Physics
HSC Course
Stage 6
Space
Part 5: Space travel and communication
Contents
Introduction ............................................................................... 2
Some difficulties of space probe exploration ............................. 4
Spacecraft communication ........................................................ 5
Communication difficulties ...................................................................7
Spacecraft velocities ............................................................... 16
Relativistic space travel........................................................... 18
The aether model ...............................................................................18
The Michelson-Morley experiment ....................................................19
Einstein ................................................................................... 27
The principle of relativity ....................................................................27
The speed of light...............................................................................30
The theory published..........................................................................32
Summary................................................................................. 34
Suggested answers................................................................. 37
Exercises – Part 5 ................................................................... 41
Part 5: Space travel and communication
1
Introduction
In the previous part you examined the nature of circular motion as a
simple model of the orbital motion of a satellite and the problems of
returning a manned spacecraft to the surface of the Earth. In this part
you will learn about some of the problems encountered when exploring
space by space probe. The focus will then shift to a consideration of the
prevailing scientific thought at the time when Albert Einstein conceived
his theory of relativity. In particular, you will learn about the
‘luminiferous aether’ and the postulates of the special theory of relativity.
Before beginning this topic you must have already studied certain
concepts. In particular you must be able to:
∑
explain the difference between low Earth orbit and geostationary
orbit
∑
describe the nature of solar radiation, electromagnetic radiation and
solar wind
∑
describe the Van Allen radiation belts
∑
describe Newton’s first law of motion
∑
r
r
r
apply the definition of velocity: v = D .
t
In this part you will be given opportunities to learn to:
2
•
discuss the limitation of current maximum velocities being too slow
for extended space travel to be viable
•
describe the difficulties associated with effective and reliable
communications between satellites and Earth caused by:
–
distance
–
van Allen radiation belts
–
sunspot activity
•
outline the features of the aether model for the transmission of light
•
describe and evaluate the Michelson-Morley attempt to measure the
relative velocity of the Earth through the aether
Space
•
discuss the role of critical experiments in science, such as
Michelson-Morley’s, in making determinations in about competing
theories
•
outline the nature of inertial frames of reference
•
discuss the principle of relativity
•
identify the significance of Einstein’s assumption of the constancy of
the speed of light.
In this part you will be given opportunities to:
•
gather, process, analyse and present information to compare the use
of microwave and radio wave technology as effective
communication strategies for space travel
•
perform an investigation and gather first-hand or secondary data to
model the Michelson-Morley experiment
•
perform an investigation to help distinguish non-inertial and inertial
frames of reference
•
analyse and interpret some of Einstein’s thought experiments
involving mirrors and trains and discuss the relationship between
theory and the evidence supporting it, using Einstein’s predictions
based on many years before evidence was available to support it.
Extract from Physics Stage 6 Syllabus © Board of Studies NSW, 1999. The
original and most up-to-date version of this document can be found on the
Board’s website at http://www.boardofstudies.nsw.edu.au.
Part 5: Space travel and communication
3
Some difficulties of space
probe exploration
In December 1972, Apollo 17 carried three men to the Moon. It was the
last time that any human has travelled further from the Earth than a low
Earth orbit. Manned space missions are risky – as demonstrated by
events such as the disastrous Apollo 13 mission or the fatal launch of
space shuttle Challenger. In addition, the spacecraft needs to provide the
living occupants with oxygen, food, water and a safe environment for the
journey, as well as having sufficient fuel reserves to return to Earth.
Unmanned, robotic spacecraft have none of these drawbacks. Their
designers do not have to worry about equipping the craft with any of
these supplies or facilities, since there are no living occupants to keep
alive and the spacecraft does not need to come back.
However, space probes have their own needs.
4
∑
If they are never to return then they must be able to communicate
their findings to us. Radio communication through space is not
difficult, however receiving that signal at the surface of the Earth
presents a unique set of problems.
∑
If they are to reach their goal within a reasonable time, they need an
appropriate speed. As you shall see, just what is appropriate depends
very much upon how far away the goal is.
Space
Spacecraft communication
Think back to the module The world communicates where you learned
about radio waves. Why is it that communication with spacecraft is
conducted by radio waves, rather than using any other portion of the
electromagnetic spectrum, such as X-rays or gamma rays?
Firstly, you should realise that the choice of radio communication was a
natural choice. The world has been using radio waves for general
communication since the turn of the twentieth century.
Guglielmo Marconi demonstrated the use of radio waves to the world in
1901 when he sent the first long distance wireless signal, from England
to Newfoundland. Since then a multitude of forms of communication
have developed using this as the basis, from AM and FM radio to mobile
telephones. Therefore, when selecting a mode for early satellite
telemetry and space capsule communication, radio was the obvious
choice.
Despite this, there is a very good physical reason why radio serves the
purpose well. Earth is constantly subject to a full range of
electromagnetic radiation from space, ranging from the very short
gamma rays to the very long wavelength radio waves. However, the
atmosphere filters out most of this radiation. This selective absorption is
represented in the diagram below.
Notice that there are two significant ‘windows’ in this absorption pattern.
Visible light and radio waves (plus a few specific infra-red wavelengths)
are not absorbed to any large extent. This means that visible light and
radio waves reaching us from space will penetrate the atmosphere and
reach the ground. This has the following consequences, amongst others.
∑
Visible light telescopes and radio telescopes can be operated from the
ground. Telescopes designed to observe other wavelengths must be
operated from above the atmosphere, that is, from space.
∑
Communications with spacecraft must penetrate the atmosphere, and
so must correspond with one of the available windows. Radio waves
were already in use and so the technology was readily available.
Part 5: Space travel and communication
5
400
x-rays
UV
visible light
gamma rays
infra-red microwave
radio
200
100
altitude
50
25
12
aircraft
6
3
land surface
0
sea level
Absorption of radiation by the Earth’s atmosphere occurs at a shading change.
The term ‘radio waves’ generally refers to any electromagnetic wave
with a wavelength longer than one millimetre. For the purposes of
communications, the shorter of these wavelengths are preferable. This is
because of the following reasons.
