Cosmic Adventure 3.07 08 Light Speed Measurement

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MEASUREMENT OF LIGHT SPEED
Cosmic Adventure 3.07

Galileo Galilei
The scientist who was credited
with being the first trying to
determine the speed of light
was an Italian called Galileo
Galilei (1564-1642).
Galileo was a physicist,
mathematician, engineer,
astronomer, and philosopher
who played a major role in the
scientific revolution during the
Renaissance.

The Giant
Galileo has been variously called
the “father of modern
observational astronomy”, the
“father of modern physics”, the
“father of science”, and “the
father of modern science”.
When Isaac Newton said that he
could see further because he
was on the shoulder of giants.”
Galileo was no doubt the giant
he referred to.

The Speed of Light by
Galileo Galilee
Galileo was quite convinced that
light did not suddenly appear out
of nowhere when a light source
was unshielded. It sounded
physically absurd that a ray of
light could be anywhere in the
universe at the same time.

Dialogues Concerning
Two New Sciences
His conviction was fully reflected in
his book entitled “Dialogues
Concerning Two New Sciences”
published in 1638.
In the book, there were three
interlocutors named Salvanti,
Sagredo and Simplicio discussing
certain scientific problems. The
following quotations from the book
embraced all the problems Galileo
knew about the speed of light.

Dialogues Concerning Two New Sciences [01]
Salvanti (who represents Galileo’s
opinion):
“We see that fires and dissolutions
are accompanied by motion, and
very swift motion; behold the
action of lightning and of
gunpowder used in mines and
bombs..... So I cannot believe that
the action of light, however pure,
cannot be a kind of motion which
is of the swiftest kind.”
Sagredo: (The inquirer) “But what kind and
how great should we take the speed of light
to be? Is it instantaneous or momentary? Or
does it, like other movements, require time?
Could we assure ourselves by experiment?”
Simplicio (An Aristotalian): “Everyday
experience shows that the propagation of
light is instantaneous. When we see an
artillery fired far away, the brightness of the
flames reaches our eyes in no time, but the
sound comes to our ears only after a
noticeable interval.”

Dialogues Concerning
Two New Sciences
Sagredo: “Well, Simplicio, from
this well-known experience, I
can only deduce than that sound
travels slower than light. It does
not assure me whether the light
is instantaneous or very fast.
Your observation is no more
conclusive than it would be to
say: “As soon as the sun reaches
the horizon, its splendour
reaches our eyes.” For who will
assure me that the rays did not
reach the horizon before they
reached our vision?”

The Galileo Experiment
With this conviction, Galileo did try to set up an experiment to measure the speed of
light in 1638. Galileo and his assistant each took a shuttered lantern, and positioned
themselves on hilltops one mile apart. As soon as the assistant saw Galileo flashing
his lantern, he would reply by opening the shutter to his own lantern. Galileo would
then mark down how long it took before he saw the light from the other lantern.
Dividing the return trip of two miles with the time, he would obtain the speed of light
in just the same way of measuring the speed of any moving daily object.

Result of Experiment
However the velocity of light is too
great for such a crude set up. In the
tick of the clock, a ray of light would
have travelled around the earth
seven and a half times. Light from
Galileo’s lantern would have only
taken 11 microseconds to cover the
return trip [a microsecond is a unit
of time equal to one millionth (10-6)
of a second]. With his naked eye,
flickering lantern, mechanical
shutter, and crude timing
instrument, the total reaction time
would have well over 0.2 second.

Father of Modern Science
It would have been a miracle
that Galileo could have
detected such an interval of
time for light.
He could only conclude that
the speed of light must have
been ten times faster than
sound – that is, about 3000
metres per second, as
compared to the modern
figure of 299,792,458 metres
per second.
Although Galileo have failed in
the attempt to produce any
precision figure, he was
undoubtedly the first man in
history making an effort to carry
out such a measurement. This,
together with his other
achievements in astronomy,
mathematics and philosophy, he
was made the pioneer genius of
all time and was crowned with
the honour of being the “Father
of Modern Science”.

The Telescope and
Astronomical Measurement
What is more, with the telescope
he improved, Galileo discovered
three of Jupiter's four largest
moons with a telescope devised
by himself, paving the way for
the discovery of the speed of
light by celestial measurement
in a later time by others.

MEASUREMENT BY OLE RÖMER
Cosmic Adventure 3.08 The First Confirmation of the speed of light

Velocity of Light in a Celestial
Scale
In the tick of a second, the light
would have circled the earth eight
times. This speed was too great for
any terrestrial observation,
particularly at a time when methods
and instruments were not yet
available. It was only observations in
the astronomical scale that the
secret of its speed was unveiled.
It happened that Ole Römer (1644-
1710) was an astronomer in contact
with light traversing across vast
celestial space. Ole Römer, 1644-1710 , Danish Astronomy known for
his determination of the speed of light in 1676.

