Maps and their centers

Here is the evening’s sky for Sunday June 9.

See the end note about enlarging illustrations.

Mercury is moving out from behind the Sun, to be at greatest elongation on June 23.  Mars, progressing slowly through the middle of Gemini, is being overtaken by the Sun, to fall behind it in September.  And the Moon is about to reach First Quarter, 90° from the Sun, in a few hours – on June 10 at 6h Universal Time, which is midnight in the middle of North America.  It will then be at, or rather just north of, the “antapex of Earth’s way”: the point away from which Earth is traveling.  In other words, the Moon at this stage is crossing behind us in our orbit.

This June after-sunset region of the sky – Gemini, Cancer, Leo – appears thus in our Map of the Starry Sky:

This sample of the map happens to show the green sample horizons that I included, to try to indicate how the sky you actually see above your horizon intersects the whole celestial sphere.  Curves of different kinds on a spherical surface can be related to each other in ways that are not simple to understand.

The Map pf the Starry Sky is an improved reincarnation of a product with the same title, which I created many years previously and which went out of print.  It was a by-product of my earliest annual Astronomical Calendars.

Back then, artwork was prepared on paper, to be photographed by whatever firm was doing the printing.  For the Astronomical Calendar‘s twelve large sky maps, on the left-hand pages for the months, I saved labor by drawing a single huge master map, which was circular, centered on the north celestial pole.  The map was pinned at its center to a back sheet of card, and there was a front sheet of card in which I had cut an elliptical window, cprrect for representing the horizon of latitude 40° north.  Then I rotated the map to twelve positions, so that through the window showed the evening sky for each month.  The thing was a sort of planisphere.

(And I pasted on little paper planets and Moons in their positions for the year.  And my master map was actually black-on-white.  It had to be covered with red plastic stuff called Rubilith, and then the printers “reversed” it.)

The horizon window couldn’t be a circle, nor could it be a true ellipse, and I forget how I calculated it before cutting it.  And the positioning of star and constellation labels on the master map was a fairly delicate matter, because I didn’t want any of them to be cut by any of the twelve horizons.

Then it occurred to me to make the master map into a separate publication: the first Map of the Starry Sky.  It, like the book, was only black-and-white.

I remember pinning a copy of this great square map to the ceiling of the room I was using in Furman University.  It sagged somewhat from the ceiling, and once a mockingbird flew in through my open window, panicked, and ended up crouching on top of the Map, before I could shepherd it out.

The later sky maps, by contrast, were properly calculated, thus  circular, with stars’ positions projected relatively to the horizon, so that they have to differ for each month and cannot be made from a master map.

Maps (celestial or terrestrial) can have many kinds of projection, but all those I’m talking about are radial.  The master map for the early Astronomical Calendars, and hence the first Map of the Starry Sky, were radial from the north celestial pole as center.  (The sky shown through the not-quite-elliptical horizon window necessarily did not have a true projection in relation to the horizon.)  The sky maps computer-calculated for the later Astronomical Calendars were radial from the zenith in the middle of each sky.  The two halves of the new Map of the Starry Sky, being maps of hemispheres, are radial from the centers of those hemispheres, on the celestial equator at 6h and 18h right ascension.

All are of the sub-species of radial projection called azimithal equidistant, which I think the simplest (as contrasted with stereographic, gnomonic, and so on) and most widely useful.  That is, angular distances are true from whatever the center is.

And this is also true for the horizon scenes like our Sunday evening one.  But here too the center for the projection can be varied.  If it’s on the horizon, the horizon will appear straight; in this case I’ve chosen 10° below the horizon – altitude minus 10 – so that the horizon makes a convex curve.  I like that because it reminds us that we’re on a globe.  A globe hurtling away from the “antapex.”

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ILLUSTRATIONS  in these posts are made with precision but have to be inserted in another format.  You may be able to enlarge them on your monitor.  One way: right-click, and choose “View image”, then enlarge.  Or choose “Copy image”, then put it on your desktop, then open it.  On an iPad or phone, use the finger gesture that enlarges (spreading with two fingers, or tapping and dragging with three fingers).  I am grateful to know of what methods work for you.

 

6 thoughts on “Maps and their centers”

  1. One of my favorite things about the old white-on-black pole-centered star charts in your early calendars was the way you represented the Milky Way with thousands of white dots. That must have taken quite a bit of effort to draw but it was the best rendering of the galaxy that I’ve seen in a star chart. It did not look like you used a “fill pattern” of white dots on a polygon, as one might do in PowerPoint, so I assumed you drew them individually by hand ~ is that correct?

    1. I doubt there was a stage when I dotted dots with a pen; I’d soon have been tired of it! I’m sure I soon took to doing it with another kind of sheet obtainable at printing supply shops, with pre-printed dots on a backing. It was transparent, you laid it on the artwork, cut carefully with an Exacto knife around the outline pf the area you wanted to cover, peeled it off the backing, and stuck it in place.

      I still have in the “Milky Way” part of my charting program four different ways of drawing it, but now almost always use the latest I created, drawing it in six levels of brightness. I spent hours or weeks (I’m not sure how many years ago) mapping points along the edges of those areas, which I derived from someone’s composite photo of the whole length of the Milky Way. I like this method best, but what you say suggests that it could be improved by somehow softening the transitions between the areas, or somehow reintroducing dots as in those older methods.

      Adobe Illustrator takes much longer, and more code, to draw a multitude of dots than to fill an area with a color. I made the million dots of the “Portrait of a Million” by using one of those pre-printed dot sheets, after first trying to program a million dots and realizing that was impractical.

  2. Thanks Guy. I have several planispheres which I enjoy looking at. They’re useful for getting a sense of which constellations and planets will be up at any given hour, where the Sun will rise and set and how high he’ll be at noon, etc. Planispheres are a connection to the history of astronomy and navigation. The different designs have practical and aesthetic pros and cons.

    I’ve always noticed how the sizes and shapes of the constellations on a planisphere are increasingly distorted the farther you get from the celestial pole (thus the value of a two-sided planisphere with the northern and southern celestial hemispheres on opposite sides), whereas an illustration of the whole sky at any given time is not obviously distorted. Now I can articulate what causes that difference — having the pole at the center of the projection vs. having the zenith at the center! Thank you!

    By the way, navigators need to understand and compensate for the differences between different map projections (although they call a map a chart, because everything on a boat needs a different name than it would have on land). If your ship follows a straight line on chart from one side of an ocean to the other, you will either not arrive at your intended port, or you’ll spend much more time and fuel getting there than was necessary.

    And another map projection issue: the Mercator projection, which puts the lines of latitude and longitude at right angles to one another, makes land masses far north and south of the equator look much bigger than they really are. Greenland (2 million square kilometers) looks bigger than Africa (30 million square kilometers) on a Mercator map. We would have a much better intuitive understanding of the world if we used equal-area projection maps like a Mollweide projection. Astronomy fans may be familiar with equal-area projections from seeing maps of the cosmos which use the galactic equator as the center line, such as illustrations of the cosmic microwave background radiation from the Planck satellite.

    P.S. It makes me happy to know that Deborah Byrd of earthsky.org follows your blog.

    1. The only non-radial projection I use is rectangular, really no projection at all, in which degrees across and up simply have the same scale. This makes the north pole, which is a point, into a line with the same length as the equator. So it too would exaggerate Greenland’s area.
      Mercator differs from this by having a more complicated formula in order to make any straight course at sea into a straight line on the map. This causes areas toward the pole to be exaggerated even more, in fact to infinity. So in practice it can’t be used at all at very high latitudes. Or so I understand it. I don’t actually know the equation for Mercator.

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