∑
The longer radio wavelength bands are heavily used for other
purposes, such as television broadcasting and mobile phones.
∑
Shorter wavelengths are more able to penetrate clouds, haze and
snow.
∑
Shorter wavelengths mean smaller spacecraft antennae are required to
send and receive the waves.
The shorter radio waves, having wavelengths from 1 to 1000 mm, are
referred to as microwaves. This range of wavelengths have been divided
up into a number of letter-identified bands, as shown in the following
table.
In the table following, the frequency range for each of the microwave bands
is indicated.
Calculate the corresponding wavelength ranges.
Recall the wave equation, v = f l , noting that the speed of all
electromagnetic waves is 3.0 ¥ 108 ms-1 through space.
6
Space
Microwave band
Frequency range
P band
0.3 GHz – 1 GHz
L band
1 GHz – 2 GHz
S band
2 GHz – 4 GHz
C band
4 GHz – 8 GHz
X band
8 GHz – 12.5 GHz
Ku band
12.5 GHz – 18.5 GHz
K band
18.5 GHz - 26 GHz
Ka band
26 GHz – 40 GHz
Wavelength range
Check your answers.
An example of the use of these microwave bands for space probe
communications is the Deep Space Network of radio telescope receiving
stations organised and financed by NASA for this purpose. All space
probes using this network, such as the Voyagers, communicate at one of
just three frequencies. These are 2 295 MHz (in the S band), 8 415 MHz
(in the X band) and 32 000 MHz (in the Ka band).
One of these stations is the Canberra Deep Space Communication
Complex, located near Canberra at Tidbinbilla.
You can find their website where you can check on the progress of all
NASA space probes currently in operation at pages on the physics website
page at http://www.lmpc.edu.au/science
Communication difficulties
There are a number of difficulties associated with communication in
space. These include problems associated with:
•
distance
•
the ionosphere
•
the magnetosphere and van Allen belts
•
the solar cycle.
Part 5: Space travel and communication
7
Distance delay
Despite having selected a mode of communication that successfully
penetrates the Earth’s atmosphere, radio astronomers face further
obstacles. As a space probe travels further away it takes radio waves,
travelling at the speed of light (3 ¥ 108 ms-1), longer to reach it. The
delay for a response from the probe to return to mission control also
increases.
At the start of the year 2000, the space probes furthest away from us are
Voyager 1 and Pioneer 10. Pioneer 10 was launched in 1972, while
Voyager 1 was launched in 1977. Each followed a path that took them
past several planets before heading out of the solar system. They are
heading in different directions, at a distance of more than eleven billion
kilometres away, looking for the heliosphere. This is the boundary
between the solar wind and the interstellar wind, and marks the limit of
the Sun’s magnetic field (see later).
At this distance it would take a microwave communication slightly more
than ten hours to reach the space probe. If the probe responds with
another message then there will be another 10 hour wait, making for a
twenty hour delay in all. This distance related delay can be bothersome
for the scientists and mission controllers involved with the project, but it
can also pose a serious risk to the well being of the probe. If some
danger should arise, such as the unexpected approach of an asteroid or
comet then, in the delay time of waiting for instructions on how to deal
with the danger, the asteroid could have crashed into the probe and
destroyed it.
In order to cope with this sort of problem, designers have sought to give
space probes a degree of autonomy. The Voyager space probes are quite
old now, but were given the ability to continually scan for faults, and
then to repair them (within limits). The much more recent, experimental
space probe known as Deep Space 1 was given artificial intelligence that
allows it to plot and then fly its own course, when communications are
prevented or are too slow, in order to achieve the goal of the mission.
The ionosphere
The ionosphere is an ionised, upper atmospheric layer, above 60 km,
parts of which have the ability to reflect certain shorter wavelength radio
waves. This property makes it useful to short wave radio users, who can
bounce radio waves off the bottom of the ionisphere, as short as one
centimetre, around the world for long range communication.
8
Space
Unfortunately, this same property hinders ground-based radio astronomy
and spacecraft communication because the radio waves useful for radio
astronomy and space communication must penetrate the ionosphere
rather than be reflected at the top of it.
ionosphere
spacecraft
communication
l < 30 cm
Earth
shortwave
radio
communication
l > 10 cm
* not to scale
Effect of the ionosphere in space craft communication.
Look back to find the frequency of radio waves used to communicate with
space probes. Calculate the wavelength of these waves.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
Check your answer.
The ions within the ionosphere are formed by the absorption of
ultraviolet and x-ray electromagnetic radiation from space. This
radiation carries sufficient energy to the atoms present in the ionospheric
layer to remove electrons, thereby creating ions. This absorption of
electromagnetic radiation is part of the absorption process mentioned
earlier.
Part 5: Space travel and communication
9
The magnetosphere and the Van Allen belts
You should recall from The cosmic engine that the Earth has two
doughnut-shaped hoops around itself called the Van Allen belts. Before
going further you need to understand how these belts are the result of the
influence of the Sun upon the Earth.
heliopause
heliosphere
interstellar wind
magnetopause
magnetosphere
Sun
solar
wind
cosmic rays
The heliosphere and the magnetosphere.
Both the Sun and Earth are surrounded by magnetic fields. The ‘sphere’
of influence of the Sun’s magnetic field is called the heliosphere.
Its boundary with the interstellar gas of space is called the heliopause.
The heliosphere is dominated by the Sun’s solar wind – an outflow of
charged particles (mostly protons and electrons) from the Sun travelling
at speeds of up to 1 ¥ 106 ms-1 (or 36 million kmh-1).
At the heliopause the solar wind meets the interstellar wind – a flow of
neutral hydrogen atoms from the galactic centre. The heliosphere is
distorted by the influence of the interstellar wind. In 1999 the space
probes Voyager 1 and Pioneer 10 were 70 AU from Earth, searching for
the heliopause, thought to be around 100 AU away. You may recall from
The cosmic engine that 1 AU is equal to the distance of the Earth from
the Sun.
