A further correction to both the position angle and the separation must be made, this time for the effects of atmospheric refraction. The correction should be made in reducing observations as well as when comparing observed with calculated values. The effects are negligible for small separations, as both components are subject to the same degree of refraction, and for stars of small zenith distance, where there is little displacement of star positions due to refraction.
The zenith distance of the star is given by cos z = sin 8sin 0 - cos 8cos 0 cos H
where z is the zenith distance
0 is the latitude of the observer H is the hour angle of the star (= local apparent sidereal time - a).
The position of the star is measured towards the pole but it is displaced towards the zenith, hence the angular difference between these two directions, the parallactic angle, needs to be calculated:
where q is the parallactic angle.
The refractive index of the atmosphere varies according to temperature and air pressure. Let C be the air temperature in degrees Celsius P be the air pressure in millimetres of mercury R be the refractive index. Then
A = 0.024 + 0.079017P - 0.0826PT B = 0.004 - 0.0001101P - 0.000028PT R = A + B.
The changes in the position angle and the separation can be found using Chauvenet's equations. These equations hold only for zenith distances less then 75°, i.e. for stars more than 15° above the horizon.
AQ = -R (tan2 z cos (Q- q) sin (Q- q) + tan z sin q tan 8) Ap = pR (1 + tan2 z cos2 (Q - q)).
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