Past Earths revisited, and the software that finds them

Here is the sky this Wednesday evening –

 – showing again the Earths of 10, 20, 30… days back.

They are exaggerated 300 times in size, otherwise most of them would be far too small to draw.  They now look a bit more real, with equators, showing that their southern hemispheres are tilting away from the Sun, to give us our early winter weather in October and November.

To show true size, however, I’ve added a string of tinier Earths that seem to be coming out of the middle of the bloated one 10 days back.  They are the Earth at 9, 8, 7, 6, 5, 4, 3, 2, and 1 day ago – getting ever nearer to the “antapex of Earth’s way,” the direction straight backward – and they are at true scale.

Even the Earth only one day’s journey back is distant from us about 2.6 million kilometers or 1.5 million miles, or 6.8 times the Moon’s distance.  (Its apparent width is 0.28°, only slightly wider than the Moon’s.)  This begins to make clear how fast our Earth travels;  how huge, compared with itself, is its orbit around the Sun.

Low to the southwestern horizon is Saturn, above the lid of the “Teapot” of Sagittarius, and almost in front of it is the past-Earth of 120 days ago, July 31.  That Earth, exaggerated 300 times in size, is at a s°istance from us of 1.72 astronomical units (Sun-Earth distances); Saturn, exaggerated 150 times, is more than 9 a.u. away.

As before, brown color picks out the past-Earth nearest to the date of the September equinox, and yellow picks out the one nearest to the date of the June solstice, now nearly half a year ago and below the sunset horizon.

You can see, not far up from the yellow June Earth, a tick across the southernmost ecliptic, representing the solstice point in Sagittarius, where Earth appears as seen from the Sun at the June solstice.

But a comment from Eric David expressed a difficulty that others may have noticed.  The brown Earth appears against the background of Capricornus.  Shouldn’t it appear where Earth is at the September equinox, much farther left (east), the point in Pisces where the ecliptic crosses the equator?

It’s a good question that has to do with the challenge of perceiving Earth’s orbital journey in three dimensions – seeing it in space as we look out from Earth itself – which is what my “past-Earths” try to help with.

The ecliptic is a plane.  The line by which we draw it on the celestial sphere is at no particular distance – is at infinite distance.  The Earth’s three-dimensional journey is in that plane (so we see it superimposed on the line of the ecliptic), but comes curling around from behind the Sun, aiming for us.  It’s like (self-quote) “a circular rail around the Sun, along which Earth is sliding.”

It’s the Sun that’s at the center of that circle.  The equinox point on the ecliptic is where that brown September Earth appears as viewed from the Sun.  Contemplate the picture again: there’s the Sun down to the right, there’s the brown September Earth, there out at infinity is the equinox point.

And, on around the circle, the Sun sees the nearest past-Earth, only  a day ago, against the background of Taurus, between the Pleiades abd Hyades; and sees us – the Earth of the present moment – about a degree farther on.

The past-Earths are rapidly expanding in apparent size as they whirl nearer, and those of only hours ago would fill the sky.

And here is the sky the next morning,

– with the actual-size future-Earths of 1 to 9 days ahead, and the 300-scale Earths of 10, 20, and so on days ahead.  They show us our way on along the circular railway around the Sun,  That of 30 days ahead (December 19) is colored blue to show that it is near to the December 21 solstice

And now you can see the Moon coming past, because it is at Third Quarter on Dec. 29.  So it too is near the direction straight ahead in our orbit, scientifically called the “Apex of Earth’s Way.”  It looks the same shape as the one-day-ahead Earth, and almost the same size – very slightly smaller – because we’re not exaggerating the Moon’s size this time.

Venus, exaggerated 150 times in size like Saturn, is almost behind the future-Earth of 100 days ahead.

The past and future Earths may make you giddy, and I may not use them any more.

Enough people have kindly asked what software I use, and whether they could share it, that I owe an answer.  The short and, I’m afraid, disappointing answer is that I write it all myself, and it would be next to impossible to share.

I write programs in Fortran.  Most of them are about astronomy, some for calculating facts and some for generating pictures with Adobe Illustrator.  I learned that almost primeval programming language initially from two or three friends who were helping me with the first few Astronomical Calendars – I was a hanger-on at the university where they were students.  I’ve taken no course in it and have continued somewhat in isolation, so that my style may differ from those of professional programmers and there may still be a lot that I could learn from them.

I try to prune, but a count shows that I have at present 368 programs, a few being much more important than others.  Some are short (though the one for these sky scenes, for instance, has grown to 3,000 lines, of which 200 are about the past-and-future Earths).  But almost every program is the small tip of an iceberg, in that it draws on my “library” of subprograms – rather like tools that can be picked up.  That library is about 18,000 lines and contains about 600 subprograms.  And there have to be other files for the programs to read, such as instructions for how they operate this time, and catalogs of stars.

Someone once told me that each line of a program represents about an hour of thought.  That has to be a rubbery estimate, since, for one thing, much thought goes into finding ways to reduce the number of lines.

My system is an interconnected maze; I have to know my way around it, which would take a lot of explaining to anyone else.  Parts of the longer answer might be interesting and I may get into it sometime.

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DIAGRAMS in this post were made with precision but had to be inserted in another format.  You may be able to enlarge them on your monitor.  One way: right-click, and from the drop-down list choose “View image”  Or from that list choose “Copy image”, then put it on your desktop, then open it.  I would welcome learning of any other methods.

This weblog asserts its right to be about astronomy or anything under the sun.

Cato ended every speech to the Roman Senate with: “Carthage must be destroyed.”  I want to end every message with: “If you’re not doing something to slow carbon emission, you’re speeding the end of civilization.”