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Physics AQA AS Level > Gravitational Fields > Flashcards

Gravitational Fields Flashcards

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1
Q

What is a gravitational field?

A
  • The force field around a mass (due to its mass).
  • If a second mass, with its own gravitational field is placed in the gravitational field of the first mass, the two masses will attract each other with an equal and opposite gravitational force of attraction.
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2
Q

When may it be difficult to see this attraction between two masses?

A

If one of the two masses, is much larger compared than, the gravitational force of attraction (due to the small mass) may be too small to move the larger body noticeably.

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3
Q

What is a field line in a gravitational field?

A
  • This is the path which a smaller test mass would follow when the gravtiational force of a larger mass acts on it
  • It is directed towards the centre of the large body.
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4
Q

What is the gravitational field strength?

A
  • The gravitational field strenth, g, is the force per unit mass on a small test mass placed in the gravitational field.
  • Different distances from the centre of the object have different gravitational field strengths, independant of the mass that is placed there.
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5
Q

When calculating the gravitational field strength of an object at a specific point, why does the test mass need to be small?

A

It needs to be small because, otherwise, it might pull so much on the other object, that it changes its position and alters the field.

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6
Q

If a small mass, m, is at a particular position in a gravitational field, where it is acted on by a gravitational force F, the gravitational field strength is given by:

A

F = mg

F = Gravitational Force (N)
m = Mass (kg)
g = Gravitational field strength (N/kg)
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7
Q

What is the gravitational field strength of the Earth at the SURFACE?

A

9.81N/kg

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8
Q

What is weight?

A

The weight of an object is the force of gravity acting on it due to its mass. Its position in the gravitational field determines the gravitational field strength at that position

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9
Q

If an object is not acted on by any other force apart from gravity its acceleration is given by…

A

…its gravitational field strength, g. (At the surface of the Earth that would 9.81ms-1). This is known as the acceleration of free fall.

This is because F = ma → F = mg → F/m = g → mg/m = g → g = g

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10
Q

What is a radial field?

A
  • A radial field is where the field lines are always directed towards the centre of a (spherical) object (not parallel or equally spaced). Any object placed in a radial field experiences a force towards the centre regardless of its position.
  • The magnitude of gravitational field strength in a radial field decreases with increasing distance from the body (inverse square law).
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11
Q

What is the uniform field?

A
  • A uniform field is where the field lines are parallel to one another and equally spaced.
  • The magnitude and direction of the gravitational field strength is the same throughout the field. For small distances much less than the Earth’s radius, e.g 100m above the Earth’s surface, the change of gravitational field strength is insignificant (9.81N/kg) so the field can be considered uniform at this point.
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12
Q

What happens to the gravitational field strength of an object, with increasing distance from the centre of the iobject?

A

With increasing distance from the centre of an object, the gravitational field strength decreases (never reaches zero though)

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13
Q

In terms of doing work, how would an object e.g. rocket escape a planet?
How would an object to completely escape the gravitational field of a planet?

A

For an object to escape a planet, it must do work against the gravitational force of attraction acting on it due to the planet.
When it does work against the gravitational force of attraction, its gravitational potential energy increases. Its value for GPE becomes more positive.
For an object to completely escape the gravitational field of an object, it must do work to increase its GPE to zero.

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14
Q

What is the maximum value of GPE and what distance does a system need to move against the gravitational field strength to achieve it?
What does this value tell us about the value of GPE at the surface of a planet?

A

The gravitational potential energy of a system is maximum at a distance of infinity and it this point is has a maximum value of zero.
This makes all other values of GPE negative (including that at the surface of a planet).

REMEMBER GPE CHANGE IS STILL POSITIVE!

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15
Q

So what is GPE?

A

GPE is the energy of an object due to its position in a gravitational field.

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16
Q

For an object at distance infinity from the centre of another object, what is the gravitational field strength on that object?

A

It is negligible.

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17
Q

What is gravitaitonal potential?

A

The gravitational potential at a point in a gravitational field is the GPE per unit mass when moving an object from infinity to that point.

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18
Q

Equation to calculate gravtiational potential?

A

V = W/m

V = Gravitational potential (Jkg⁻¹)
W = Work done (J)
m = mass (kg)

The equation is rearranged to W = V/m to calculate GPE when the field is not uniform.

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19
Q

When work is done for a mass to move against the direction of the gravitational field, what energy store is the energy transferred to?

A

The gravitiational potential energy store of the object.

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20
Q

What are equipotentials?

A

These are surfaces of constant potential.

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21
Q

What is the work done to move a mass along an equipotential surface?

A

The work done to move a mass along an equipotential surface is zero.
I.E. if your gravitational potential is constant, your gravtiational potential energy remains constant.

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22
Q

On maps what depicts surfaces of constant equipotential?

A

Contour lines. Where contour lines are closer, the steepness of the ground is greater.

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23
Q

Describe the equipotentials around the Earth.

