Longitude and the Speed of Light (a crash course in celestial navigation)

As late grade schooler I was browsing through my sister’s college astronomy textbook. There was an item about a German named Römer calculating the speed of light in 1671 based on a 15 minute variation in the observed times of the eclipses of the moons of Jupiter throughout the year compared to the calculated times of the eclipses.   Römer’s interpretation was that 15 minutes was the length of time required by light to cross the diameter of the earth’s orbit depending on whether we were seeing Jupiter as we passed the planet on the same side of the sun or whether we were observing Jupiter past the sun when the earth is farthest from Jupiter.   The dimensions of the solar system; as known at that time permitted Römer to calculate a modern value for the speed of light; and this was before it was known that light’s travel is not instantaneous.  I soon wondered what sort of obsessive-compulsive astronomers were busy calculating the eclipses of Jupiter’s moons and observing them in such minute detail.  Incidentally reluctance to accept that light’s travel is not instantaneous resulted in several much more complicated explanations of the 15 minute variation than Römer’s interpretation.

Years later I inferred the answer about obsessive-compulsive astronomers, when I was reading about Galileo, who among other better known accomplishments, was awarded a prize for a method of determining longitude.  The donor of the prize was a prince in northern Europe, but Galileo never received the prize because he was prevented from traveling   He was on house arrest for heresy occasioned by promoting his evidence that the sun was the center of the solar system.  Determining longitude requires knowing the difference between local time where the navigator happens to be and Greenwich time. Greenwich, England, is on the principal meridian, the line of zero degrees longitude.

Until the nineteenth century it seemed hopeless to devise a clock maintaining its accuracy long enough to know Greenwich time months after setting the clock before a voyage. Such awesome clocks now exist and are called chronometers.  With Galileo’s method Greenwich time was determined at night by the predicted time of an eclipse of a moon of Jupiter (observable with opera glasses).  The local clock only had to be adequate to know local time at the moment of the eclipse.  The instant of local noon could be determined by a sextant, the instrument already in use for determining latitude.  So the clock error in about 12 hours, or from noon to night when the eclipse occurred, determined the error of calculated longitude.

Now to explain the relation of the clock error to miles on the ground (or water): there are a total of 24 hours for 360 degrees of longitude; so each hour of difference in time compared to Greenwich represents 15 degrees of longitude or about 1000 miles at the equator.  The circumference of the earth is 25,000 miles.  An hour contains 3600 seconds (60x60).  Each second of clock error then results in 1000/3600 miles or about ¼ mile on the ground. Galileo’s method was used to determine the width of the Atlantic Ocean hundreds of years ago to within less than ½ mile.  This required a clock error of less than 2 seconds between noon and night observations; small wonder that chronometers for long voyages didn’t exist until modern times.  Of course radio time signals and satellite navigation have totally altered the details of navigation, but the principles remain the same.

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The determination of the moment of local noon is much simpler than the above.  Look up sextant in the encyclopedia.  The angle of the sun above the horizon (from which latitude can be directly calculated) is recorded repeatedly for a few minutes before and after the moment of noon.  The time of the maximum angle of the sun above the horizon is precisely “high” noon, and can only be determined precisely in retrospect.

Lest you think that navigators have it easy, consider the complication that mean solar time (the time your watch is supposed to keep) and actual solar time are not equal.  An analemma, the figure of 8 in the Pacific Ocean of some globes, by its width on the map shows this navigation error scaled to the earth’s surface, several hundred miles on average.  The error is zero only four times a year, at the solstices and once each in early spring and late summer in the northern hemisphere.

When I looked up on the internet the date of Römer’s calculation of the speed of light, the source confirmed my inference about why so much detail about the eclipses was available to him.  As a matter of fact the reference librarian who helped me with the internet was out to lunch when I first went for help.  The lady at the main desk asked what I needed.  I said tell Lisa that some guy was looking for the date of Römer’s “modern” calculation of the speed of light.  When I returned, Lisa already had the answer.  She had even inferred who the questioner had been.   Don’t sell librarians short.

Here is some final clear thinking about longitude. When you cross the international date line, you gain or lose a day.  Here is how to remember which.  Consider traveling all the way around the world.  You will gain or lose one hour at a time 24 times, the number of time zones. On crossing the date line you must do the opposite of what you have been doing one hour at a time.  Otherwise your personal calendar would be one day different from that of people who stayed at home.

John A. Frantz M.D.

June 15, 2002

Con artists

What is the difference between a con artist and a salesman? Answer: the quality of the product.

This aphorism occurred to me as I toured a mine 50 years ago with the chief engineer. He was my guide because I was filling in as company doctor while the regular one was on vacation.  There was a great deal of interesting information such as a brick of gold worth \$30,000, one month’s production of an incidental by-product of the lead and zinc operation.

Along the way he described the origin of the Gullible Mining Company (a fictitious name), a large international consortium, which operated the local lead and zinc nine.  The fraudulent originators of this company were selling worthless gold mining stock.  To reassure customers who chose to check up on their claim of a mining property in Saskatchewan, they had a mining claim recorded in the court house there. But the skeptical stockholders didn’t stop with a telephone check. They sent a mining engineer to inspect the property.  He found no development whatsoever, but he cracked some local rock specimens with his hammer and found a rich vein of gold.  Suddenly the Gullible Mining Company went “legit”.  Hence the origin of my aphorism.

John A. Frantz M.D.