10
Space
In addition to the solar wind, space is filled with a random scattering of
charged particles called cosmic rays. These are protons and atomic
nuclei, travelling at high speed and therefore possessing great energy.
Cosmic rays are thought to have been produced by supernovae
(exploding stars) and, while travelling the galaxy, have had their paths
distorted by stellar magnetic fields, until they are randomly scattered.
The sphere of influence of the Earth’s magnetic field is called the
magnetosphere. The solar wind distorts its boundary, called the
magnetopause. Looking at the previous figure, you can see that the Earth
is subjected to two different streams of charged particles – the solar wind
and cosmic rays.
Magnetic fields have an interesting property in relation to charged
particles – they are able to capture them. As shown in the following
diagram, any charged particle moving across a magnetic field is forced to
spiral along the magnetic field lines.
magnetic field lines
_
+
charged
particle
+
Magnetic fields capture charges.
The charged particles from the solar wind and cosmic rays are captured
in this way by the Earth’s magnetic field. The particles are forced to
spiral along the field lines, bouncing between the poles as well as sliding
sideways until they eventually circle the globe as the two Van Allen
belts. The lower Van Allen belt captures higher energy particles while
the upper belt tends to capture lower energy particles.
The radiation within the Van Allen belts can become quite intense as the
ions accumulate, and pose a threat to the life of space travellers in orbit
and electrical equipment, as well as being an obstacle to radio
communication.
Part 5: Space travel and communication
11
The van Allen belts.
As can be seen from the diagram, satellites in low Earth orbit are below
the lower Van Allen belt, thereby avoiding communication problems and
damage. A satellite in a geostationary orbit at 35800 km lies just within
the upper belt, being near its upper boundary (and has had to traverse the
lower belt in order to reach its orbital altitude). This position poses
several technical problems for satellite designers.
∑
The orbit is so high that there is very little protection from the
bombardment of particles from the solar wind and cosmic rays.
∑
The charged particles of the upper Van Allen belt continuously flow
past the satellite, giving it a substantial electrostatic charge.
Electrostatic charges can damage electronic equipment.
∑
The microwave communications with the satellite must penetrate the
current of charged particles of both Van Allen belts.
These problems can be overcome however, provided the Van Allen belts
remain stable. Unfortunately, when the solar wind fluctuates and solar
storms occur the Van Allen belts become unstable and satellite
communications break up, or sometimes fail. In severe cases, the
satellites can be damaged beyond repair.
The solar cycle
Solar storm activity on the Sun is at times quiet and at other times active.
The fluctuation between these two conditions appears to follow an
11-year long cycle, called the solar cycle.
12
Space
When quiet, the Sun and solar wind are stable and predictable. However
when active, the Sun displays erratic features, such as sunspots, flares
and coronal holes.
The Solar system. © NASA
Sunspots
Sunspots are regions of stronger magnetic fields and cooler surface
temperatures. They appear darker than the surrounding surface and
appear to move across the face of the Sun as it rotates. The number of
sunspots in a year varies from zero, during a solar minimum, to 150 to
200 during a solar maximum. You may recall learning about these in the
module The cosmic engine.
Sunspots. © NASA
Part 5: Space travel and communication
13
Solar flares
Solar flares are huge outbursts of energy that are the result of the twisting
and buckling of magnetic field lines, sometimes erupting out of the
surface, carrying material with them. Solar flares cause a sudden
increase in both EM radiation and solar wind emanating from the sun.
Solar flares. © NASA
Coronal holes
Coronal holes are cooler and less dense than their surroundings. At these
places the Sun’s magnetic field lines are open to space resulting in the
dumping of a flood of high speed particles into the solar wind.
Erratic fluctuations
Along with these irregular features, occur irregular fluctuations in the
electromagnetic radiation and solar wind emitted by the Sun.
Erratic fluctuations in the electromagnetic radiation impact upon the
Earth very quickly. In just over eight minutes fluctuations affect the
ionosphere, altering the degree of ionisation and changing its reflection /
absorption / transmission properties.
14
Space
This, in turn, interrupts satellite and spacecraft communications often
with only brief notice. This interuption can last for extended periods.
Erratic fluctuations in the solar wind are much slower to reach the Earth.
Even at up to three million kilometres per hour, the particles of the solar
wind take several days to reach the Earth. When they do arrive,
however, the unstable solar wind can have severe effects.
∑
Solar wind fluctuations can distort the magnetosphere from its usual
shape, shifting field lines and producing geomagnetic storms.
∑
The intensity of the charge current in the Van Allen belts is made to
fluctuate. This causes the electrostatic charge acquired by
geostationary satellites to vary erratically. This can result in the
electrical failure of equipment.
∑
The flow of charges within the lower Van Allen belt will become
erratic, having a disruptive effect on the behaviour of the ionosphere
and, therefore, communications.
∑
There are several other effects that can be noted at this point:
–
extra heating and expansion of the atmosphere occurs,
encouraging premature orbital decay of satellites in low Earth
orbits
–
power grids may suffer damage such as occurred in 1989 at the
Quebec hydro electricity grid in Canada. (You learned about
this in the module, The cosmic engine.)
–
the Aurora may occur further north or south from the poles than
is usually the case. In 1989 the Southern lights were seen as far
north as the NSW central coast.
Part 5: Space travel and communication
15
Spacecraft velocities
When was the last time you walked down to the corner shop? Most
people walk at about four kilometres per hour, so if the shop is one
kilometre way then it would have taken 15 min to get there and another
15 min to get back.
A thirty-minute walk makes for a good exercise but that sort of travel
time makes it very tempting to look for an alternative means of transport,
especially if you are in a hurry. Certainly a bicycle or car ride would be
much quicker. So, while walking speed is certainly quick enough for
journeys around your back yard or street, it is just sufficient for short
trips to the corner shop, but largely inadequate for travelling further
afield.
The same is true of the speeds currently achievable for space probes on
journeys around the solar system. The fastest speed achieved by any
space probe at the time of printing of this module is approximately
150 000 kmh-1, but this was during a close encounter with the Sun.
