Ole Römer observed discrepancies in the timing of eclipses of Jupiter's moon Io that varied depending on Earth's position in its orbit around the Sun. He realized this was because light takes a finite amount of time to travel between Earth and Jupiter. By calculating how the discrepancies changed over Earth's orbit, Römer was able to determine light travels at about 186,000 miles per second. This was the first direct measurement of the finite speed of light and helped overturn the prevailing view that light traveled instantaneously.

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MEASUREMENT OF LIGHT SPEED

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Finite speed of waves by
Christiaan Huygens
In the 1670’s, the Dutch physicist
Christiaan Huygens (1629-1695)
advocated the idea that light is a
series of shock waves which
propagate through an invisible
medium the ether - like water
wave on the surface of a pond.
This theory demanded that light
have to travel at a finite speed,
quite contrary to what people
popularly believed at the time.

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Velocity of light in celestial
scale
In the tick of a second, the light
would have circled the earth
seven and half 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.

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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

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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

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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

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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

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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

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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

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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

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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. 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.
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𝑐𝑐 =
𝑎𝑎 − |𝑏𝑏|
∆𝑡𝑡

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Finite speed of light confirmed
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).
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.
186,000
miles per second
299,340
km per second

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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.

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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 ⤬1010cm per second
For most practical purposes, it will be
sufficiently accurate to use the approximate
figure:
c = 2.998 ⤬1010cm s-1
= 2.998 ⤬ 108m s-1
= 2.998 ⤬106km s-1
c = 2.998 ⤬1010cm s-1
= 2.998 ⤬ 108m s-1
= 2.998 ⤬106km s-1