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Fred Hebard wrote:

> as best as I can tell, the only time you
> will see significant (>0.1' of arc) systematic shift will be within 10
> minutes of meridian passage.

This is only true for extremely high altitudes, namely over 89.5 deg!!

Dependent on the meridian altitude of a celestial body, the diurnal arc that
it traces in the sky as seen from an observer on earth can be anywhere
between a smooth curve not changing curvature much, or a straight line up in
the east and straight line down in the west, with a sharp bend in-between.

As a general guideline, therefore, the higher the meridian altitude, the
more pronounced the non-linearity effect will be in the vicinity of the
meridian and the faster it will drop to comparatively lower levels (but
still considerable in absolute terms) away from the meridian. The lower the
meridian altitude, the smaller the maximum effect, but also the longer the
period during which the error persists.

For a body with a meridian altitude of 60 deg, the error caused by linear
interpolation between two sights 5 minutes apart is 0.3' at meridian
transit. This error remains the same for a full hour before and after
meridian transit (azimuth between 150 and 210 deg) and drops to half of that
within the next hour (azimuth 130 - 230 deg).

For a body with meridian altitude = 75 deg, this error for two sights 5
minutes apart is 0.8' at meridian transit. It drops to 0.3' within the next
hour and to 0.1' within the next 40 minutes after that.

For a body with a meridian altitude of 45 deg, the same error is only 0.2'
at meridian transit, but an error of 0.1' persists within 3 hours on each
side of meridian passage.

Herbert Prinz

   

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