational potential energy -> The energy that a mass has due to its position in a gravitational field

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17
Q

What is the equation for gravitational potential?

A

V = -GM / r

Where:
* V = Gravitational potential (J/kg)
* G = Gravitational constant = 6.67 x 10^-11 Nm²/kg²
* M = Mass of point mass (kg)
* r = Distance from centre of point mass (m)

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18
Q

What is unusual about gravitational potential and GPE? Why?

A

-They are negative, since you can think of it of as negative energy since work has to be done to move an object out of the field
-They becomes less negative with distance from the point mass
-At infinite distance, the gravitational potential is 0J/kg and GPE is 0J

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19
Q

How is g = GM / r² derived?

A
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20
Q

Describe how gravitational potential (and GPE) changes with distance from a planet’s surface.

A

-Most negative on the planet’s surface
-Becomes less negative with distance from the planet
-0J/kg at infinite distance

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21
Q

What does the gradient of a V-r graph for a point mass show?

A

The value of g

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22
Q

What is escape velocity?

A

-The velocity at which an object’s kinetic energy is equal to minus its gravitational potential energy
-It is the minimum velocity at which an object must travel in order to escape a gravitational field

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23
Q

What is an object’s total energy when it travels at escape velocity?

A

Zero
* Because the kinetic energy and GPE sum to 0 (since GPE is always negative)

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24
Q

What is the equation for escape velocity?

A

v = √(2GM/r)

Where:
* v = Escape velocity (ms⁻²)
* G = Gravitational constant = 6.67 x 10^-11 Nm²/kg²
* M = Mass of point mass (kg)
* r = Distance from centre of point mass (m)

(Not given on formula sheet)

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25
Q

Derive the equation for escape velocity.

A

KE = 1/2mv²
GPE = -GMm/r
1/2mv² = GMm/r
1/2v² = GM/r
v² = 2GM/r
v = √(2GM/r)

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26
Q

What is the equation for GPE relative to G, M and r instead of mgh?

A

GPE = -GMm/r

This is derived from V = -GM/r

(Not given on formula sheet)

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27
Q

How do you derive GPE = -GMm/r

A

Work done = m x V.

V = -GM/r

replace V with mV (which is work done) =
mV = -GMm/r, which is
GPE = -GMm/r

28
Q

How do you find the change in kinetic energy of a satellite when it moves from and orbit of R1 to a lower orbit of R2?

A

(GPE lost = KE gained).

v = √(GM / r).

KE = 1/2 mv^2.

KE = 1/2 m(√(GM / r))^2

KE = GMm/2r

Change in KE = GMm/2(R1) - GMm/2(R2)

29
Q

Is escape velocity dependent on the mass of the object?

A

No, it is the same for all masses in a gravitational field.

30
Q

What is gravitational potential difference?

A

The energy needed to move a unit mass between two gravity sonar potentials.

31
Q

What is the equation for gravitational potential difference?

A

ΔV = Vf - Vi (J kg-1)

Gravitational potential difference = Final gravitational potential - Initial gravitational potential

32
Q

What is the equation for the work done when moving an object through a gravitational potential difference?

A

ΔW = mΔV

Where:
* ΔW = Work fine (J)
* m = Mass (kg)
* ΔV = Gravitational potential difference (J/kg)

33
Q

What are equipotentials?

A

Lines (in 2D) or surfaces (in 3D) that join all of the points with the same potential (V).

If you travel along an equipotential, your potential doesn’t change.

No work is done moving an object along an equipotential.

34
Q

Describe how equipotential and field lines are related in gravitational fields.

A

They are perpendicular.

35
Q

What force keeps an object undergoing circular motion in orbit?

A

Centripetal force

36
Q

In the case of a satellite orbiting the Earth, what is the centripetal force?

A

Gravitational force.

They are kept in orbit by the gravitational “pull” of of the mass (Earth) they orbit.

37
Q

Give the relationship between the time period and radius of an orbit.

