NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: refraction
From: Paul Hirose
Date: 2005 Aug 5, 12:56 -0700
From: Paul Hirose
Date: 2005 Aug 5, 12:56 -0700
Marcel E. Tschudin wrote: > > Yes, how do I get in this? Just trying to cover in a self-made program the > situation from an object at the horizon (over sea level) as seen from a > mountain or air craft. The problem is similar to a rise/set calculation, isn't it? That is, you want to know the altitude the object would have if refraction were turned off and you could see through the Earth. That equals dip of the horizon plus the total curvature due to refraction of the light from the object to the observer. Imagine a theodolite at the summit of say a 100 meter mountain overlooking the sea. A star is precisely on the horizon. Dip of the horizon at H meters high is about 1.75′√H, so in this example the telescope must be 17.5′ below horizontal to center the star and horizon in the crosshairs. That sets it parallel to the arriving light rays at the theodolite. However, it is not parallel to the rays at the distant point where they're tangent to the sea. To make it so, the scope has to be tilted down a little more, by the amount of refraction between the tangent point and the observer. According to the Explanatory Supplement to the Astronomical Almanac, it equals about .37′√H for H in meters, or 3.7′ in this example. Finally, you tilt the scope down still more to allow for the refraction between the tangent point and the celestial body. This is simply the horizontal refraction, about 34′ in standard conditions. You end up with the telescope 55′ below horizontal. It is now parallel to the rays from the star before they enter the atmosphere. The 1.75′√H and .37′√H terms can be combined, in which case the depression angle expression is -34′ - 2.12′√H. I don't think that will be accurate at great height, though. For example, the .37′√H term for refraction between horizon and observer can increase without bound. In reality, it should never exceed the horizontal refraction (34′).