--------------------- #1503 - How did we learn the speed of light?
- How you can learn the speed of light by using some astronomy. You will need some binoculars or a telescope. Find Jupiter in the night sky high above the Constellation Orion. With binoculars you can easily see the four moons of Jupiter:
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------------------------ Ganymede
------------------------ Io
------------------------ Callisto
------------------------ Europa
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- The moons in orbit around Jupiter change positions every night. Io is the closest and orbits every 42.5 hours. Pick any monthly astronomy magazine and it will show a chart of the positions of Jupiter’s moons each day of the month. I will pick October 31, 2012 at 12:45 AM Viewed through the telescope the south pole of Jupiter is up, not down. This is because the telescope lens flips the image, north to south. At that time the moons are located:
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---------------------- Callisto is far to the left, west
--------------------- Europa is not as far to the right, east
--------------------- Ganymede and Io are closer to Jupiter about the same distance, 15 arc seconds to the right, east
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- I picked this time for the unusual event that you can see Ganymede’s shadow on the face of Jupiter. It is the black dot at the top near the south pole. When Io passes behind Jupiter, is eclipsed by Jupiter, it repeats every 42 hours, 30 minutes. It is like a pendulum in a clock.
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- If you continue these measurements throughout the course of the year there will be a time delay of 22 minutes, from the shortest time to the longest time. This represents the point that the Earth orbit is closest to Jupiter, and when it is farthest from Jupiter six months later. That 6 months represents one half a complete orbit which spans the distance of the diameter of an Earth orbit. The distance to the Sun is 93,000,000 miles. Therefore the diameter is 186,000,000 miles.
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- The 22 minute delay is the time it takes light to travel that extra distance across the diameter of Earth orbit. We can calculate the velocity:
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-------------------- Velocity = 186,000,000 miles / 22 minutes
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-------------------- Velocity = 8,450,000 miles per minute
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--------------------- Velocity = 141,000 miles per second.
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- Well that was with 25% of the right answer. Close is good for astronomy measurements. The speed of light is 186,282 miles per second.
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----------------------- 141,000 / 186,282 = 76%
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- We need to realize that Jupiter is in orbit too. Io’s eclipses actually appear to follow a 13 month cycle. So, we need some refinements in our calculations.
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- In the 17th century when mariners first tried to use Io eclipses as a clock, they found the time to be earlier and later than expected depending on the time of year. The clock turned out to be not accurate enough to avoid the rocks. They did not realize that they had to take into account the Earth’s orbit about the Sun. Astronomers first realized that the time difference was actually the greater distance across the diameter of Earth’s orbit. They got their answer with about 5% for the speed of light.
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- To get even better accuracy astronomers started to measure the parallax of distant stars. In 1728 the astronomers began measuring the parallax shift as the Earth orbited the Sun. One particular star’s position, that of Gamma Draconis, shifted by an angle of 0.006 degrees. Basic trigonometry was used to calculate how fast light traveled between the Sun and the Earth. The result of 8 minutes and 12 seconds was only 7 seconds shorter than the right answer. They estimated that light travels 10,210 times faster that Earth’s orbital velocity. This overestimate of light speed is with 1% correct.
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- In 1850 an electric motor was used to spin a disk having fine teeth with gaps between. A mirror was placed 5 miles away. Returning light pulses with a slow moving disk returned through the same slot. Spinning the disk faster allowed a tooth to block the returning light pulse. Spinning still faster and the returning light pulse passes through the adjacent gap. Using this method the round trip journey for the light pulse could be measured. The result only overestimated the speed of light by 4%.
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- In 1920 scientists bounce light beams off a rotating mirror that was located 21 miles away. The mirror was a spinning octagonal mirror. It would reflect the light beam back to the source only when the mirror face was exactly perpendicular to beam. By varying the speed of the rotation they could calculate the time for each reflecting beam. This measurement put the speed of light at 299,796 + or - 4 kilometers per second,
186, 208 miles per second.
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- Today’s best measurements put light speed at:
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----------------------------- 299,792.458 kilometers per second
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---------------------------- 186,282 miles per second.
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- When radar was used during World War II precise speeds were needed to calculate accurately incoming planes, missiles, and ships. To get even more accuracy scientists combined microwaves inside a cavity of precisely known dimensions. The standing waves produced by the microwaves were known to within 0.8 microns. Measuring the frequency accurately allowed the calculation of the speed of light multiplying frequency times wavelength:
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------------------------- c = f * w
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- This measurement got the result to within 299,792.5 + or - 3 kilometers per second. You could make the same measurement in your microwave oven if you could measure accurately the standing wave on a pad of butter and you knew the frequency of the magnetron to be 2.45 GHz. c = f * w
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- By 1980 light speed was one of the most accurate constants known. It became the standard to determine the length of one meter. A meter became the distance the light travels in a vacuum in 1 / 299,792.458 seconds.
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- All attempts to date to prove that light is not this constant speed in a vacuum have failed. Electromagnetic radiation instantly travels at this constant speed, and is usually abbreviated as “c”.
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------------------ as in: E = m * c^2
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Want to learn more about light?
Here are some more reviews available upon request:
# 1386 Light speed
# 1389 The power of light
# 940 Not enough light
# 934 Light’s mysteries
# 915 Light - atomic interferometer
# 1335 Light spectrum
# 1043 The strangeness of light
# 1044 Light to matter, stranger still
# 615 The energy of a quantum of light
# 912 Wave-particles, anti-matter, and entanglement.
# 768 The wave-particle duality of light
# 34 Getting light from electricity and magnetism
# 589 Light
# 645 How far away is the Sun.
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707-536-3272, Wednesday, October 24, 2012
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