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Determine Your Longitude With Jupiter's Moons

Morris Jones


 

... My experiment was missing a crucial piece of equipment that an 19th-century surveyor would have had ...

 

 

It was MIT physicist Philip Morrison on a television documentary who taught me how to use Jupiter's moons as a system for synchronizing clocks, the first step in calculating longitude with astronomical observations. With an ephemeris for Jupiter satellite transits and occultations that is accurate for the time at the Royal Greenwich Observatory, you can synchronize your clock to the observatory's by watching the scheduled event. The difference between your local time and Greenwich local time reveals your longitude.

On a clear night in late February, I decided to try this experiment. I set up my 4-inch refractor on my back deck outside my house in San Rafael, California. My favorite Jupiter ephemeris (www.projectpluto.com/jevent.htm) predicted an occultation of Europa for 0510 Greenwich Mean Time (GMT) the following day, or 9:10 p.m. Pacific Standard Time, my local "standard" clock. This event provided a splendid opportunity to synchronize my own GMT clock.

These days it's easy to set your watch to GMT. My computer stays synchronized to a variety of reference clocks available on the Internet using the network time protocol (NTP). So I already knew that my watch was correct.

At about 8:40 p.m., I had my mount aligned and tracking, and Jupiter was looking big and beautiful. I wanted to test my ability to judge the precise moment when the occultation was complete, so I stopped looking at my watch. I knew it was several minutes before the ephemeris's predicted time when I first saw Europa brushing against Jupiter's limb. It was like watching a very distant sunset as Europa sank further behind Jupiter's disk, appearing as a tiny lump on the edge. The lump shrank to a smaller dot, but it was still there. Would I be able to tell the exact moment of occultation? I looked again and couldn't see Europa — but wait, I thought, "There's still a tiny pinpoint on the edge. Or is it just my imagination?"

Finally it was clear that nothing was left. No odd pinpoints appeared even when I used averted vision. It was time. I looked at my watch. It was 9:10:30: dead center in the designated minute.

Following through with the experiment, now that I had a clock synchronized to GMT, I could calculate the sidereal time at Greenwich. Sidereal time, the right ascension coordinate crossing overhead at any particular moment, is the key to calculating longitude. Longitude is simply the difference between the sidereal time at a reference location (Greenwich) and the local sidereal time, expressed as degrees instead of hours, minutes, and seconds.

But my experiment was missing a crucial piece of equipment that an 19th-century surveyor would have had: a transit scope. A transit scope points only along the meridian. The mount would be plumbed to vertical, and aligned very carefully with the north celestial pole. I could approximate a transit scope by turning off my mount's clock drive, and reorienting the mount so the telescope is constrained to rotate along a line including the zenith and the north celestial pole. Alas, most telescope mounts, mine included, won't twist into such a configuration.

But if I had such a device, I could watch for any charted star to cross my local meridian. At that moment, my local sidereal time would match the right ascension of that star. I would consult my recently synchronized GMT clock, and convert that time to the Greenwich sidereal time, using published tables. Take the difference between local sidereal time and Greenwich sidereal time, convert it to degrees, and bingo! Longitude.

 


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