A
  • T² = 4π²r³ / GM
    So
  • T² ∝ r³

(Not given on formula sheet)

38
Q

How is the speed of a satellite related to its orbital radius?

A
  • v = √(GM / r)
    So:
  • v ∝ 1 / √r

So greater radius = lower speed

(NOTE: This comes from the first part of the T² ∝ r³ derivation.)

39
Q

If T² ∝ r³, what can be said to be constant?

A

T² / r³ = Constant

40
Q

What can be said about the energy of an orbiting satellite?

A

It is constant, since the kinetic and potential energy always sum to a constant value.

41
Q

Why is a satellite’s energy constant in elliptical orbit?

A

-The satellite speeds up as it’s orbital radius decreases and slows down as orbital radius increases
-So kinetic energy increases as potential energy decreases (and vice versa)
-So the total energy remains constant

42
Q

What is a synchronous orbit?

A

Where the orbital period is the same as the rotational period of the orbited object.

43
Q

What are the two types of satellite?

A

-Geostationary
-Low orbit

44
Q

What are geostationary satellites?

A

Satellites that have the same angular speed as the Earth turns below them, so that they stay in the same position above the Earth.

45
Q

Describe the orbit that geostationary satellites have.

A

Synchronous, along the equator.

46
Q

What is the time period of orbit of a geostationary satellite?

A

1 day

47
Q

What is the orbital radius of a geostationary satellite?

A

42,000km (about 36,000km above the Earth’s surface)

48
Q

What are geostationary satellites used for?

A

Sending TV and telephone signals.

49
Q

What are low orbit satellites?

A

Satellites that orbit between 180-2000km above the Earth, so that they do not stay in the same place relative to the Earth.

50
Q

Describe the orbit that low-orbit satellites have.

A

Usually in a plane that includes the north and south pole.

51
Q

Compare the advantages of low orbit satellites and geostationary satellites.

A

Low orbit
* Cheaper to launch
* Require less powerful transmitters since they are close to Earth
Geostationary
* Do not require multiple satellites to achieve constant reception in one area

52
Q

What are low orbit satellites used for?

A

Communications -> Cheap to launch and do not require powerful transmitters, although many are required for constant coverage
Imaging and weather -> Due to being close enough to see surface in high detail

53
Q

What kind of satellite is the ISS?

A

Low orbiting

54
Q

State 2 reasons why rockets launched from the Earth’s surface do not need to achieve escape velocity to reach their orbit?

A

They don’t need to escape gravitational field, only need to reach the orbit = less energy required.

Energy is added during the flight (with fuel) providing a continuous thrust.

55
Q

What is the equation for the work done to move a mass through a gravitational field?

A

ΔW = mΔV

Where:
* ΔW = Work done (J)
* m = Mass (kg)
* ΔV = Potential difference (ΔV)

56
Q

Derive the equation for the work done to move a mass through a gravitational field.

A

g = -ΔV / Δr = F / m (since the gravitational field is considered near uniform near the Earth)
mΔV = -FΔr
ΔW = mΔV

57
Q

What is Kepler’s third law?

A

The time of one orbit T, and the distance from the planet to the sun r, are related by T² ∝ r³

58
Q

How many geostationary satellites would be able to cover the entire earth?

A

3 placed into orbit 120 degrees apart above the equator

59
Q

What is the equation for GPE in a radial field?

A

GPE = –GMm/r

note this is not change in GPE

60
Q

Is gravitational potential a scalar or vector?

A

Scalar

61
Q

Is gravitational field strength vector or scalar?

A

Vector

62
Q

Is the force between two masses vector or scalar?

A

Vector

63
Q

Is gravitational potential energy vector or scalar?

A

Scalar

64
Q

What is the unit for gravitational potential?

A

J kg-1

65
Q

What is a synchronous orbit?

A

An orbit where the satellite has a period equal to that of the body being orbited

Physics paper 2 (7 decks)

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