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Peter Fogg wrote-

| Here's a thought: if the time of apparent sunrise/sunset was observed
regularly;
| the extent of the difference or inaccuracy shown by observation
| compared to calculated data could be evaluated on a regular basis and
| contrasted with other information about position.

Well, it could be observed from a fixed position on the coast, by anyone who
was fortunate enough to live in a spot with a wide horizon to his East or
West, whenever the Sun's disc could be seen on rising or setting. It could
be compared with prediction, knowing his position and height of eye, and a
statistical analysis made. Then he would know, for that location, the range
of variation in refraction of light coming in from space to just skim the
horizon and arrive at the observer.

But that's all. I don't see how that result could be employed to determine
anything else more useful.

Peter continued-

| Given that the effects of anomalous refraction can constitute a
| significant constraint upon the accuracy of observations taken from
| the deck of a small boat, thus from within the lowest band of
| atmosphere, and that there is no way of knowing whether they are
| present, let alone the extent of inaccuracy introduced;

I think Peter may be thinking here about "anomalous dip", rather than
"anomalous refraction".

Astronomical altitudes are usually measured at a high enough angle that
there's little net bend caused by air-layers at different temperatures, in
which case refraction corrections are very predictable. The serious
unpredictable effects of refraction, that affect light arriving at a
near-horizontal angle, do not apply in that case, because the geometry of
the light path is so different.

But such an altitude is always measured up from the horizon (where the
observer sees it to be) and not from the true horizontal, and the difference
between the two is the dip, which must be corrected for. A significant part
of the dip is caused by bending of the light from the horizon to the
observer's eye, along that path, usually just a few miles long, and always
within a few feet of the sea-surface. That bend is seriously affected by
temperature gradients in the air just above the sea-surface, which are
unpredictable.

The total dip correction, predicted in tables, is made up of two components,
both of which vary in the same way with height-of-eye. The major component
is exactly geometrical, due to the curvature of the surface, and is
precisely predicable. The refractive bend component is on average about one
twelfth of the geometrical one, usually working against it, but is
enormously variable.

A mean value for that bend is included in dip tables, based on an average
value for air temperature gradients just above the sea surface. However, it
can commonly vary by the odd arc-minute either way from the predicted value,
and sometimes by much more, setting a limit on the achievable accuracy of
sextant observations.

Extreme deviations of dip from the predictions are called "anomalous dip",
which is I think a confusing term. "Anomalous" usually means "contrary to
expectation", but in this case all it seems to mean is that it's at the
outer limits of the natural scatter. Inaccurate sextant observations are
often blamed on anomalous dip, in some cases rightly so.

What I think Peter is suggesting (and perhaps he will confirm whether I have
it right) is that the scatter in Sunrise/set will provide some measure of
the variation in dip. And the answer is no.

To understand what's going on, think about retracing back along the path of
light, that arrived at the observer's eye from the upper sliver of the Sun's
disc, having just skimmed the sea surface at the horizon, which is, say, 5
miles distant. Over that last 5 miles, the bend in the light from that
sliver is exactly the same as the bend in the light from the horizon itself,
because they follow the same path. That bend is the varying, unpredictable,
part of the dip. So if that changes, it shifts the view of the sliver and
the horizon together, in exactly the same way, and does not affect the
timing of sunrise/set one jot.

But that was only the last 5 miles of the light-path. Now, go back another 5
miles, from the point at the horizon towards the Sun. Because the light was
tangential as it skimmed the horizon, and the picture is therefore
symmetrical, at that distance the light will be at exactly the same height
above the sea as was the observer's eye. And the bend in that 5 miles of the
path will be the same in amount as was the bend part of the dip, because of
that symmetry.

But so far we have followed the light path back for only 10 miles from the
observer, no more that a few feet above the sea surface, and the total bend
in that 10 miles is just twice the bend-component of the dip. But light from
a setting Sun has to travel through HUNDREDS of miles of the atmosphere to
get to that point, and the accumulated bend along that long path is far
greater that the bend-component of the dip, and just as unpredictable. And
it depends on very different factors than the bend in the dip does: on
air-layers up in the atmosphere, as opposed to local gradients just above
the waves.

| If this known difference between observed and calculated
| sunrise/sunset should change, could it be a indication of the extent
| of anomalous refraction likely to affect sights taken close to that
| time, eg; star sights just before dawn, or just after sunset?
| Particularly sights taken in that direction?

No. It would be relevant only to observations made for objects that were
viewed at the horizon itself, which excludes stars, which can be seen only
when a few degrees above it.

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.


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