When I was in grade school -- probably some time around 7th grade -- I
happened upon an article in Scientific American about the Anasazi Sun
Dagger on Fajada
Butte in Chaco Canyon. On the solstices and equinoxes, a thin
dagger of light is positioned just right so that it moves across a
spiral that's carved into the rock.
I was captivated. What an amazing sight it must be, I thought.
I wondered if ordinary people were allowed to go see it.
Well, by the time I was old enough to do my own traveling, the answer
was pretty much no. Too many people were visiting Fajada Butte ...
I keep seeing people claim that 40% of consumer food in the US is thrown
away uneaten, or hear statistics like 20 pounds of wasted food per
person per month.
I simply don't believe it.
There's no question that some food is wasted.
It's hard to avoid having that big
watermelon go bad before you have a chance to finish it all,
especially when you're a one- or two-person household and the market
won't sell you a quarter pound of cherries or half a pound of ground
beef. And then there's all the stuff you don't want to eat: the bones, the
fat, the banana peels and apple cores, the artichoke leaves and corn cobs.
But even if you count all that ... 40 percent?
2/3 of a pound per day per person?
And that's supposed to be an average -- so if Dave and I
are throwing out a few ounces, somebody else would have to be throwing
out multiple pounds a day. It just doesn't seem possible.
Who would do that?
When you see people quoting a surprising number -- especially when you see
the same big number quoted by lots of people -- you should always
ask yourself the source of the number.
Galen Gisler, our master of Planetarium Tricks,
presented something strange and cool in his planetarium show last Friday.
He'd been looking for a way to visualize
the "Venus Pentagram", a regularity where Venus'
inferior conjunctions -- the point where Venus is approximately
between Earth and the Sun -- follow a cycle of five.
If you plot the conjunction positions, you'll see a pentagram,
and the sixth conjunction will be almost (but not quite) in the
same place where the first one was.
Supposedly many ancient civilizations supposedly knew about this
pattern, though as Galen noted (and I'd also noticed when researching
my Stonehenge talk), the evidence is sometimes spotty.
Galen's latest trick: he moved the planetarium's observer location
up above the Earth's north ecliptic pole. Then he told the planetarium to
looked back at the Earth and lock the observer's position so it
moves along with the Earth; then he let the planets move in fast-forward,
leaving trails so their motions were plotted.
The result was fascinating to watch. You could see the Venus pentagram
easily as it made its five loops toward Earth, and the loops of all
the other planets as their distance from Earth changed over the course
of both Earth's orbits and theirs.
You can see the patterns they make at right, with the Venus pentagram
marked (click on the image for a larger version).
Venus' orbit is white, Mercury is yellow, Mars is red.
If you're wondering why Venus' orbit seems to go inside Mercury's,
remember: this is a geocentric model, so it's plotting distance from
Earth, and Venus gets both closer to and farther from Earth than Mercury does.
He said he'd shown this to the high school astronomy club and their
reaction was, "My, this is complicated." Indeed.
It gives insight into what a difficult problem geocentric astronomers
had in trying to model planetary motion, with their epicycles and
Of course that made me want one of my own. It's neat to watch it in
the planetarium, but you can't do that every day.
So: Python, Gtk/Cairo, and PyEphem. It's pretty simple, really.
The goal is to plot planet positions as viewed from high
above the north ecliptic pole: so for each time step, for each planet,
compute its right ascension and distance (declination doesn't matter)
and convert that to rectangular coordinates. Then draw a colored line
from the planet's last X, Y position to the new one. Save all the
coordinates in case the window needs to redraw.
At first I tried using Skyfield, the Python library which is supposed
to replace PyEphem (written by the same author). But Skyfield, while
it's probably more accurate, is much harder to use than PyEphem.
It uses SPICE kernels
(my blog post
on SPICE, some SPICE
examples and notes), which means there's no clear documentation or
list of which kernels cover what. I tried the kernels mentioned in the
Skyfield documentation, and after running for a while the program
died with an error saying its model for Jupiter in the de421.bsp kernel
wasn't good beyond 2471184.5 (October 9 2053).