Most other space probes achieve speeds of approximately 60 000 kmh to
80 000 kmh-1. These may seem to you to be very high speeds, however
the question is whether they are adequate to reach the desired goal within
a reasonable period of time (just like walking to the corner shop).
Assume that a given space probe is able to reach a speed of
100 000 kmh-1. This would be achieved by a combination of rocket
thrusting and slingshot manoeuvres. However, having achieved this
velocity the space probe is able to turn off all thrusters and simply coast
along at 100 000 kmh-1, as described by Newton’s first law of motion.
Calculate how long this space probe would take to reach each of the
destinations listed in the table below, travelling at this velocity.
16
Space
Goal
Approximate closest
distance (km)
Moon
363 ¥ 103
Venus
40 ¥ 106
Jupiter
590 ¥ 106
Neptune
4.3 ¥ 109
Alpha Centauri
41 ¥ 1012
Galactic centre
260 ¥ 1015
Travel time
Is this an
acceptable time
frame?
Check your answers.
As you can see from your calculations, current space probe velocities are
quite adequate for the purpose of travelling about our solar system,
enabling them to reach their destination within years. However, for
interstellar journeys these speeds are not adequate and would result in
exceedingly long travel times.
This is illustrated well by the calculation of the travel time to Alpha
Centauri, one of our closest neighbouring stars. Mission controllers
would need to wait nearly 47 000 years before a space probe could arrive
at this destination. The distance to this star can also be expressed as
4.3 light-years, and this also means that when the space craft had
reached its destination and sent news of its arrival back to Earth using
radio waves, mission control would have to wait a further 4.3 years just
for the message to arrive. Clearly, these types of distances offer
challenges that cannot be overcome using current technology.
Part 5: Space travel and communication
17
Relativistic space travel
What would space travel be like if it was possible to travel at a
significant proportion of the speed of light? These kinds of spacecraft
speeds are not possible with current technology, however if interstellar
travel is ever to become viable then speeds of ten to ninety percent of the
speed of light may be necessary. In order to try to understand what it
would be like to travel at these speeds you must first have an
understanding of Einstein’s special theory of relativity.
The aether model
The story of the development of the theory of relativity begins in the
nineteenth century. Physicists had been trying for some time to
determine whether light rays were made up of particles or waves. In
1801, Thomas Young seemed to solve the dispute by performing an
experiment that showed that light rays could interfere with each other to
produce patterns. This was a property unique to waves, so this seemed
conclusive evidence that light was a form of wave.
In trying to better understand the behaviour of light, the physicists of the
day turned to the behaviour of other well known waves, such as water
waves, sound waves, and earthquake waves.
One thing that all of these waves have in common is that they require a
medium through which to travel. Water waves travel across the surface
of water; sound waves travel through air (as well as other media);
earthquake waves travel through the ground.
It seemed logical, then, that light waves also needed a medium through
which to travel. The problem was that none could be found. Certainly
light can travel through water and glass, however, in order to reach us
from the Sun the light has travelled through space.
18
Space
Belief in the need for the existence of a medium in space was therefore
strong, despite the failure to find it, and the medium was named the
luminiferous aether. The aether formed an absolute frame of reference
in the Universe and light waves were supposed to have a fixed velocity
relative to the aether. Nineteenth century physicists were able to define
an expected set of properties that the aether should have.
The aether must:
∑
fill all of space and be stationary in space
∑
be perfectly transparent
∑
permeate all matter
∑
have a low density
∑
have great elasticity in order to propagate light waves.
All that was left was to find it. The search for the aether lasted for most
of the nineteenth century, before it was realised that it could not be
detected (as shown by the Michelson-Morley experiment) and,
furthermore, it was not even needed (as shown by the theory of
relativity).
Today it is much easier for us to accept that the aether does not exist,
however it was not a theory easily shaken and, with hindsight, it can be
said that it appears to have been dead-end theory that actually delayed the
development of physics.
The Michelson-Morley experiment
If the aether existed, then it was reasoned that the Earth should be
moving through it as it orbits the Sun. This would create an apparent
‘aether wind’ of about 30 kmh-1 (which is the orbital speed of the Earth
around the Sun). This is analogous to travelling along in a car on a
windless day. Wind the window down and put your hand outside and
you will feel a rush of air, or an apparent wind.
There were many experiments designed to detect the aether wind. They
all failed to detect anything. The value of each was discounted after the
event due to a lack of sensitivity. If the aether did exist then it was
extremely difficult to detect and eventually the sensitivity required of
such an experiment was calculated, according to the elaborate details of
the aether model.
Part 5: Space travel and communication
19
The first experiment to try to detect the aether, that was of the required
sensitivity, was performed by A A Michelson and E W Morley in 1887.
Their achievement was such that they received the Nobel Prize in 1907
for this work. However, as sensitive as the apparatus was, it still failed to
detect any presence of an aether wind.
Their method was to direct two light rays along two separate paths – one
into the aether wind and one across it. The two rays started out in phase
with each other and their phase relationships were compared after their
journeys.
In order to help understand this method you should complete the
following activity based on an analogy, in which two pigeons are raced
along two separate paths.
A pigeon race
In this analogy two trained pigeons, called Blue and Red, are raced
against each other instead of light rays, and a regular wind is substituted
for the aether wind. The object of the exercise is to see how the wind
affects their finishing times for the race. Both birds have identical air
speeds and the courses they must fly are shown in the following diagram.
C
checkpoint
N
12 km
Blue
wind
Red
C
12 km
18 kmh-1
from west
The pigeon race
A prevailing wind of 18 kmh-1 applies from the east. From their home
base, Blue is going to fly 12 km north to a checkpoint and then return
home; Red is going to fly 12 km west and then home again. Both birds
fly at 30 kmh-1 relative to the air around them.
20
Space
AVG = 18 kmh-1
velocity of air (wind)
relative to ground
BVA = 30 kmh-1
velocity
of blue
relative
to ground
BVG
velocity of
blue relative
to air
BVG
BVA
=?
