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Moon Beams and the Speed of Light

On September 15th Jupiter reaches opposition when it lines up with the Earth between it and the Sun. This is when the distance between Earth and Jupiter is minimum and Jupiter's apparent size is maximum. One of the sights which amateur astronomers await is the occultation (the equivalent of eclipses here on Earth) of the Galilean moons (Io, Europa, Ganymede and Callisto) by the shadow of Jupiter. Jovian occultations occur frequently because of Jupiter's shadow is large and the Galilean moons move rapidly around the giant planet (1¾ days for Io to 162/3 days for Callisto). Occultations makes quite a show in a small telescope. You can find the times for occultations published in magazines like Sky and Telescope or The Astronomical Almanac (available in the public library).

Watching occultations of Jovian moons can be more than just a fascinating recreation. In 1676, scarcely eight years after Galileo first discovered the moons of Jupiter, a Danish astronomer Olaf Roemer's timings of occultations led to something truly significant. From his observations of occulations, Roemer was able to make the first reasonably accurate estimation of the speed of light. He discovered occultations while Jupiter was at opposition occurred about a quarter to a third of an hour earlier than occultations while Jupiter was across the Solar system.

Roemer was using very crude time measuring devices. Accurate clocks were developed long after these measurements. In the 17th century, the best measurements of the distances of the Earth and Jupiter from the Sun fell short by ten percent. The periods of the Galilean moons were newly determined and not very accurate. In spite of all these handicaps, Roemer's data estimated the speed of light at about 209000 kilometers (130000 miles) per second, approximately 70% of the accepted value. While his estimates were off by 30%, they were many times more accurate than previous attempts.

His technique was simple but very clever. The occultations acted like a big clock which can be viewed from Earth. When Jupiter is in opposition, the distance to Earth is about four AUs. (An AU [astronomical unit] is the average distance of the Earth to the Sun.) One half a year later the distance from Earth to Jupiter is about six AUs. The extra two AUs are simply the added width of the Earth's orbit. Everything else was the same, reasoned Roemer, so the extra time to sight the Jovian occultations must be due to the time light takes to cross the Earth's orbit. (To be strictly honest, I have simplified Roemer's method a bit by waiting exactly half a year. Roemer actually timed multiple intermediate steps, but the idea remains the same.) Putting together all these numbers yields the speed of light.

Let's use modern numbers and make the same calculation. The Earth orbit is 2 AUs or about 299 million kilometers (186 million miles) across. Suppose we measure the time of an occultation of the moon Europa. About a half year later we go out to see another predicted occultation of Europa. However, the time differs from the prediction by just about 1000 seconds (162/3 minutes). Earth has moved across to the other side of its orbit in half a year. From these facts, we deduce that the speed of light of is about 299000 kilometers (186000 miles per hour) per second, which agrees quite well with the laboratory measured values. This is the type of experiment that a bright middle school student can make with a little coaching. Simple as it is, this experiment demonstrates scientific thinking at its purest.

Having spent so much time with Jupiter, lets not forget the other major planet visible in September, Saturn. Saturn will rise about an hour and a half after Jupiter in the East. Saturn's rings are tipped so that we see their under (South) side. Saturn sits astride the junction of three constellations, Pieces (the Fish), Aries (the Ram) and Cetus (the Whale). None of these constellations are very distinctive, so you will have to rely on Saturn's brightness to find it.

Leslie Coleman
Author:
Leslie Coleman
Entry Date:
Sep 1, 1998
Published Under:
Leslie Coleman's Columns
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