Rather than spend half a day searching for other SPICE kernels,
I gave up on Skyfield and rewrote the program to use PyEphem,
which worked beautifully and amazed me with how much faster it was: I
had to rewrite my GTK code to use a timer just to slow it down to
where I could see the orbits as they developed!
It's fun to watch; maybe not quite as spacey as Galen's full-dome view
in the planetarium, but a lot more convenient.
You need Python 3, PyEphem and the usual GTK3 introspection modules;
on Debian-based systems I think the python3-gi-cairo package
will pull in most of them as dependencies.
I'm jazzed about this show. I think it'll be the most fun
planetarium show we've given so far.
We'll be showing a variety of lunarfeatures:
maria, craters, mountains, rilles, domes, catenae and more.
For each one, we'll discuss what the feature actually is and how it
was created, where to see good examples on the moon,
and -- the important part -- where you can go on Earth,
and specifically in the Western US,
to see a similar feature up close.
Plus: a short flyover of some of the major features using the
full-dome planetarium. Some features, like Tycho, the
Straight Wall, Reiner Gamma, plus lots of rilles, look really great
in the planetarium.
If you can't get to the moon yourself,
this is the next best thing!
The Hitchhiker's Guide to the Moon:
7pm at the PEEC nature center. Admission is free.
Come find out how to explore the moon without leaving your home planet!
The Mercury transit is over. But we learned some interesting things.
I'd seen Mercury transits before, but this is the first time we had an
H-alpha scope (a little 50mm Coronado PST) in addition to a white light
filter (I had my 102mm refractor set up with the Orion white-light filter).
As egress approached, Dave was viewing in the H-alpha while I was on
the white light scope. When I saw the black-drop effect at third
contact, Mercury was still nowhere near the edge in the H-alpha:
the H-alpha shows more of the solar atmosphere so the sun's image
is noticably bigger.
This was the point when we realized that we should have expected this
and been timing and recording. Alas, it was too late.
Mercury was roughly 60% out in the white light filter -- just past the
point where the "bite" it made in the limb of the sun -- by the time
Dave called out third contact. We guessed it was roughly a minute,
but that could be way off.
For fourth contact, Dave counted roughly 45 seconds between when I
couldn't see Mercury any more and when he lost track of it. This is
pretty rough, because it was windy, seeing was terrible and there
was at least a 15-second slop when I wasn't sure if I could any
indentation in the limb; I'm sure it was at least as hard in the
Coronado, which was running at much lower magnification.
So we had a chance to do interesting science and we flubbed it.
And the next chance isn't til 2032; who knows if we'll still be
actively observing then.
I wanted to at least correlate those two numbers: 45 seconds and
60% of a Mercury radius.
Mercury is about 10" (arcseconds) right now. That was easy to find.
But how fast does it move? I couldn't find anything about that,
searching for terms like mercury transit angular speed OR velocity.
I tried to calculate it with PyEphem but got a number that was orders of
magnitude off. Maybe I'll figure it out for a later article, but I wanted
to get this posted quickly.
I didn't spend much time trying photography. I got a couple afocal snaps with
my pocket digital camera through the white-light scope that worked out pretty well.
I wasn't sure that would work for the Coronado: the image is fairly dim.
The snaps I did get show Mercury, though none of the interesting detail
like faculae and the one tiny prominence that was visible. But the
interesting thing is the color. To the eye, the H-alpha scope image is
a slightly orangy red, but in the digital camera it came out a
startling purplish pink. This may be due to the digital camera's filters
passing some IR, confusing the algorithms that decide how to shift the color.
Of course, I could have adjusted the color in GIMP back to the real color,
but I thought it was more interesting to leave it the hue it came out
of the camera. (I did boost contrast and run an unsharp mask filter, to
make it easier to see Mercury.)
Anyway, fun and unexpectedly edifying! I wish we had another transit
happening sooner than 2032.
Mercury Transit 2006, photo by Brocken Inaglory
Next Monday, November 11, is a transit of Mercury across the sun.
Mercury transits aren't super rare -- not once- or twice-in-a-lifetime
transits -- but they're not that common, either.
The last Mercury transit was in 2016; the next one won't happen til 2032.