= 30 kmh-1
AVG = 18 kmh-1
forward leg
1
return leg
Examine Blue’s race as shown in the diagram above.
This bird’s task is to fly across the prevailing wind and back again.
In order to fly this course in a straight line it must fly into the wind and
allow the wind to carry it back onto the course.
Enter the available data (the bird’s air speed and the wind speed) onto
the diagram, and then use Pythagoras’ theorem to calculate the velocity
of Blue relative to the ground.
_____________________________________________________
_____________________________________________________
2
Given that the distance from the house to the checkpoint is 12 km,
calculate the time taken to fly this leg of the journey.
_____________________________________________________
_____________________________________________________
3
The return leg of the race is very similar to the first leg. Therefore,
determine the total time taken by Blue to complete the race.
_____________________________________________________
_____________________________________________________
velocity of red
relative to ground
AVG = 18 kmh-1
velocity of red
relative to air
RVA = 30 kmh-1
velocity of red relative to ground
RVG = ?
forward leg
Part 5: Space travel and communication
21
RVA = 30 kmh-1
AVG = 18 kmh-1
RVG = ?
return leg
Red’s race.
4
Now examine Red’s race as shown in the diagrams above.
The bird’s task is to fly the first leg of its journey with the wind, and
the return leg against the wind. Consider the first leg, in which the
bird is flying in the same direction as the wind. Calculate the
velocity of Red relative to the ground.
______________________________________________________
______________________________________________________
5
Given that the checkpoint is 12 km from the house, calculate the
time taken by Red to fly the first leg of the race.
______________________________________________________
______________________________________________________
6
Now consider the return leg of Red’s race. This time the bird is
flying into the wind. Calculate the velocity of the bird relative to the
ground.
______________________________________________________
______________________________________________________
7
Calculate the time taken by Red to fly the return leg of the race.
______________________________________________________
______________________________________________________
______________________________________________________
8
Now add the times for the first and second legs of the race to
determine the total time taken by red to fly the race.
______________________________________________________
______________________________________________________
9
For the purpose of comparison, record both birds’ race times here:
Blue: ___________________ Red: _________________________
10 Which bird won the race? _________________________________
22
Space
11 If the wind speed was halved, how would this affect the finishing
times?
_____________________________________________________
12 Does the pigeon flying across the wind always win, regardless of
wind speed?
_____________________________________________________
13 If the wind speed was not known, would it be possible to calculate it
from a knowledge of the bird’s air speed and their finishing times?
(This is what the Michelson-Morley experiment attempted to do.)
_____________________________________________________
14 What would it mean if the birds arrived back at the house at the same
time, that is, if the race was a tie? Explain. (This is what happened
in the Michelson-Morley experiment.)
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
Check your answers.
The real experiment
Shown below is the apparatus used by Michelson and Morley. It was set
up on a large stone block floating on mercury. This allowed it to be
easily rotated – an important feature as you shall see.
Michelson-Morley experimental setup.
A light ray from the source strikes a half-silvered mirror and is split into
two by it. One ray heads into the aether wind then reflects against a
mirror and returns. The other ray heads across the aether wind before
reflecting back. Both rays finish their journey at the telescope where
they are compared. This is shown in the figure following.
Part 5: Space travel and communication
23
mirror
M2
v
aether
wind
2
M
light
source
1
mirror
M1
half - silvered
mirror
telescope
The path of light in the Michelson-Morley experiment.
This exercise is a lot like the pigeon race analogy, except that here it is
two light rays that are racing. Because a light ray is a continuous stream
of light it is more difficult to decide upon the ‘winner’ of the race.
What must be done is to compare the phases of the two light rays as they
arrive at the finishing line (the telescope). You should recall from the
module The world communicates that when two waves occupy the same
place in a medium then they superimpose, or ‘interfere’. The apparatus
of this experiment directs both rays of light into a telescope where they
interfere to produce a pattern of light and dark bands, as shown below.
Interference pattern.
24
Space
Because this device uses an interference effect to compare the light rays
it is called an 'interferometer'. Observing an interference pattern itself
proves nothing, as a pattern is produced whether the aether wind exists or
not. It is at this point that Michelson and Morley rotated the whole
apparatus (remember it was floating on mercury) by ninety degrees.
If the aether wind really existed, so that the light ray heading across the
aether wind was indeed faster, then when rotated 90° the other ray would
become the ray heading across the aether wind and it would become the
faster ray. This ray reversal would change the phase relationship of the
two rays in the interferometer so that the interference pattern would be
seen to shift.
Despite the sensitivity of the experiment, no interference pattern shift
was observed. This result is equivalent to a tied race in the pigeon race
analogy used earlier.
Michelson and Morley repeated the experiment many times, varying the
time of day and even the time of year to try to change the direction that
the apparatus was moving through space as the Earth rotated and orbited
the Sun. However, no interference pattern shift was ever observed.
Repeatability is an important aspect of the scientific method. After
Michelson and Morley published their results, the experiment was
repeated many times by other physicists in different laboratories around
the world. The result was always the same. No aether wind was
detected. This is referred to as a ‘null result’.
Did the null result actually disprove the aether model? No, it did not.
The experiment merely failed to find any evidence of the existence of the
aether. However, the experiment was, by calculations based on the
aether model, supposed to be sensitive enough to detect the aether if it
was there.
The attitude taken by many physicists at the time was that this result
simply showed that the details of the model were in error. They were
still convinced that the aether must exist.
There followed a series of modifications to the model, such as allowing
large objects like planets to drag the aether along with them, which
would mean no aether wind at the surface of the Earth and would explain
Michelson and Morley’s null result. Each time a modification was
offered it was subjected to close scrutiny and was found to be valid.
It was not until 1905, when a young Albert Einstein asserted that the
concept of the aether was not necessary at all, that the scientific
community became prepared to set the matter aside.
Part 5: Space travel and communication
25
To see websites that discuss the Michelson-Morly experiment in more detail
see the physics website page at: http://www.lmpc.edu.au/science
26
Space
Einstein
The principle of relativity
Einstein’s relativity theory began with a simple idea first stated by the
Italian scientist Galileo, who lived three hundred years earlier. Today the
idea is called the principle of relativity and it states that all steady
motion is relative and cannot be detected without reference to an outside
point.
