Wednesday, 12 December 2012

The Moon on a stick*

*well, on a disc of MDF, anyway.  

Want to know how to find the moon?  Of course you do!

So far on this blog I have constructed and calibrated a medieval planetary equatorium, and shown you how to use it to find the longitudes of the planets (most recently Mercury).  Now it's the turn of the Moon.

This will be a two-part post, because - unlike for the planets - our equatorium will not only tell us the longitude of the Moon, but also its latitude.

Celestial longitude is measured on the ecliptic, which is a circle in the sky angled at about 23½° to the celestial equator (the projection of the earth's equator outwards onto the sky).  Throughout the year, the Sun, Moon and planets move steadily around the ecliptic.  The Sun, by definition, sits on it; the Moon and planets may stray a little from it, but won't go far.  That's why medieval astronomers didn't worry about the planets' latitude (which is a measure of angle above or below the ecliptic).

The Moon, though, is different.  Classical and medieval astronomers were certainly interested in knowing its latitude.  Can anyone guess why?  (Feel free to comment; you may even win a prize.)  So our equatorium will tell us the Moon's latitude, and that will be the subject of my next post.

But let's talk about longitude now.  The Moon's longitude was modelled by Ptolemy in broadly the same way as for the planets, with a deferent and epicycle (for a refresher, read my explanation here).  There's one crucial difference, though: there's no equant.  Remember that the equant point was the centre of the motion of the epicycle around the deferent, which helped to model the irregular motion of the planets.  But since, for obvious reasons, the Moon's motion as seen from Earth is much more regular, there's no need for an equant point.

But we do still have a rather complicated setup with a moving deferent centre.  This accounts for the fact that, for medieval astronomers, the Moon's movement still seemed somehow to be linked to the Sun's.  (Hardly surprising to us, since the Earth orbits the Sun and the Moon orbits the Earth, but not so obvious to medieval scholars.)  In order to find the Moon's deferent, we need to look up the Moon's mean motus (the location of the centre of the epicycle, as measured from the constellation Aries) in our tables.  From this, we subtract the Sun's mean motus to find the deferent centre (if you get a negative answer, add 360°).

The deferent centre thus moves in a circle around the Earth.  Opposite it on that circle is another point known as the centrum oppositum.  We'll make use of that in a minute.

So, once we've worked out the location of those two points and marked them with our black and white string (pictured right), we get out our big Epicycle.  We put it with its common centre deferent reference point on the Moon's deferent centre.  Then:

1. As with the planets, we move the "black" string to mark the Moon's mean motus on the edge of the face of the equatorium.
2. We move the centre ("pole") of the big Epicycle so it's under the black string, while keeping the common centre deferent in place.  Note: we haven't done the trick with the parallel white string - remember there's no equant this time.  (This change seems to have flummoxed the author of the Equatorie of the Planetis manuscript I'm studying - he was a bit confused on this point.)
Step 3
3.  Run your white string from the centrum oppositum, over the pole of the Epicycle, to the far side of the Epicycle (see picture).
4.  Starting from where the white string crosses the far side of the Epicycle, turn the movable pointer ("label") clockwise [unlike with the planets where we turn it anticlockwise] to mark out the number of degrees corresponding to the Moon's mean argument, which we find in our tables.
5.  As with the planets, stretch the black thread to the mark for the Moon on the label (see below).
6.  Where the black thread crosses the edge of the face, is the Moon's true place (longitude).

And that's it!  Now you can find the Moon, even on a cloudy night.  In the next post, we'll learn how to use the equatorium to find its latitude.  Don't pretend you're not excited...


  1. The lunar latitude was important to determine the exact path of the moon. The moon traverses its own diameter in about 0.54 degrees, equivalent to 111 miles of longitude. By measuring when the moon occulted certain stars one could determine this to an accuracy of a couple of miles. By measuring when such events occurred in local time, and calculating when they occur in local time at one's home port, one could work out the difference in latitude. Such calculations could be made on some astrolabes or devices like the Antikythera mechanism. Lower resolution measurements could be used by a suitable sighting mechanism to measure the angle between a star near the moons path.