The satellites of Jupiter
The story started with Jupiter -
the fifth planet from the Sun
and the largest planet in the
solar system.
Jupiter has many moons
(satellites) - about 62 already
known. They caught the eye of
two astronomers because of
their strange behaviour under
the telescope.
Io was among one of the four
largest satellites which became
the centre of attention.
Callisto
Io
Ganymede
Europa
Jupiter Sizes not to scale

Observation of Io eclipses
Io goes round Jupiter at a
regular pace just like the moon
round the earth.
Every time it is behind Jupiter, it
disappears from sight and an
eclipse of Io occurred. It would
be some time before Io emerges
from the other side of Jupiter.
This was usually expected to be
a regular phenomenon and the
normal eclipse time is expected
to be in a regular interval.
Io hides behind
Jupiter and
becomes
invisible
Jupiter
Io
Earth
Orbit of Io

However the observers
were based on earth and
the earth as we know it is
moving round the sun like
any other planet in the
solar system.
Earth station in motion
Earth moves
round the sun
Jupiter
Io
Earth
Io hides
behind
Jupiter
and
becomes
invisible

Owing to the orbital movement of the earth,
there is bound to be half a year when the
earth is moving away from Jupiter and the
other half towards Jupiter.
Annual movement of
Earth
Jupiter
Io
Earth moving
towards Jupiter
Earth moving away
from Jupiter

As a result of the difference in
orbit and speed, the timing of
the eclipse was quite not the
same.
Earth Movement
Distorted Observation
Jupiter
Io
Earth moving
towards Jupiter
Io hides
behind
Jupiter
and
becomes
invisible
Earth moving away
from Jupiter

Shorter and longer
eclipse periods
In the Royal Observatory of Paris, an Italian
astronomer called Giovanni Cassini (1625-
1712) had been making observations of the
eclipses of the satellites by Jupiter since 1666.
He found that when the earth is approaching
Jupiter, the eclipse times are shorter; when
moving away from Jupiter, the periods are
longer.
These discrepancies were also noted by
another young Danish astronomer Ole Römer
since1671 while he was working in the
observatory of Uraniborg near Copenhagen. Earth
approaching
Jupiter
Earth receding
from Jupiter

Light took time to reach
different parts of earth
In 1672, Ole Römer went to Paris and joined
Cassini as assistance to continue their
observation of Jupiter’s satellites,
particularly the satellite Io. They both
attributed such discrepancies to the finite
speed of light and Cassini publicized his
findings in the Academy of Sciences on 22
August 1676:
This second inequality appears to be due to
light taking some time to reach us from the
satellite; light seems to take about ten to
eleven minutes [to cross] a distance equal to
the half-diameter of the terrestrial orbit Earth
approaching
Jupiter
Earth receding
from Jupiter

Observation affected by
movement of earth
While Cassini did not follow up
with this reasoning, Römer
further analysed the data and
consolidated the findings with
calculations.
He observed that the cycle of
shortening and lengthening
repeated itself once a year. This
meant that the phenomenon has
much to do with the orbital
motion of the earth and nothing
to do with Io.
ba
𝑐 =
𝑎 − |𝑏|
∆𝑡

Finite speed of light confirmed
As the earth moves away from Jupiter,
the eclipses lagged more and more
behind the expected time, until they
were running about eight minutes late.
Then they began to pick up again, and
after about six months were running
eight minutes early, making a
difference of 16 minutes.
For light to cover a distance equal to
the diameter of the earth’s orbit which
is about 182 million miles, it needs a
speed of about 186,000 miles per
second (299,340 km per second).
186,000
miles per second
299,340
km per second
186,000
miles per second

Finite Speed Finally
Although later measurements
with better methods and
instrumentation yielded more
accurate values, Römer’s
discovery was the first
conclusive proof that the
speed of light was finite,
putting an end to the reign of
Aristotle’s idea after nearly
two thousand years.

Subsequent Measurements
In 1728 James Bradley (1693-
1762), an English physicist,
estimated the speed of light in
vacuum to be around 301,000
km/s.
By 1879, Michelson had
determined the speed of light to
an accuracy of +/- 50 km/s and
for the first time the error was
smaller than the back and forth
speed of the Earth around the
Sun (2x30 km/s), the next fastest
accessible speed.

The Final Figures
Following these successes, more
sophisticated instruments and
methods were devised to measure the
velocity of light in vacuum. Modern
method involves the use of high
technology laser and atomic clocks.
The most update figure adopted by
the 17th Conférence Général de
Poidset Measures in Paris held in 1983
is:
c = 2.997,924,58 ⤬1010 cm per second
For most practical purposes, it will be
sufficiently accurate to use the
approximate figures:
𝑐 = 2.998 ⤬1010 cm s-1
= 2.998 ⤬ 108 m s-1
= 2.998 ⤬106 km s-1
= 186,000 miles per second

Further Measurements
Date Country Experimental Speed Uncertainty Error
Method (108m/s)
1600 Galileo Italy Lanterns and shutters "Fast" ?
1676 Roemer France Moons of Jupiter 2.14 ? 28%
1729 Bradley England Aberration of Light 3.08 ? 2.70%
1849 Fizeau France Cog Wheel 3.14 ? 4.70%
1879 Michelson US Rotating mirror 2.9991 75000.0 400 in 106
Michelson US Rotating mirror 2.99798 22000.0 18 in 106
1950 Essen England Microwave cavity 2.997925 1000.0 0.1 in 106
1958 Froome England Interferometer 2.997925 100.0 0.1 in 106 1972
Evenson US Laser Method 2.997924 1.1 2 in 109
1974 Blaney England Laser Method 2.997924 0.6 3 in 109
1976 Woods England Laser Method 2.997924 0.2 3 in 109
1983 International 2.99792458 0.0 Exact
Data From History of the Speed of Light by Jennifer Deaton and Tina Patrick. 1996.

UNIVERSE OF FINITE LIGHT SPEED
To be continued on: Cosmic Adventure 3.09

Cosmic Adventure 3.07 08 Light Speed Measurement

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