It is harder to imagine this idea than to state it. This is because you are
used to being able to easily tell whether you are moving or not.
When you are cruising in a car you can tell that the car is moving by the
bumps in the road and the trees and signs flitting past – however when
you see and feel these things you are referring to outside points. If you
could not do this then you could not tell if you were moving.
A good example of where you really can’t tell whether you are moving
or not is on a plane flight in a large jet travelling at constant velocity at
night. If the window shutter shade is down you may be travelling at
600 kmh-1 but you can’t feel movement and can easily walk up and down
the aisles of the plane with no sense of the outside motion of the plane
relative to the ground at all. If you’ve been on a plane flight you can
probably recall this. If you haven’t you may have a flight in the future or
you should discuss this with someone who has.
When the Apollo spacecraft went to the Moon, the strategy to get there was
to accelerate toward it for a short period of time and then to turn off the
engines and ‘coast’ the rest of the way. In this condition there are no trees
or signs flitting past and there are no bumps in the road. There is no rush of
air past the vehicle and no speedometer to check. The only indication of
movement is the Earth getting smaller in the window of the spacecraft.
Imagine that you are the astronaut in such a spacecraft, and you are not
allowed to look out the window. There is no way to tell that you are
moving, or how fast! This is the principle of relativity in operation.
Part 5: Space travel and communication
27
Notice that this principle refers to ‘steady motion’. This means
‘non-accelerated’ motion, that is, stationary or travelling with a uniform
velocity. These types of conditions are called ‘inertial’.
The principle of relativity does not apply to situations (physicists like to
say ‘frames of reference’) that involve acceleration. These are referred to
as ‘non-inertial frames of reference’. If there is acceleration then there is
a net force (Newton’s second law of motion). A net force can be felt or
shown using an accelerometer.
Inertial and non-inertial frames of reference
This is a very simple activity to help you distinguish between inertial and
non-inertial frames of reference.
You will need:
•
the help of another person who can drive, you are to be a passenger
•
a plumb bob (any mass such as a nut hanging on a short length of
string will do).
Method:
1
Once in the car, ask your driver to take a short trip that involves
some straight, smooth sections of road as well as some bends. Seat
yourself in the back seat and hold up your plumb bob. Notice that it
hangs directly down to begin with, but it will not do so for the whole
trip.
2
Note in the table below when the plumb bob hangs directly down
and when it does not. In each case you should record whether the
car is stationary, travelling at a steady velocity, accelerating, braking
or turning a corner.
A good optional variation on this is to record the position of the
plumb bob with a video camera fixed to a door of the car so it can’t
move. You can then describe and record with voice what is
happening to the plumb bob as you go along different sections of the
road.
Recall from the module Moving about that speeding up, slowing
down and turning a corner all involve a change of velocity, and
therefore are all non-inertial frames of reference (that is, they are
forms of acceleration), while standing still and travelling with
uniform velocity are inertial frames of reference (not accelerated).
28
Space
Events when plumb bob hangs
straight down
1
Events when plumb bob does not
hang straight down
Is your plumb bob able to distinguish between inertial and non-inertial
frames of reference? Explain your answer.
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
2
Was the principle of relativity verified by your results?___________
Explain why it did, or why it did not.
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
3
Would you be able to tell how fast you were travelling at a steady
velocity in a straight line, using just the plumb bob? (Assume the
car has blacked out windows, super soft suspension and you cannot
hear or feel the engine.)
_____________________________________________________
Check your answers.
Part 5: Space travel and communication
29
A problem for the principle of relativity
In the nineteenth century the principle of relativity was recognised, but
only as a mechanical effect. This was because the aether model implied
that the principle of relativity did not hold for optical experiments.
The aether was assumed to be stationary in space and light was assumed
to have a fixed velocity relative to the aether. This aether model meant
that a measurement of the speed of light inside a moving vehicle would
yield a different velocity to a similar measurement made inside a
stationary building. For instance, a physicist measuring the speed of
light from the back to the front of a train moving at 100 kmh-1 would
record a speed 100 kmh-1 less than the speed measured from the ground.
This optical experiment, if it were true, would violate the principle of
relativity by not only distinguishing between the speed of light when
stationary and moving at a steady velocity, but also by allowing that
velocity to be measured without reference to an outside point by simply
measuring the speed of light. This, in turn, meant that the principle of
relativity held for some types of physics (mechanical) but not for others
(optical). But only if the aether model that light waves travelled through
the aether, was true.
The speed of light
For Albert Einstein, the violation of the principle of relativity outlined
above posed a real dilemma. Something was not right and he was
determined to sort it out.
Einstein had a habit of posing major problems as deceptively simple
thought experiments. A thought experiment can be a useful tool when, as
in this case, the conditions of the experiment cannot be produced.
However, there is a danger of getting the wrong answer because what
you imagine might happen in a given situation based upon your personal
experiences.
In this case, the conditions of the thought experiment were far from
personal experience, which made Einstein wary. He discussed his
thoughts at length within a circle of trusted academics, and even then, he
later admitted, he was driven to near emotional collapse, by the
conclusions he was drawing.
30
Space
His thought experiment in this case was as follows:
Suppose I am sitting in a train that is travelling at the speed of light.
If I hold up a mirror in front of me and look into it, will I see my own
reflection?
Before you read on write down what you think would happen.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
The problem sounds a very simple problem, doesn’t it? It encapsulates
the light-speed measurement problem discussed earlier. Einstein could
only see two possible answers, and both of them had real problems for
him.
•
No, he would not see his reflection. This would be because the train
was already going as fast as light can travel. Therefore, the light
leaving his face would not be able to reach the mirror in order to
return as a reflection. By not being able to see his reflection, he
would immediately know that the train was travelling at light speed,
without reference to an outside point. This is the violation of the
principle of relativity predicted by the aether model.
