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Greg originally asked-

>Please excuse the neophite question but; Why does the USNO on-line
>almanac show the following?:
>
> declination of polaris:
> month        d   m
> may         89.17.5
>june         89.17.4
>july         89.17.3
> aug         89.17.3
>sept         89.17.4
> oct         89.17.6
> nov         89.17.7
> dec         89.17.9
>-------2007------
> jan         89.18.1
> feb         89.18.1
> mar         89.18.1
> apr         89.18.0
> may         89.17.8
>june         89.17.7
>july         89.17.6

Among other answers, Gary LaPook replied-

Precession and nutation, the earth's axis wobbles and precesses in a
big
circle taking  26,000 years. It just happens to be pointing near
Polaris
at this time but it is just passing through. See chapter of online
Bowditch at http://www.i-DEADLINK-com/bowditch/  and see:
http://cse.ssl.berkeley.edu/lessons/indiv/beth/beth_precess.html


Greg responded-

|  I follow that 100% , what I am not getting is if it takes 26,000
| to go 360 deg it should only be moving about 50" of arc a year - no?
| is there also a "shorter term wobble" that is in effect?

=======================

Greg is right. He asking a very good question, and hasn't yet had a
good answer fron Nav-l. He is right to persist

Neither precession nor nutation (both caused largely by the pull of
the Moon on the Earth, in different ways) are enough to produce the
short-term variation in the declination of Polaris that Greg has
perceived.

Most of the short-term shift in the (apparent) position of Polaris,
and other stars, over the course of a year, as noticed by Greg, is due
to the aberration of light. It's nothing to do with any shift of the
Earth's axis. It's really quite a simple matter, when you think about
it.

The Earth is travelling round the Sun, in its orbit, once a year. The
Sun's distance (and I will use non-metric units to humour US readers)
is about 94 million miles, so measuring round the orbit, that's a
journey of nearly 600 million miles, each year. That corresponds to
about 18.6 miles per second. The direction, in space, changes
throughout the year. In relation to that direction, at any moment some
stars are seen ahead, some astern, and some abeam. The light from
those stars is arriving at a speed  of 186,000 miles per second, which
is 10,000 times faster than the Earth is travelling. The Earth's
motion, then, is rather trivial in comparison with the speed of light,
but it does have a subtle effect.

It's a bit like travelling into a wind. If you are pushing upwind, the
wind feels stronger, but its apparent direction is unchanged by your
speed against it. Going downwind, the wind feels lighter, but it still
seems to blow from the same direction that it did before. But with a
beam wind, things are quite different. The DIRECTION of that wind
appears to change, to come from somewhere nearer to your bow, more and
more the faster you travel. That's why a fast catamaran is nearly
always sailing rather upwind, no matter what the true wind direction
is, because it is travelling at such a large fraction of the true
windspeed.

It's very much the same with light, but of course the effect is much
less. Light coming from a star that's abeam, in relation to the
Earth's travel at that moment, appears to come from slightly further
ahead, by an angle corresponding to 1 part in 10,000, which is about
one-third of an arc-minute. Not a lot, but detectable to a careful
observer with a good sextant, and well worth while correcting for in
the almanac. Six months later, the Earth will be moving in the
opposite direction, and light from that same star will appear to be
deflected by the same small angle, but in the opposite direction.
Stars in different parts of the sky will appear deflected through
angles up to that 0.3 arc-minute maximum, at different times of the
year.

That's the effect of aberration that Greg finds tabulated in his
almanac. For most navigational purposes, the odd third of an
arc-minute is neither here nor there, but for lunars it becomes
important. The almanac, careful as always, bothers.

Aberration was discovered by Bradley in the 1750s, while he was
looking for something entirely different. The finite speed of light
had by then been known for many years, from the work of Romer.

=============================

While we are at it, let's discuss some other effects on star
positions, starting with precession, as described by Gary LaPook.
About this, Greg wrote- "if it takes 26,000 to go 360 deg it should
only be moving about 50" of arc a year - no?". Well, yes and no.
That's a bit misleading.

It's easiest to visualise precession when you look at an ordinary
globe of the Earth, usually placed on a tilted stand so that the
Earth's polar axis is 23.5 degrees from the vertical. The plane of the
ecliptic, in which the Earth travels around the Sun, is almost exactly
constant, and horizontal. Precession is caused mostly by the pull of
the Moon on the equatorial bulge of the Earth. As a result, the effect
is that the Earth's polar axis moves like a slowly wobbling top about
that vertical line, tracing out a path rather similar to the surface
of an ice-cream cone, taking about 26,000 years to make a circuit..
You can simulate that by rotating the base-plate of the globe's stand,
sitting on a table, through one turn, 360 degrees, in 26,000 years.
Note, though, that because that cone is a rather narrow one, the
Earth's axis itself isn't tilting at that rate, but by rather less
than half of it.

The coordinate system, that we measure sky-positions from, starts at
"Aries", which is the intersection line of two planes, the equator and
the ecliptic. That system was invented to make the Sun's movements
systematic, even though it complicates the positioning of stars.
Because of precession, the Aries line moves around steadily, at 26,000
years for a rotation, or as Greg says, about 50" per year. That's not
a shift of the stars, just a shift of the Earth's axis and the
resulting coordinate system, causing changes in both dec and SHA,
varying according to a star's position. That's the main reason why
star positions on an almanac get slowly out-of-date, from one year to
the next.

By the way, even the Greeks, from the days of Hipparchus, were fully
aware of the existence of precession. They had a rough idea of the
actual rate, but argued about the details. Since their time, the First
point of Aries, at the beginning of the 30-degree Aries sector of the
scale of celestial longitude around the zodiac, has shifted because of
precession to be no longer among the stars of the constellation Aries.
Instead, it's now in the next-door constellation, of Pisces.

=========================

The next effect that list members have alluded to is nutation. This is
another effect mainly of the Moon, on the Earth's axis, but is a
shorter-term "wobble". Its maximum effect is less than half that
discussed above for aberration, and the period, 19 years, is much
longer, so it played a negligible part in the changes that Greg
noticed in the almanac.  However, it has to be considered, when
predictions are being made. That, too, was first discovered by
Bradley.

=========================

A few brighter stars are close enough to us that we can detect their
actual angular motion in space, with respect to the solar system;
known as proper motion. This applies particularly to Arcturus, at just
over 2 arc-seconds per year, and Sirius, at rather more than 1. But
these shifts are quite unimportant for our purposes, though of course
they add up, over the centuries..

==========================

Many closer stars show an annual parallax, an apparent motion over the
year due to the shift of an observer's viewpoint from one side of the
Earth's orbit to the other, six months later. That was what Bradley
was trying to detect when he discovered aberration. But those shifts
are only a fraction of a second and are quite unimportant to us.

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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