Speed of light [3 of 4] Light speed measured by Ole Romer

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MEASUREMENT OF LIGHT SPEED


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.


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.


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



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


Earth moving away from Jupiter


Shorter and longer eclipse periodsIn 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 earthIn 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. 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


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.

186,000miles per second

299,340km 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.


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

Speed of light [3 of 4] Light speed measured by Ole Romer

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