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Physics Year 13 > Chapter 18 - Gravitational Fields > Flashcards

Chapter 18 - Gravitational Fields Flashcards

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
what is the equation for E (GPE using Vg)
``` E = mVg or Delta(E) = m(deltaVg) ```
26
how can you change GPE when in a uniform field
- 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
what is the equation for GPE and roughly how to derive it
E = -GMm/r because E = mVg and Vg = -GM/r
28
what does the area under a (gravitational) force against r graph represent
GPE
29
how can we calculate escape velocity
``` set GPE from point r equal to KE so 1/2mv^2 = -GMm/r V^2 = -2GM/r V = sqrt(2GM/r) ```
30
state Kepler's first law of planetary motion
"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
state what aphelion and perihelion mean
``` aphelion = point of orbit furthest from the sun perihelion = point of orbit closest to the sun ```
32
state Kepler's second law of planetary motion
"a line segment joining a planet and the sun sweeps out equal areas in equal time periods"
33
what is a result of Kepler's second law
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
state Kepler's third law and give the proportionality that arises from it
"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
how can we model the orbits of the planets
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
which two equations arise from modelling the planetary orbits as circular motion
V = sqrt(GM/r) T^2 = (4(pi)^2/GM) (r^3)
37
what is the gradient of a line of T^2 against r^3
4(pi)^2/GM
38
state how we can model orbits
as circles so gravitational force = centripetal force so v = sqrt(GM/r)
39
what can we say about all satellites at the same altitude/radius
they are all at the same speed
40
name 5 uses of satellites
- communications - military uses - scientific research - weather and climate monitoring - GPS
41
what are the 3 types of orbit
polar, low earth orbit, geostationary
42
state the features of a polar orbit
- orbits the poles - earth rotates underneath it so it can obtain a view of the whole earth - good for mapping/reconnaissance
43
state the features of a low earth orbit
- low altitude - as T^2 is direct prop to r^3, it has a low orbital period - orbital period usually < 2 hours
44
state the features of a geostationary orbit
- orbit above the equator - orbit in the same direction as the earth's rotation - orbital period = day length = 24 hours
45
for an object in orbit around a planet/star what two forms of energy does it have and how can we calculate total energy
- kinetic energy - GPE total energy = kinetic energy + (GPE) but remember GPE has a negative sign so effectively Etot = Ek - GPE
46
if something is x radii above the surface of a planet of radii r, what is its actual radius
(x+1) r
47
why is it not possible to be in a (geo)stationary orbit over the south pole of a planet
- orbit must be equatorial/coincide with the centre of mass of the planet - must orbit in same direction as planet
48
why must geostationary satellites orbit around the equator
so they stay at the same point in the sky

Physics Year 13 (15 decks)

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