•
Yes, he would be able to see his reflection, that is, the principle of
relativity is not violated. This means that the light leaving his face
travels at the usual speed of light, as measured by him on the train.
But this would mean that an observer standing on the ground next to
the train should be able to measure the speed of that light as twice
the usual speed of light!
Do either of these responses correspond closely with yours given above?
Perhaps you can appreciate now why this problem caused Einstein such
anguish. You have the luxury of simply reading on to find out how the
dilemma was resolved, but there was no easy answer for Albert Einstein.
It is not true to say that he had no one to guide him, however. Through
his circle of friends he found guidance in the writings of people such as
Ernst Mach, who had stated that he believed that there were no
mechanical absolutes in nature (referring to concepts such as space and
motion). Einstein tussled with the problem for ten years, from 1895 to
1905, before reaching a conclusion.
Part 5: Space travel and communication
31
Einstein believed strongly in the unity of physics, and could not accept
that an optical experiment could violate the principle of relativity while a
mechanical experiment could not. He decided therefore that:
•
the aether model must be wrong
•
the principle of relativity is never violated
•
he would see his reflection in the mirror.
This still posed the problem of the person outside the train seeing light
travelling at twice its known speed. He decided then that the speed of
light must have the same value regardless of the motion of the observer.
In other words, the person on the train and the person outside the train
will both see the same light travelling at the same velocity.
This, in itself, seemed an impossibility until Einstein realised that the key
lay in the definition for speed, being distance divided by time. His
conclusion, therefore, was that the both people watching the same event
(the reflection of the image from the mirror) observe different distances
and different time intervals, such that distance divided by time always
equals the same number, the speed of light. In other words, the two
different observers perceive space (distance) and time differently!
This was a very radical conclusion at the time, and is still difficult to
grasp on first reading. Einstein had shifted from the Newtonian view of
distance and time being absolute terms to a new view, in which these are
relative terms and the speed of light is the only absolute term.
Read back over the last three paragraphs several times until you begin to
feel comfortable with this idea that the speed of light is the constant. To
keep the speed of light constant, space and time are varied.
The theory published
The ideas behind Einstein’s answer to his thought experiment were first
published in a physics journal called Annalen der Physik as a paper he
wrote, titled On the electrodynamics of moving bodies. (In 1864 James
Maxwell had mathematically shown the existence of electromagnetic
waves, calculated their speed and shown that light was just one of these
waves; hence the term ‘electrodynamics’ to refer to the behaviour of
light.) The article by Einstein presented two postulates and one
statement, as follows.
∑
32
The first postulate. The laws of physics are the same in all frames of
reference. In other words, the principle of relativity always holds and
cannot be violated by optical experiments. (This implied that the
aether does not exist.)
Space
∑
The second postulate. The speed of light in empty space always has
the same value, which is independent of the motion of the observer.
In other words, everybody observes the same speed of light
regardless of his or her motion. (This, in turn, has very significant
implications for space and time.) The speed of light is given the
symbol c.
∑
The statement. The luminiferous aether is superfluous, that is, it is no
longer needed to explain the behaviour of light. The null result of the
Michelson - Morley experiment by all who had performed it gave
Einstein the confidence to set this concept aside.
His article was a short one but it laid the foundation that was to become
the special theory of relativity. This theory, later modified to the general
theory of relativity by the inclusion of gravity, has been regarded as one
of the two most important scientific theories of the twentieth century, the
other being quantum mechanics.
In this part you have learned about some of the difficulties of exploring
space, by space probe. You learned about the difficulty that the
enormous distances of space pose in terms of travel times and for
communication. You also learned about the means used to communicate
with satellites and spacecraft, and the conditions that can lead to
disruption of those communications. Finally, you learned of the
luminiferous aether model and the Michelson-Morley experiment to
detect it, as well as the difficulties with the concept that led Einstein to
develop the theory of relativity. In the next part, you will learn about
space/time, and some of the strange consequences of relativity, such as
length contraction and time dilation.
Part 5: Space travel and communication
33
Summary
34
∑
Current space travel velocities are adequate for interplanetary travel
but are not adequate for interstellar travel.
∑
Communications with satellites can be done with microwaves or
radio waves because the atmosphere does not absorb these waves.
Microwaves are preferred for their shorter wavelengths and higher
frequencies.
∑
These waves travel at the speed of light. This finite speed results in
communication time-lags over large distances.
∑
There are three charged layers around the Earth – the top layer of the
atmosphere called the ionosphere as well as the inner and outer Van
Allen belts. When unstable, they can disrupt satellite and spacecraft
communications systems. Instability is caused by fluctuations in the
electromagnetic radiation and solar wind emitted by the Sun.
∑
The aether was the hypothesised medium for light and other
electromagnetic waves. It was transparent and could not be detected,
yet belief in its existence was strong since all other known
waveforms require a medium through which to travel.
∑
The Michelson-Morley experiment was devised to detect the aether
using light and an effect called interference. It was of sufficient
sensitivity according to the aether model, yet failed to detect any
presence of the aether.
∑
An inertial frame of reference involves no acceleration. It allows
for uniform velocity or a state of rest only.
∑
The principle of relativity states that it is not possible from within an
inertial frame of reference to detect uniform velocity without
referring to another frame.
∑
While the principle of relativity was established for mechanical
experiments, the aether model suggested that it did not apply to
optical experiments.
∑
Einstein extended the principle of relativity to include all the laws of
physics, including optics.
Space
∑
Einstein postulated that the speed of light has the same value c in all
reference frames, that is, to all observers.
∑
Distance (space) and time become relative terms once it is accepted
that the speed of light is an absolute term.
