Give it a place and a bearing and it tells you what rose or set there, at whatever
epoch you like, with precession and each star's own motion applied. Then it tells you the thing every
other alignment calculator leaves out: how often a bearing picked at random would have hit
something too.
the sighting
site
latitude
bearing
epoch (year)
horizon alt.
tolerance
what you are willing to accept as a target
every star is counted twice, once rising and once setting, because a wall points both ways.
the horizon, and what is on it
what your bearing hits
and how impressed to be
How to read this
An alignment is an argument of the form this cannot be a coincidence. That argument has
two halves, and almost everything published about ancient alignments supplies only the first.
The first half is easy and this tool does it in a millisecond: your bearing, at your latitude, over
your horizon, corresponds to exactly one declination, and any body at that declination rose or set
there. The arithmetic is a single line of spherical trigonometry and it has no opinions.
The second half is the base rate. Before you can be impressed that a wall points
at something, you have to know how hard it would have been to point at nothing. That depends entirely
on how long a list of acceptable targets you were carrying, and how much slop you allow. Add the Moon's
standstills and you have doubled your targets. Add every star down to third magnitude and you have
added three hundred and seventy more. Widen your tolerance from half a degree to two and every one of
them gets four times as wide.
The number in the right-hand panel is the honest answer: the fraction of the whole circle that is
within tolerance of something on your accepted list. It is exact, not simulated, because the
union of arcs on a circle can just be computed. Drag the tolerance slider and watch the ring fill in.
For a generous target list the answer is that a bearing chosen with your eyes shut hits something more
often than not, and at that point an alignment has stopped being evidence of anything at all.
Nobody appears to have published this number. Schaefer and Stamm (2020), reviewing light-and-shadow
claims in the American Southwest, put it flatly: "Many workers have recognized the critical nature of the
false alarm rate, but no one has ever quantified the rate." They then quantify it for their own case and
find that 20 to 33 per cent of apparent sun daggers are coincidences. For the simpler question this page
asks, a bearing against a target list, the only computed figures I could find are Heggie's estimate that
Newgrange's passage would admit a solstice sunrise in about one in thirteen orientations, quoted in Ray's
1989 paper, and a blog post by the statistician Sherry Towers working the same arithmetic for the Big
Horn Medicine Wheel. The union of arcs is not hard to compute. It just does not get computed.
This is not an argument that ancient alignments are fake. Some are overwhelming: a passage
that admits light for a few minutes on one morning a year is not competing with a base rate, because
its designers had to solve a much harder problem than hitting a bearing. The point is narrower and it
cuts both ways. A hit against a short, pre-committed target list at tight tolerance is worth a great
deal. The same hit against a long list, chosen after looking, is worth almost nothing, and the
difference is a number you can compute rather than a matter of taste.
What it will not do
The tool refuses in two places, and both refusals are more useful than an answer would have been.
Outside its precession model it stops. Star declinations change over millennia and
the polynomial used here is fitted near the present day. Beyond its stated validity it does not
degrade gracefully, it diverges, so past that point the tool says so and declines to name targets
rather than naming plausible wrong ones. The model here is Vondrák, Capitaine and Wallace (2011), which is defined over plus or minus 200,000 years and holds to a few arcseconds throughout recorded history, so in practice what bounds an answer first is the obliquity model at 10,000 years, and beyond that the tool says so.
Below half a degree it tells you to stop. Schaefer and Liller measured horizon
refraction 144 times at seven sites and found it ranges from 0.23° to 1.68°, against a mean of 0.55°.
Their conclusion is the one number every alignment argument should carry: "the range in the declination
will be 0°.45. This uncertainty in the indicated declination sets a fundamental limit on the accuracy of
any alignment." Set the tolerance finer than that and the tool says so, because below it you are not
measuring the monument, you are measuring the weather on the morning somebody looked.
It will not tell you whether your bearing rises or sets. It cannot: rising and
setting bearings mirror each other about the meridian, so a line on the ground is compatible with both,
and every alignment claim has to settle that from the architecture rather than the geometry. A doorway
faces one way. A pair of stones does not.