Finding Your Place in the World

mapIt was the night of Saturday, August 23, 1806. Lieutenant Zebulon Pike, who, along with twenty three soldiers, had escorted fifty one Osage Indians back to their homes, was staying in their village. There he broke out his telescope and turned it toward Jupiter. Unfortunately, there wasn’t good viewing that night. Scattered clouds prevented him from seeing the moons crossing the planet, which he really needed to see. Yes, needed. For unless he saw the transit of the moons of Jupiter, he’d have no idea of exactly where he was.

Even to those of us who remember the days before GPS might find this odd. Surely Lieutenant Pike knew where he was at. Didn’t he? Well, yes and no. He had some idea where he was at, but not precisely. Maps, unless they were made from survey plats, were at best approximations, and Lieutenant Pike didn’t even have that. So, to determine the exact position of the Osage village, Pike had to calculate the latitude and longitude.

Latitude, based on the elevation of the Sun, is easy to determine. Using proper instruments (never look directly at the Sun – early navigators became blind because their primitive instruments required this), you measured the angle of the Sun at its highest elevation, looked up the date in a table to determine how high the Sun would be at the equator, and then simple math gave you the longitude.

Let’s say and explorer measured the elevation of the Sun at local noon as 42º 20’ 30.2”. He looks in his almanac and finds the declination of the Sun, the degrees from straight overhead if he was standing at the equator, is – 7º 39’ 29.8” So, if he was standing at the equator, the elevation of the Sun would be 90º – 7º 39’ 29.8” = 82º 201 30.2”. To find his latitude he would subtract his observed elevation from what the Sun’s elevation would be on the equator: 82º 201 30.2” – 42º 20’ 30.2” = 40º.

Longitude, though, isn’t so simple. While the declination of the Sun is a handy reference whenever it can be seen, there wasn’t one for longitude. That’s because it’s essentially based on time. If the Sun is at its high point, it’s on the meridian, the line running from the North Pole to the South Pole, at that particular location. Since there’s 360º in a circle, and there’s 24 hours in a day, in one hour the Sun moves 360º ÷ 24 = 15º. Now, if you have an accurate clock, and know it’s high noon in Washington, DC, but the Sun is an hour from noon at your location, you know you’re 15º west of Washington. If the Sun is one hour past noon on at your location, but at that moment it’s noon in Washington, you know that you’re 15º east of Washington. The calculations aren’t hard. The problem is that until the 18th Century, accurate portable clocks didn’t exist, and in 1806 they were very expensive. For this reason Lieutenant Pike couldn’t just check the angle of the Sun, compare it with his watch, and calculate his longitude from Washington. Back then each country usually picked their own starting point for longitude, and for the US it was Washington, DC. That starting point wouldn’t be set to Greenwich, England, until 1884.

If Lieutenant Pike didn’t have an accurate clock, how could he figure out his longitude? Through astronomy. There are events visible at the same time on Earth that allows a comparison of time. This is done by using the local time. We’re accustomed to local time being determined by time zones, but actually it depends on the Sun. When the Sun reaches its high point each day, it sets noon at that location. There are slight variations, due to the Earth’s orbit and angle toward the Sun, but these are easy to take into account with a table or even a graph called an analemma. Since local time in respect to Washington would be determined by latitude, first explorers would carefully establish the local time by setting their clocks to noon when the Sun reached its high point, or zenith, then waiting for an astronomical event. If, say, there was a lunar eclipse visible in Washington and your location, you could look up when it was supposed to occur in Washington and note the time you saw it. Then all you had to do was to carefully measure noon the day after, note how much your clock lost and gained, use that to correct your observed time of the event, and then calculate your longitude. Unfortunately, lunar eclipses are rare and aren’t visible in all locations.

However, there was another type of eclipse usually happened nightly: The transit of the moons of Jupiter. Astronomers can calculate when these occur and list it in a table. Then you can compare your observed time with when it was visible in Washington, an calculate your longitude. That’s what Pike was doing that Saturday night. He’d established his latitude and set his clock at noon, and was waiting to note the transit of the moons of Jupiter.

This made tables of the transits of the moons of Jupiter an important thing for surveyors, cartographers, and explorers. It revolutionized the world more than GPS has done in our time. At last it was possible to create accurate maps. It also turned up quirks, such as the difference between the predicted and observed times depending on how far Jupiter was from Earth, which led to an estimate of the speed of light.

Of course, there’s another time piece in the sky, one that doesn’t require a telescope. That’s the Moon. So, why wasn’t it done before Galileo discovered the moons of Jupiter? Because it’s hard. It depends on tables and star charts done to an accuracy that just didn’t exist in Galileo’s day. Methods were developed in the 18th Century, and were used by Captain James Cook and other explorers. But though mariners would use both chronometers and “Lunars” to calculate their longitude (and to verify their chronometers), using the moons of Jupiter to determine longitude was simpler. What calculating longitude by the Moon had going for it is that you could do so on ship, whereas it was impossible to use a telescope to view the moons of Jupiter due to the motion of the waves.

Thomas Jefferson was enamored by the lunar method, so much so that Lewis and Clark were to use it to determine their longitude. Lewis spent three weeks with astronomer Andrew Ellicott to learn celestial navigation and how to make observations for latitude and longitude. The expedition was to record the observations, and their positions calculated on their return. Unfortunately, the book Lewis carried with him had a typo that led to erroneous results. After a few tries, Lewis gave up and just noted his lunar observations for someone else to figure out. Meanwhile, Pike was using the simpler moons of Jupiter method to good effect – until he got picked up by the Spanish for trespassing.

It’s worth noting that Lewis and Clark carried a foreign-made chronometer, the most expensive item on their expedition, costing $250 in 1806. That would be as much as over $7,000 today. Small telescopes were cheaper.

These breakthroughs in navigation brought changes that rival the introduction of GPS. In 1707, four ships of the Royal Navy wrecked returning home, killing over 1,500, because they had no way to tell where they were. In 1773, James Cook, using both a Harrison Chronometer and the Lunar method to determine longitude, created charts so accurate that some copies are still in use today.

Now imagine Columbus heading west, far beyond sight of land, unable to do more than estimate how far he traveled. That took an incredible about of guts.

Do we have that kind of guts today? Looking up at the Moon, where we now send robots where we once sent men, it’s easy to wonder.

Advertisements