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Physics Year 13 > Chapter 18 - Gravitational Fields > Flashcards

Chapter 18 - Gravitational Fields Flashcards

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1
Q

describe the key points about a gravitational field (3)

A
  • all objects with mass create a gravitational field around them
  • any object with mass in this field experiences an attractive force
  • this field extends to infinity
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2
Q

Define Gravitational field strength

A

“The Gravitational field strength, g, at a point within a field is the gravitational force exerted per unit mass on a small object placed in that field”

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3
Q

what is the equation for gravitational field strength and its units

A 
g = f/m
g = ms^-2 or Nkg^-1
f = N or kgms^-2
m = kg
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4
Q

what sort of quantity is gravitational field strength

A

vector

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5
Q

how do we map gravitational fields and what are the key points to remember about it (4)

A

using gravitational field lines:

  • they never cross
  • show the direction of attraction
  • equidistant = uniform field
  • closer lines = stronger field
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6
Q

what sort of field do spherical objects form and why can we model them as point masses

A
  • radial fields
  • lines pointing into the centre
  • point masses form almost identical fields so we can model even very large spherical objects as point masses
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7
Q

define newtons law of gravitation

A

“Newton’s law of gravitation states that the force between two 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

state the equation for newtons law of gravity

A

F = -GMm/r^2

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9
Q

what is the value of G

A

G is the gravitational constant

6.67 x 10^-11

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10
Q

what do we need to remember in questions where an object is acted upon by multiple forces

A

do vector addition/resolving in order to find the overall force

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11
Q

why do we gave a negative sign when doing force due to gravity or gravitational field strength

A

they are vectors, they act towards the mass

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12
Q

what do graphs of f against r and f against 1/r^2 look like

A

f against r is a negative reciporical (squared)

f against 1/r^2 is a straight line of negative gradient -GMm

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13
Q

what happens to the strength of the gravitational field in a radial field

A

it decreases with distance from the object

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14
Q

how to derive the equation not including force for g

A 
g = f/m
f = -GMm/r^2
so 
g = -GMm/r^2m
g = -GM/r^2
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15
Q

what proportionalities does gravitational field strength for a radial field have

A
  • it is directly proportional to the mass of the object forming it
  • it is inversely proportional to the square of the distance from the object forming it
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16
Q

what do graphs of g against r and g against 1/r^2 look like

A

g against r is a negative square reciporical

g against 1/r^2 is a straight line of negative gradient -GM

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17
Q

define gravitational potential

A

gravitational potential, Vg, at a point in space is the work done per unit mass in bringing an object to that point from infinity

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18
Q

what are the key points to remember about gravitational potential

A
  • it’s always negative as a value
  • it is scalar
  • it has units of JKg^-1
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19
Q

what is the gravitational potential equation, what are the two factors
what are the two factors on gravitational potential

A

Vg = -GM/r

Vg is directly proportional to the mass of the object forming the gravitational field
Vg is inversely proportional to the distance from the massive object’s centre

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20
Q

what is a rough way to derive Vg

A 
W = Fx
we know F = -GMm/r^2
so W = -GMm/r
and as Vg is the work done PER unit mass
Vg = W/m = -GM/r
21
Q

what will a graph of Vg against r look like

A

a negative reciporical

22
Q

what will a graph of Vg against 1/r look like

A

a straight line with a negative gradient

gradient = -GM

23
Q

what occurs to the value of Vg when you move towards or away from an object

A

towards = r decreases, so Vg becomes more negative

away from = r increases, so Vg becomes less negative

24
Q

define gravitational potential energy

A

The gravitational potential energy, E, of any object with mass within a gravitational field is defined as the work done to move that mass from infinity to a point within the gravitational field of potential Vg

25
Q

what is the equation for E (GPE using Vg)

A 
E = mVg
or
Delta(E) = m(deltaVg)
26
Q

how can you change GPE when in a uniform field

A
  • GPE changes when Vg changes and therefore when r changes

- this occurs when r increases, so the object moves up, not to the side

27
Q

what is the equation for GPE and roughly how to derive it

A

E = -GMm/r

because E = mVg and Vg = -GM/r

28
Q

what does the area under a (gravitational) force against r graph represent

A

GPE

29
Q

how can we calculate escape velocity

A 
set GPE from point r equal to KE
so
1/2mv^2 = -GMm/r
V^2 = -2GM/r
V = sqrt(2GM/r)
30
Q

state Kepler’s first law of planetary motion

A

“The orbit of a planet is an ellipse with the sun at one of the two foci”

most planetary motion tends to have low eccentricity

31
Q

state what aphelion and perihelion mean

A 
aphelion = point of orbit furthest from the sun
perihelion = point of orbit closest to the sun
32
Q

state Kepler’s second law of planetary motion

A

“a line segment joining a planet and the sun sweeps out equal areas in equal time periods”

33
Q

what is a result of Kepler’s second law

A

the planet must be moving faster at the points closer to the orbital centre in order to sweep out the same area as it has a lower radius

34
Q

state Kepler’s third law and give the proportionality that arises from it

A

“the square of the orbital period, T, is directly proportional to the cube of its average distance, r, from the sun”

T^2 directly proportional r^3
or T^2/r^3 = k

35
Q

how can we model the orbits of the planets

A

model as circular motion
gravity = centripetal force
GMm/r^2 = mV^2/r
GM/r = V^2

V = 2(pi)r/T
and substitute in to get T^2 = ….

36
Q

which two equations arise from modelling the planetary orbits as circular motion

A

V = sqrt(GM/r)

T^2 = (4(pi)^2/GM) (r^3)

37
Q

what is the gradient of a line of T^2 against r^3

A

4(pi)^2/GM

38
Q

state how we can model orbits

A

as circles so
gravitational force = centripetal force
so
v = sqrt(GM/r)

39
Q

what can we say about all satellites at the same altitude/radius

A

they are all at the same speed

40
Q

name 5 uses of satellites

A
  • communications
  • military uses
  • scientific research
  • weather and climate monitoring
  • GPS
41
Q

what are the 3 types of orbit

A

polar, low earth orbit, geostationary

42
Q

state the features of a polar orbit

A
  • orbits the poles
  • earth rotates underneath it so it can obtain a view of the whole earth
  • good for mapping/reconnaissance
43
Q

state the features of a low earth orbit

A
  • low altitude
  • as T^2 is direct prop to r^3, it has a low orbital period
  • orbital period usually < 2 hours
44
Q

state the features of a geostationary orbit

A
  • orbit above the equator
  • orbit in the same direction as the earth’s rotation
  • orbital period = day length = 24 hours
45
Q

for an object in orbit around a planet/star what two forms of energy does it have and how can we calculate total energy

A
  • kinetic energy
  • GPE

total energy = kinetic energy + (GPE)
but remember GPE has a negative sign so effectively

Etot = Ek - GPE

46
Q

if something is x radii above the surface of a planet of radii r, what is its actual radius

A

(x+1) r

47
Q

why is it not possible to be in a (geo)stationary orbit over the south pole of a planet

A
  • orbit must be equatorial/coincide with the centre of mass of the planet
  • must orbit in same direction as planet
48
Q

why must geostationary satellites orbit around the equator

A

so they stay at the same point in the sky

Physics Year 13 (15 decks)

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