A
  • The equipotentials around Earth are circles.
  • As distance from the Earth’s surface ↑ , the GFS ↓
  • ∴ less work is done against the GFA ↓
  • ∴ rate of increase of GPE/the gain of GPE per metre of height gained ↓
  • ∴ rate of increase of potential/ the gain of GP with height ↓
  • ∴ for equal increases of potential, the equipotentials are spaced further apart.

Check with sir.

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24
Q

How do equipotentials tell you a field (i.e. the field strength) is uniform?

A

The equipotentials are horizontal and parallel to the ground. The equipotentials are equidistant for equal changes of potential. This can be seen at the surface of the Earth, where every 1m increase in height for a mass of 1kg through the uniform field, the gain in energy is 9.81J.

25
Q

For a uniform field, which equation can you use to clculate thegain in gravitational potential energy?

A

GPE = mgh

GPE = Gravitational potential energy (J)
m = mass (kg)
g = gravitational field strength of uniform field (Nkg⁻¹)
h = height moved (m)
26
Q

What is the potential gradient?

A

The potential gradient at a point in a gravitational field is the change of potential per metre at that point.

At the Earth’s surface, the potential changes by 9.81Jkg⁻¹ for every metre of height gained so potential gradient at surface of Earth is constant and equal to 9.81Jkg⁻¹m⁻¹.

27
Q

Equation to calculate potential gradient?

A

potential gradient, g = - ΔV/Δr

negative of gravitational field strength = ΔV/Δr

potential gradient has units Jkg⁻¹m⁻¹
g = gravitational field strength (Nkg⁻¹)
V = gravitational potential (Jkg⁻¹)
r = distance moved

28
Q

Define gravitational field strength in terms of potential gradient

A

The potential gradient is the negative of the gravitational field strength. The negative tells us that potential gradient acts in the opposite direction to gravitational field strength (it is a vector).

29
Q

If the field is uniform, what is the potential gradient?

A

If the field is uniform, potential gradient = -negative gravitational field strength of the uniform field.

Does the field have to be uniform?

30
Q

What is Newton’s Law of Gravtitation?

Equation?

A

This assumes that the gravitational force between any two points is:

  • Always attractive force
  • Proportional to the PRODUCT of the mass of each object.
  • Inversely proportional to r², where r is the distance between their centres.

F = Gm₁m₂/r²

F = Gravitational force (N)
G = Universal constant of Gravitation (6.67x1⁻¹¹ Nm²kg⁻¹)
m₁ = Mass of object 1
m₂ = Mass of object 2
r = distance between the object's centres

*When talking about planets we change m₁ to M and m₂ to m.

31
Q

How can we calculate gravitational field strength using the gravitational force equation?

A

F = mg -> g = F/m

F = Gm₁m₂/r²

Combine:

g = GM/r²

g = gravitational field strength (Nkg⁻¹)
G =  Universal constant of Gravitation (6.67x10⁻¹¹ Nm²kg⁻¹)
M = Mass of object
r = distance from the centre of mass M
32
Q

What is the gravitational field strength at the surface of a planet of mass M?

A

gᵣ = GM/R²

g = gravitational field strength (Nkg⁻¹)
G =  Universal constant of Gravitation (6.67x10⁻¹¹ Nm²kg⁻¹)
M = Mass of object
R = radius of planet with mass M
33
Q

How does the gravitational field strength vary with increasing distance from a planet of radius R?

A

Gravitational field strength increases linearly up to the point when distance from the centre of the planet equals the radius of the planet. Beyond r= R, gravitational field strength decreases in inverse proportion to r².

34
Q

Draw the graph of how gravitational field strength varies with distance from a planet of radius R

A

IN BOOK

35
Q

How can you calculate the gravitational potential V at distance r from the centre of a planet of mass M?

A

V = - GM/r

G =  Universal constant of Gravitation (6.67x10⁻¹¹ Nm²kg⁻¹)
M = Mass of object
r = distance from the centre of mass M
36
Q

How can you calculate the work done for an object to escape the gravitational field of a planet from its surface?

A 
W = mV
V = - GM/R

Combine:

W = GMm/R

G =  Universal constant of Gravitation (6.67x1⁻¹¹ Nm²kg⁻¹)
M = Mass of object
r = radius of the planet

*This is calculating the work done to move it from infinity to the surface of the planet.

37
Q

What is the escape velocity (from a planet)?

A

The escape velocity is the minimum velocity an object must be given to escape from the gravitational field of a planet when projected vertically.

38
Q

How to calculate escape velocity?

A

Vᵉˢᶜ = Square root of 2gR
OR
Vᵉˢᶜ = Square root of 2GM/R

Vᵉˢᶜ = escape velocity
g = gravitational field strength
G =  Universal constant of Gravitation (6.67x1⁻¹¹ Nm²kg⁻¹)
M = Mass of object
R = radius of planet
39
Q 
Draw a graph of the force needed to move a mass of 1kg against the distance from the centre of the planet.
Label R (Radius) and what does the area under the graph tell you.
A

In book, pg348. Can the graph touch the x axis?
Area under graph tells you the work done to move the 1kg mass from infinity to the surface. Therefore it can be used to calculate the gravitational potential at the surface.

