Star - Annual Aberration
Aberration is the term used to represent the apparent deviation in the position of an object because the observer are moving and the light velocity being finite.
In the case of the Stars we have the Annual Aberration that is due to the orbital movement of the Earth around the Sun (or more precisely around the barycentre of the Solar System).
Let
l and b be the celestial longitude
and latitude of the star,
k the constant of aberration,
the
true longitude (geometric) of the Sun, e
the eccentricity of the Earth's orbit and p
the longitude of the perihelion of his orbit, where:
e = 0.016708634 - 0.000042037T - 0.0000001267T2
p = 102º.93735 + 1º.71946T + 0º.00046T2
So, the corrections to make in the right ascension a and declination d of the star due to the annual aberration are:
Da2
= - k(cos(a)cos()cos(e)+sin(a)sin())/cos(d)
+ ek(cos(a)cos(p)cos(e)+sin(a)sin(p))/cos(d)
Dd2
= - k[cos()cos(e)(tan(e)cos(d)
- sin(a)sin(d))
+ cos(a)sin(d)sin()]
+ ek[cos(p)cos(e)(tan(e)cos(d) - sin(a)sin(d)) + cos(a)sin(d)sin(p)]
To total corrections to need to be made to a and d, due to nutation and to aberration are in fact Da1+Da2 and Dd1+Dd2, respectively. These expressions can be calculated by the previous expressions and they will result in arcseconds (in the case of Dy, De and k are expressed in the same units).