Positional Astronomy BR Precession
Positional Astronomy BR Precession
Positional Astronomy BR Precession
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http://star-www.st-and.ac.uk/~fv/webnotes/chapt16.htm
Positional Astronomy:
Precession
{Note: If your browser does not distinguish between "a,b" and ", " (the Greek letters "alpha, beta") then I am afraid you will not be able to make much sense of the equations on this page.}
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http://star-www.st-and.ac.uk/~fv/webnotes/chapt16.htm
Exercise:
The Vernal Equinox occurs nowadays
when the Sun is in the constellation of Pisces.
Pisces covers a section of the ecliptic
from longitude 352 to longitude 28;
at longitude 28 the ecliptic passes into Aries.
How many years would we have to go back,
to find the Sun at the First Point of Aries
at the vernal equinox?
Click here for the answer.
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Because of precession,
our framework of Right Ascension and declination is constantly changing.
Consequently, it is necessary to state the equator and equinox
of the coordinate system to which any position is referred.
Certain dates (e.g. 1950.0, 2000.0) are taken as standard epochs,
and used for star catalogues etc.
To point a telescope at an object
on a date other than its catalogue epoch,
it is necessary to correct for precession.
Recall the formulae relating equatorial and ecliptic coordinates:
sin() = sin() cos() + cos() sin() sin()
sin() = sin() cos() - cos() sin() sin()
cos() cos() = cos() cos()
Luni-solar precession affects the ecliptic longitude .
The resulting corrections to Right Ascension and declination
can be worked out by spherical trigonometry.
But here we use a different technique.
Consider luni-solar precession first,
recalling that it causes to increase at a known, steady rate d/dt,
while and remain constant.
To find how the declination changes with time t,
take the first equation and differentiate it:
cos() d/dt = cos() sin() cos() d/dt
To eliminate and from this equation,
use the third equation:
cos() d/dt = cos() sin() cos() d/dt
i.e.
d/dt = cos() sin() d/dt
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Exercise:
The coordinates of the Galactic North Pole are given officially as
= 12h49m00s, = +2724'00",
relative to the equator and equinox of 1950.0.
What should they be,
relative to the equator and equinox of 2000.0?
(For this calculation, take the values of m and n for the year 1975:
m = 3.074s per year;
n = 1.337s per year = 20.049" per year.)
Click here for the answer.
Alternatively, the Astronomical Almanac lists Besselian Day Numbers throughout the year.
Take a stars equatorial coordinates from a catalogue,
and compute various constants from these,
as instructed in the Astronomical Almanac.
Combine these with the Day Numbers for a given date,
to produce the apparent position of the star,
corrected for precession, nutation and aberration.
Previous section: Aberration
Next section: Calendars
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