This year's transit isn't ideal for US observers. The transit will
already be well underway by the time the sun rises, at least in the
western US. Here in New Mexico (Mountain time), the sun rises with
Mercury transiting, and the transit lasts until 11:04 MST.
Everybody else, check
Mercury Transit page for your local times.
Mercury is small, unfortunately, so it's not an easy thing to see
without magnification. Of course, you know that
you should never look at the sun without an adequate filter.
But even if you have safe "eclipse glasses", it may be tough to
spot Mercury's small disk against the surface of the sun.
One option is to take some binoculars and use them to project an image.
Point the big end of the binoculars at the sun, and the small end at
a white surface, preferably leaning so it's perpendicular to the sun.
I don't know if binocular projection will give a big enough image
to show Mercury, so a very smooth and white background, tilted so
it's perpendicular to the sun, will help.
(Don't be tempted to stick eclipse glasses in front of a
binocular or telescope and look through the eyepiece! Stick to
projection unless you have filters specifically intended for
telescopes or binoculars.)
Of course, a telescope with a safe solar filter is the best way to see a
transit. If you're in the Los Alamos area, I hear the Pajarito
Astronomers are planning to set up telescopes at Overlook Park.
They don't seem to have announced it in any of the papers yet, but
I see it listed on the
There's also an event planned at the high school where the students
will be trying to time Mercury's passage, but I don't know if
that's open to the public. Elsewhere in the world, check with your local
astronomy club for Mercury transit parties: I'm sure most clubs have
I was discussing the transit with a couple of local astronomers earlier
this week, and one of them related it to the search for exoplanets.
One of the main methods of detecting exoplanets is to measure the dimming
of a star's light as a planet crosses its face.
For instance, in
55 Cancri e,
you can see a dimming as the planet crosses the star's face, and a
much more subtle dimming when the planet disappears behind the star.
As Mercury crosses the Sun's face, it blocks some of the sun's light
in the same way. By how much?
The radius of Mercury is 0.0035068 solar radii, and the dimming is
proportional to area so it should be 0.00350682, or
0.0000123, a 0.00123% dimming. Not very much!
But it looks like in the 55 Cancri e case, they're detecting dips
of around .001% -- it seems amazing that you could detect a planet
as small as Mercury this way (and certainly the planet is much bigger
in the case of 55 Cancri e) ... but maybe it's possible.
Anyway, it's fun to think about exoplanets as you watch tiny Mercury
make its way across the face of the Sun.
Wherever you are, I hope you get a chance to look!
Dave and I will be presenting a free program on Stonehenge at the Los
Alamos Nature Center tomorrow, June 14.
The nature center has a list of programs people have asked for, and
Stonehenge came up as a topic in our quarterly meeting half a year ago.
Remembering my seventh grade fascination
with Stonehenge and its astronomical alignments -- I discovered
Stonehenge Decoded at the local library, and built a desktop
model showing the stones and their alignments -- I volunteered.
But after some further reading, I realized that not all of those
alignments are all they're cracked up to be and that there might not
be much of astronomical interest to talk about, and I un-volunteered.
But after thinking about it for a bit, I realized that "not all
they're cracked up to be" makes an interesting topic in itself.
So in the next round of planning, I re-volunteered; the result is
tomorrow night's presentation.
The talk will include a lot of history of Stonehenge and its construction,
and a review of some other important or amusing henges around the world.
But this article is on the astronomy, or lack thereof.
The Background: Stonehenge Decoded
Stonehenge famously aligns with the summer solstice sunrise, and
that's when tens of thousands of people flock to Salisbury, UK to
see the event. (I'm told that the rest of the time, the monument is
fenced off so you can't get very close to it, though I've never had
the opportunity to visit.)
Curiously, archaeological evidence suggests that the summer solstice
wasn't the big time for prehistorical gatherings at Stonehenge; the
time when it was most heavily used was the winter solstice, when there's
a less obvious alignment in the other direction. But never mind that.
In 1963, Gerald Hawkins wrote an article in Nature, which he
followed up two years later with a book entitled Stonehenge Decoded.
Hawkins had access to an IBM 7090, capable of a then-impressive
100 Kflops (thousand floating point operations per second; compare
a Raspberry Pi 3 at about 190 Mflops, or about a hundred Gflops for
something like an Intel i5). It cost $2.9 million (nearly $20 million
in today's dollars).