Part 5: Space travel and communication
35
36
Space
Suggested answers
Space craft communication
Microwave band
Frequency range
Wavelength range
P band
0.3 GHz – 1 GHz
1 000 mm – 300 mm
L band
1 GHz – 2 GHz
300 mm – 150 mm
S band
2 GHz – 4 GHz
150 mm – 75 mm
C band
4 GHz – 8 GHz
75 mm – 37.5 mm
X band
8 GHz – 12.5 GHz
37.5 mm – 24 mm
Ku band
12.5 GHz – 18.5 GHz
24 mm – 16.2 mm
K band
18.5 GHz - 26 GHz
16.2 mm – 11.5 mm
Ka band
26 GHz – 40 GHz
11.5 mm – 7.5 mm
The ionosphere
These are 2 295 MHz (in the S band) with a wavelength of 0.13 m, 8 415
MHz (in the X band) with a wavelength of 0.035 m and 32 000 MHz (in
the Ka band) with a wavelength of 0.009 m.
Part 5: Space travel and communication
37
Spacecraft velocities
Goal
Approximate
closest distance
(km)
Travel time
Is this an
acceptable time
frame?
Moon
363 ¥ 103
3.63 hours
yes
Venus
40 ¥ 106
16.7 days
yes
Jupiter
590 ¥ 106
246 days
yes
Neptune
4.3 ¥ 109
4.9 years
yes
Alpha Centuari
41 ¥ 1012
46 800 years
no
Galactic centre
260 ¥ 1015
297 million years
no
A pigeon race
1
Velocity of Blue relative to the ground = 30 2 - 182
2
r
r Dr
12
v=
\ 24 =
Dt
t
12
\t =
= 0.5 h
24
3
Time for return leg = 0.5 h
= 24 kmh -1
Total time taken by Blue = 0.5 + 0.5 = 1 h
4
5
6
38
During forward leg, velocity of Red relative to ground = velocity of
wind + velocity of bird = 30 + 18 = 48 kmh-1
r
r Dr
12
v = r \ 48 =
Dt
t
12
\t =
= 0.25 hours
48
During return leg, velocity of Red relative to ground = velocity of
wind + velocity of bird = 30 - 18 = 12 kmh-1
Space
7
v=
Dr
12
\ 12 =
Dt
t
12
\t =
= 1.0 hour
12
8
Total time =1+ 0.25 hours= 1.25 hours
9
Comparison: Blue: 1 hour Red: 1.25 hours
10 Winner: Blue
11 If the wind speed was halved, then the times of both birds would be
shortened but Blue would still win.
12 Yes, the pigeon flying across the wind always wins the race, as long
as there is a wind.
13 Yes, expressions can be derived to calculate wind speed from the
finishing times.
A tie would only happen if the wind speed is zero, that is, there is no
wind.
Inertial and non-inertial frames of reference
1
Yes. The plumb bob is on an angle when in non-inertial frqmes of
reference. It hangs straight down in inertial frames of reference.
2
Yes. When the car was at rest or moving with constant velocity the
plumb bob hung staraight down so you could only tell your sense of
motion from external points. When the car was accelerating or
slowing the plumb bob was on an angle indicating a non-inertial
frame of reference.
3
No.
Part 5: Space travel and communication
39
40
Space
Exercises – Part 5
Exercises 5.1 to 5.10
Name: _________________________________
Exercise 5.1
a)
Explain why satellite and spacecraft communications are done using
radio waves and microwaves.
_____________________________________________________
_____________________________________________________
b) What are microwaves are how are they distinct from radio waves?
_____________________________________________________
_____________________________________________________
c)
Why would satellite and spacecraft designers choose to use
microwaves rather than radio waves?
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
d) Describe the effect of distance on effective communication with a
spacecraft.
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
Part 5: Space travel and communication
41
Exercise 5.2
The Apollo missions were the only manned missions to venture higher
than a low Earth orbit, and shielding was an important issue in
protecting the astronauts. Describe the radiations from which the
astronauts needed to be shielded.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
Exercise 5.3
Describe the formation of
a)
the ionosphere
______________________________________________________
______________________________________________________
______________________________________________________
______________________________________________________
b) the Van Allen belts.
______________________________________________________
______________________________________________________
______________________________________________________
______________________________________________________
Exercise 5.4
a)
Describe the link between sunspot activity and fluctuations in the
solar wind and electromagnetic radiation.
______________________________________________________
______________________________________________________
______________________________________________________
42
Space
b) Explain the potential impacts that these fluctuations can have upon
satellite and spacecraft communications.
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
Exercise 5.5
Explain why current maximum velocities are too slow for extended space
travel to be viable. Include examples in your answer.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
Exercise 5.6
a)
What was the luminiferous aether?
_____________________________________________________
_____________________________________________________
b) Describe the supposed features of the aether.
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
c)
What was the reason that nineteenth century scientists felt so
strongly that the luminiferous aether had to exist?
_____________________________________________________
_____________________________________________________
Part 5: Space travel and communication
43
Exercise 5.7
a)
What was the objective of the Michelson-Morley experiment?
______________________________________________________
______________________________________________________
b) Draw a simplified diagram of the light ray paths in this experiment,
assuming that you have an aether wind from right to left across your
page. Indicate on the diagram which should be the faster ray.
c)
How are the rays compared in this experiment?
______________________________________________________
______________________________________________________
d) What was the result of the Michelson-Morley experiment?
______________________________________________________
______________________________________________________
e)
Did this result disprove the existence of the aether?
______________________________________________________
______________________________________________________
Exercise 5.8
a)
What is the difference between an inertial and a non-inertial frame of
reference?
______________________________________________________
______________________________________________________
______________________________________________________
______________________________________________________
44
Space
b) How can you tell if the frame of reference in which you are located
(car, bus, rocket and so on) is inertial or non-inertial without
reference to an outside point?
_____________________________________________________
_____________________________________________________
c)
If your frame of reference is inertial, can you tell how fast you are
going without reference to an outside point? Explain.
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
Exercise 5.9
a)
What is the principle of relativity?
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
b) The aether model provided a way to violate the principle of relativity
using an optical experiment. Describe this.
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
c)
Einstein saw a dilemma in this violation of the principle of relativity.
Describe the thought experiment he used to analyse the problem.
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
Part 5: Space travel and communication
45
Exercise 5.10
Describe Einstein’s response to the dilemma posed by the aether’s
apparent violation of the principle of relativity.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
46
Space