  2. Thanks for your comment. Of course the lunar distance method of navigation was to become popular around the 18th century, but in the period when this instrument was made, the method was not available to navigators: tables of lunar distances hadn't been compiled, and there were no instruments that could take observations with sufficient accuracy on a moving ship. But apart from that, I might venture to say that longitude wasn't something that greatly concerned medieval navigators, since most sea travel was in coastal waters - navigators could fix their position by taking sightings of known objects on land.

    I think it's fair to say that medieval astronomers were chiefly interested in lunar latitude in order to predict eclipses, as I explain in the post following this one. Why did they want to predict eclipses? For broadly astrological reasons, but that's a topic I have yet to investigate in much depth.

    Regarding the Antikythera mechanism, it could model the Ptolemaic system with sufficient accuracy to predict eclipses, but as far as I'm aware it had no navigational function - it was used to track the movements of celestial bodies over much longer periods, and could not be used for timekeeping.

  3. The Cantino map (1502) appears to be accurate to 30 nautical miles of longitude. It may have been influenced or even made by Chinese cartographers about 1421 during the time of the Chinese explorations. No-one knows, nor is it known how the measurements of longitude were made. There is certainly no known connection between European navigation methodology and the Cantino map, although they may have been the same. It may well have been based on lunar eclipses but it is unlikely the Chinese knew of Ptolemy or Hipparchos. Further, the number of lunar eclipses available over the voyages seem to me to be insufficient, although fixing certain points on land and then interpolating would reduce this requirement. It would also seem at least possible that they used shore-based measurements as they were plotting the lands rather than the seas, and would have benefited from sighting equipment. Nothing is known of how this was done, however.

    In the Mediterranean coastal sailing was not essential and was not rigidly adhered to; rocky shores often made it hazardous, especially in on-shore-winds at night, and as many ancient ships could sail only at a small angle to the wind they were limited in what directions they could travel at any time; flexibility in setting your course could have been important in avoiding wrecking and in getting your cargo to market, but that implied you could at least estimate your position. The descriptions of ancient voyages shows a knowledge of the region - the wreck of St Paul's ship in the Book of Acts caused by the decision to sail at the end of the season rather than by incompetent seamanship, and the route Amaratus took in bringing Bishop Synesius along the north African shoreline, a low shore with few landmarks so as useless to navigation as the open sea, and exteremly hazardous when a strong wind is blowing from the north - but how did they know where they were and more importantly where to head? Certainly the Persians of the fifth century BC suffered badly from lack of local knowledge in the Med. SO was it only knowledge of winds and currents at each time of year that rendered Med navigation so effective two millenia ago? Did they not need latitude to get around? It is possible, so how likely is it?

  4. Thanks again for another interesting comment. Although I am interested in navigation, I must admit to ignorance of the history of cartography. I would just note that latitude and longitude did not appear on charts until the fifteenth century, which is after the instrument I am working on was designed. Before then, of course, charts were portolan-style, which did depend on accurate coastal fixes.

    As far as Mediterranean navigation is concerned, the lack of any significant tides there makes dead reckoning quite an effective method for an experienced navigator - as long as sailors could measure their speed, direction and time, they could estimate their position to a sufficient degree of accuracy to be able to plot a sensible course until they next saw an identifiable landmark. Of course it wasn't perfect, but that may account for some of the shipwrecks that took place!

    Latitude was of course important - especially when the Portuguese began to explore the coast of Africa, and it was reasonably easy to calculate (harder in heavy seas, of course). But longitude was an unattainable goal - this is clear even on the "Cantino map" you mention: the meridian of Tordesillas, which theoretically circled the globe, was omitted in the eastern hemisphere.