NavList:

Thank you for your report; it has helped me track down the errors in my procedure.  In between clouds, I have been searching for Venus when it has been below the sun, with little success.  I have been using the azimuth circle on the telescope to find azimuth and a level to find altitude.  My problem has been that the telescope was tilted 4 or 5 degrees.  My reference objects for setting true azimuth were near the horizon and I wasn’t having any trouble in the morning, when Venus was above the Sun but still at 10-30 degrees altitude.  My view of the late afternoon sky is obscured, so I was restricted to before 4 pm or so in the afternoon.  Then Venus was quite high, 45 degrees altitude, and at an azimuth of about 270, which is 90 degrees beyond my prime azimuth-reference object,  These were ideal conditions for the observed azimuth on the circle to be in error by 4-5 degrees, far outside the field of view of my oculars.  I finally found Venus in the west below the sun, with a large azimuth error.  So I started exploring the effect of tilt on the apparent azimuth.  The purpose of this post is to present those results, and hopefully have them vetted by folks more conversant with trigonometry than myself.

 I began by imagining the effect of tilt on azimuth when the telescope ia pointed near the horizontal plane.  There is none as best I can imagine.  I could calculate the major and minor axis ratio of the ellipse projected by the tilted azimuth circle on the horizontal plane.  If you start at 0 along the major axis, at 90 degrees on the azimuth circle you will be at 90 degrees in reality.  You will arrive back at the origin at 360 degrees.  I don’t believe there is any deviation, say at 45 degrees.

But if the azimuth is 0 in the direction of tilt, then when rotated to an azimuth of 90 degrees and raised to 90 degrees altitude, the azimuth will be off by the amount of tilt.  Those were, more or less, the conditions for me.  I could find Venus when it was low, altitude 10-20 degrees, pointing near the direction of tilt, but raising the telescope to 45 and rotating 90 degrees in azimuth made it hard to find.

The solution is to level my telescope, which I am doing.  I’m also using the graph below to estimate how accurate the leveling need be.  The bottom line is that tilts of less than 0.5 degrees are acceptable, as the field of view of the ocular will be at least that much.

But is my model correct?  It assumes the effect of tilt on altitude will be nullified by using the level to set the correct altitude.  So:

change in azimuth = tilt - tilt*cos(altitude).

If you want to find the effect at azimuths other than 90 degrees from the direction of tilt, then multiply the change in azimuth by the sine of modified azimuth, where modified azimuth is set to 0 in the direction of tilt.

My primary question is, is it proper to use cos(altitude) in the above formula or should it just be:

change in azimuth = tilt*altitude/90,

or something else yet again?

Thanks for considering my question. 

Fred