40
Q

We have looked at how gravitational field strngth varies with distance from centre of the planet. We have looked at how force needed to move a 1kg mass varies with distance fromt eh centre of the planet. How does gravitational potential vary with distance from the centre of a planet? Draw a graph.

A

The graviational potential is inversley proportional to the distance from the centre of the planet. Using equation V = -GM/r

41
Q

What does the gradient of a gravitational potential against distance graph tell you?

A

The potential gradient at that specific point. This is the same as the negative gravitational field strength at that point.

42
Q

What is Kepler’s Third Law?

A

The square of a object’s (e.g. a plant or satellite) orbital time period is proportional to the cube of its distance from e.g. a star or planet (the Sun), given by r³/T²

43
Q

How did Newtons prove Kepler’s Law? Give derivation.

A

Any object udndergoing circular motion is kept in its path by a centripetal force. In the case of a satellite orbiting a plant or a planet orbiting the Sun, this force is the gravitational force of attraction.

Centripetal Force, F = mv²/r
Gravitational Force, F = GMm/r²

We can therefore set the two expressions equal to each other and rearrange to find the orbital speed squared:

v² = GM/r

As speed is equal to 2πr/T, we can re write this as
(2πr/T)² = GM/r
4π²r²/T² = GM/r

This can be rearranged to give
r³/T² = GM/4π²

GM/4π² is a constant e.g. k
so r³ = kT² which tells us that r³ ∝ T².

44
Q

What is the equation calculate the kinetic energy of a satellite?

A

We know that
v² = GM/r
To find kinetic energy, we can times both sides of the equation by 1/2m. This gives 1/2mv² = GMm/2r

so KE = GMm/2r

where:
G = Universal constant of Gravitation (6.67x1⁻¹¹ Nm²kg⁻¹)
M = Mass of planet (kg)
m = Mass of satellite (kg)
r = distance between the satellite’s centre and the planet’s centre (m)

45
Q

What is the equation calculate the gravitational potential energy of a satellite?

A

GPE = mV = -GMm/r

where:
G = Universal constant of Gravitation (6.67x1⁻¹¹ Nm²kg⁻¹)
M = Mass of planet (kg)
m = Mass of satellite (kg)
r = distance between the satellite’s centre and the planet’s centre (m)

46
Q

What is the total energy of a satellite?

A 
E = GPE + KE
E = -GMm/r + GMm/2r = -GMm/2r

Notice that the total energy is always negative. As kinetic energy increase, potential energy will decrease and vice versa - this means that the total energy remains constant.

47
Q

What is a synchronous orbit?

A

This is when an orbiting object has the same orbital period as the rotational period of the object is it orbiting.

48
Q

What is an example of object in synchronous orbit?

A

Geostationary satellites

49
Q

How do geostationary satellites work?

A
  • Their orbital period is equal to the Earth’s rotataional period. To achieve this their orbit is always directly above the plane of the equator. They are always above the same point on Earth.
50
Q

At which speed do geostationary satellites above the Earth travel at? What is the time period of this geostationary satellite?

A
  • Geostationary orbits have the same angular speed as the Earth and moves in the same direction as the Earth.
  • The orbital period of Earth is 24 hours, and therefore the orbital period of the geostationary satellite is also 24hours.
51
Q

What height is a geostationary satellite above the Earth’s surface?

A

36,000km

52
Q

What are geostationary satellites used for?

A

Useeful for sending TV and telephone signals - as the satellits position remains the same, the angle of the reciever/transmitter does not need to be altered.

53
Q

What are low orbiting satellites?

A

Satellites which orbit between 180km and 200km above the Earth.
- Their orbits usually lie in a plane that includes the north and south pole.

54
Q

Benefits of low orbiting satellites?

A
  • Cheaper to launch

- Requires less powerful transmitters as they are closer which makes them useful for communications

55
Q

Disadvantages of low orbiting satellites?

A

Close proximity to the Earth and high orbital speed in comparison to Earth’s rotational speed means you need multiple satellites working together to maintain coverage.

56
Q

What is a benefit of low orbiting telescopes being at a close proimity to the Earth’s surface?

A

Able to capture to the surface of the Earth in a high level of detail. For this reason, imaging satellites used for mapping, spying and monitoring weather, are usually placed in low orbit.

57
Q

The low orbiting satellite has a differnet orbital speed to the to rotational speed ofEarth. What is a benefit of the satellite having a different angular speed to the Earth?

A

As the satellite and planet rotate at different angular speeds, the satellite does not stay over the same part of the Earth, therefore the whole of the Earth’s surface can be scanned.

58
Q

What is the gravitational energy of two point masses?

A

Ep = -Gm₁m₂/r

59
Q

Where is the position where gravitational potential is zero, and what does this mean?

A

The position of zero potential is at a distance of infinity, this means all other values of gravitational potential is negative.

Physics AQA AS Level (16 decks)

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