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



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 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

Science

Transcript of Cosmic Adventure 3.07 08 Light Speed Measurement