Using the 7090, Hawkins mapped the positions of all of Stonehenge's
major stones, then looked for interesting alignments with the sun and moon.
He found quite a few of them.
(Hawkins and Fred Hoyle also had a theory about the fifty-six Aubrey
holes being a lunar eclipse predictor, which captured my seventh-grade
imagination but which most researchers today think was more likely
just a coincidence.)
But I got to thinking ... Hawkins mapped at least 38 stones if you
don't count the Aubrey holes. If you take 38 randomly distributed points,
what are the chances that you'll find interesting astronomical alignments?
A Modern Re-Creation of Hawkins' Work
Programmers today have it a lot easier than Hawkins did.
We have languages like Python, with libraries like PyEphem to handle
the astronomical calculations.
And it doesn't hurt that our computers are about a million times faster.
Anyway, my script,
takes a GPX file containing a list of geographic coordinates and compares
those points to sunrise and sunset at the equinoxes and solstices,
as well as the full moonrise and moonset nearest the solstice or equinox.
It can find alignments among all the points in the GPX file, or from a
specified "observer" point to each point in the file. It allows a slop
of a few degrees, 2 degrees by default; this is about four times the
diameter of the sun or moon, but a half-step from your observing
position can make a bigger difference than that. I don't know how
much slop Hawkins used; I'd love to see his code.
My first thought was, what if you stand on a mountain peak and look
around you at other mountain peaks? (It's easy to get GPS coordinates
for peaks; if you can't find them online you can click on them on a map.)
So I plotted the major peaks in the Jemez and Sangre de Cristo mountains
that I figured were all mutually visible. It came to 22 points; about
half what Hawkins was working with.
Yikes! Way too many. What if I cut it down? So I tried eliminating all
but the really obvious ones, the ones you really notice from across
the valley. The most prominent 11 peaks: 5 in the Jemez, 6 in the Sangres.
That was a little more manageable. Now I was down to only 22 alignments.
Now, I'm pretty sure that the Ancient Ones -- or aliens -- didn't lay
out the Jemez and Sangre de Cristo mountains to align with the rising
and setting sun and moon. No, what this tells us is that pretty much any
distribution of points will give you a bunch of astronomical alignments.
And that's just the sun and moon, all Hawkins was considering. If you
look for writing on astronomical alignments in ancient monuments,
you'll find all people claiming to have found alignments with all
sorts of other rising and setting bodies, like Sirius and
Orion's belt. Imagine how many alignments I could have found if I'd
included the hundred brightest stars.
So I'm not convinced.
Certainly Stonehenge's solstice alignment looks real; I'm not disputing that.
And there are lots of other archaeoastronomy sites that are even
more convincing, like the Chaco sun dagger. But I've also seen plenty of
web pages, and plenty of talks, where someone maps out a collection of
points at an ancient site and uses alignments among them as proof that
it was an ancient observatory. I suspect most of those alignments are more
evidence of random chance and wishful thinking than archeoastronomy.
Last night, as we drove home from the
-- one of Los Alamos's best annual events, a night exhibition of
dozens of carved pumpkins all together in one place -- I noticed a
glow on the horizon right around Truchas Peak and wondered if the moon
was going to rise that far north.
Sure enough, I saw the first sliver of the moon poking over the peak
as we passed the airport. "We may get an extended moonrise tonight",
I said, realizing that as the moon rose, we'd be descending the
"Main Hill Road", as that section of NM 502 is locally known, so we'd
get lower with respect to the mountains even as the moon got higher.
Which would win?
As it turns out, neither. The change of angle during the descent down
the Main Hill Road exactly matches the rate of moonrise, so the size
of the moon's sliver stayed almost exactly the same during the whole
descent, until we got down to the "Y" where a nearby mesa blocked our
view entirely. By the time we could see the moon again, it was just
freeing itself of the mountains.
Neat! Made me think of The Little Prince: his home asteroid B6-12
(no, that's not a real asteroid desgination) was small enough that by
moving his chair, he could watch sunset over and over again.
I'm a sucker for moonrises -- and now I know how I can make them last