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A questioner asked-

>Listed below are declinations of two stars tabulated
>every 90 days or so, from the 2005 Nautical Almanac.
>
>Alpheratz 2005
>   01 Jan N29?07.2
>   31 Mar N29?07.0 (-0.2)
>   30 Jun N29?07.1 (+0.1)
>   30 Sep N29?07.4 (+0.3)
>   31 Dec N29?07.6 (+0.3)
>
>Elnath 2005
>   01 Jan N28?36.8 ( 0.0)
>   31 Mar N28?36.8 ( 0.0)
>   30 Jun N28?36.8 ( 0.0)
>   30 Sep N28?36.8 ( 0.0)
>   31 Dec N28?36.9 (+0.1)
>
>Why does one vary first south, then north, and then
>not return to its "starting point"?
>
>Why does the second vary at a rate far different from
>the first?
>
>Is it varying parallax (from Earth's orbit) for two
>stars at greatly varying distances from earth? If so,
>why does Alpheratz not return to its starting point?
>Parallax from the "expanding universe"??

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

Response from George.

No, it's NOTHING to do with parallax. The Earth's orbit is so tiny compared
with star distances that even for the nearest stars parallax is quite
negligible (0.8" max) at the precision of 0.1' that the Almanac quotes.

There are a number of other effects that combine together. Not only do they
affect declination, but also Right Ascension (and so SHA), and so affect
GHA.

1.The most important is a steady change in the direction of the Earth's
spin axis due to PRECESSION, which causes the direction of the "North Pole"
in the sky to move in an immense circle, taking about 26,000 years to do
so. The plane of the Earth's equator  tilts accordingly. As declinations
are measured from the plane of the equator, the declination of a star
steadily changes even though the star itself is fixed in the sky. Some
stars show a steadily increasing declination, some decreasing, depending on
their position in the sky with respect to the equator and Aries, the
maximum change being about ?20" per year. Precession is the main reason why
the declination hasn't returned to its initial value after a year has
elapsed.

The main reason for the difference in the declination changes over the
year, comparing Alpheratz and Elnath, is that the SHA of Alpheratz is near
to 360 degrees, which makes its declination sensitive to precession,
whereas Elnath has a SHA roughly 270 degrees, which means the declination
does not much change with precession.

2. NUTATION is another motion of the Earth's polar axis, mostly caused by
the Moon. The main component is a cyclic wobble with a period of nearly 19
years and can affect declinations by up to ?9" or so, but there are many
smaller and faster terms. Stars are differently affected by nutation,
according to their position in the sky.

3. ABERRATION. The Earth is travelling in its orbit at a speed that's much
less than the speed of light, but still fast enough to distort slightly the
direction that light appears to be coming from. Stars seen in the direction
that the Earth is travelling towards (and from) are unaffected, but of
course that direction changes through the year, so there's an annual
displacement of the apparent position of stars, depending on where they are
in the sky, of up to ?20" or so. This will affect the declinations of stars
away from the equator more than stars near it. It's a rather important
effect and the Almanac takes it into account.

4. PROPER MOTION. Some stars are close enough, and are moving fast enough,
that their apparent motion with respect to the sky background of "fixed"
stars has to be taken into account For example, the close star Rigil Kent
(Alpha Centauri by another name) has a dec that changes by about +.7" per
year, and Right Ascension that changes by about -3.6" per year. That change
will go on for ever, so it can accumulate up, even if it's not very
important over one almanac-year.

Even the Greeks understood about precession, but in my view it was a
considerable achievement of astronomers of the 17th/18th centuries to sort
out the other corrections.

If the questioner is keen to follow up these matters, and isn't upset by a
mathematical approach, I recommend investment in a copy of Meeus,
Astronomical Algorithms, which has all he could ask for, and much more.

George.



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