NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Refraction.
From: Frank Reed CT
Date: 2004 Jul 7, 18:11 EDT
From: Frank Reed CT
Date: 2004 Jul 7, 18:11 EDT
Can a star's apparent position ever be pushed away from the zenith by refraction? Yes, but rarely and probably not under circumstances that would ever be observable with a handheld sextant.
To see this, first consider the case of a star exactly in the observer's zenith. Can the position of this star ever be changed by refraction? Yes, and the reason is that the atmosphere does not have to be "plane parallel" (George brought this up in his second message on the topic). A simple case of this would be an advancing weather front. Let's idealize the model by assuming that the atmosphere (minus the front) consists of perfectly plane parallel layers that diminish with density as we climb higher in altitude. Let's idealize the front by representing it as a "wedge" of denser air that has a front surface inclined 45 degrees to the horizontal. Let's suppose that the front is advancing from west to east so that all air to the left of that 45 degree plane is denser than all air to the east. The middle of the "wedge" is a few thousand feet directly above the observer.
What happens to light from a star in the observer's zenith wen it encounters an inclined discontinuity in the atmosphere as described above? As it enters the atmosphere, it encounters layers which are perfectly horizontal and increasing steadily in density. The ray is not refracting in any direction during this portion of its trip to the observer's eye. But when it reaches the inclined leading edge of the front, it will be deflected because it is striking that surface at an angle of 45 degrees (you can easily replace a perfect edge with layers of changing density --the key is that they are at an angle with respect to the horizontal). How much would the deflection be? If we assume that the difference in air density from one side of the front to the other is 5% (large but not impossible), then the index of refraction of the air on the dense side of the front will be 5% farther from 1.0. In normal air, the index is 1.0003, so if the air is 5% denser, the index would be about 1.000315. Using these indices and assuming that the ray is incident on the front at an angle of 45 degrees, I find a deflection of the light ray away from the zenith of just about 3 seconds of arc towards the east (the ray deflects west, the apparent image deflects east). That's small, but measurable. OK so far?
Now let's add a few more stars. Picture a small 'cross' composed of five stars at the observer's zenith. One star is directly overhead. The other four stars are each one degree away from the zenith towards the four points of the compass. How would the above weather front affect the positions of these stars in the sky? It is not hard to continue the analysis above and show that each star's apparent position would be shifted towards the east by nearly 3 seconds of arc. The star on the east side of the cross is being deflected away from the zenith. The stars north and south remain at about the same distance from the zenith. The star on the west side is deflected towards the zenith. Of course each of these stars is also experiencing a small amount of "standard" refraction towards the zenith for the usual reasons; their light rays are passing through the atmosphere at a slight incline to the otherwise parallel layers and so their images are all pushed slightly towards the zenith. At 89 degrees altitude, this effect, standard refraction, is about 1 second of arc. So the net refraction (standard plus the weather front) is 4" of arc TOWARDS the zenith on one side of the zenith and 2" of arc AWAY from the zenith on the other side.
Make sense?
Why would this almost never be of concern for a navigator? Well, most of these substantial changes of air density are accompanied by something else... clouds. The fair weather and mostly clear skies that are required by celestial navigation would usually not be accompanied by serious deviations from a "plane parallel" model of the atmosphere. Also, it's only a couple of seconds of arc. It's not a big angle even for the most demanding of celestial sights.
Frank R
[ ] Mystic, Connecticut
[X] Chicago, Illinois
To see this, first consider the case of a star exactly in the observer's zenith. Can the position of this star ever be changed by refraction? Yes, and the reason is that the atmosphere does not have to be "plane parallel" (George brought this up in his second message on the topic). A simple case of this would be an advancing weather front. Let's idealize the model by assuming that the atmosphere (minus the front) consists of perfectly plane parallel layers that diminish with density as we climb higher in altitude. Let's idealize the front by representing it as a "wedge" of denser air that has a front surface inclined 45 degrees to the horizontal. Let's suppose that the front is advancing from west to east so that all air to the left of that 45 degree plane is denser than all air to the east. The middle of the "wedge" is a few thousand feet directly above the observer.
What happens to light from a star in the observer's zenith wen it encounters an inclined discontinuity in the atmosphere as described above? As it enters the atmosphere, it encounters layers which are perfectly horizontal and increasing steadily in density. The ray is not refracting in any direction during this portion of its trip to the observer's eye. But when it reaches the inclined leading edge of the front, it will be deflected because it is striking that surface at an angle of 45 degrees (you can easily replace a perfect edge with layers of changing density --the key is that they are at an angle with respect to the horizontal). How much would the deflection be? If we assume that the difference in air density from one side of the front to the other is 5% (large but not impossible), then the index of refraction of the air on the dense side of the front will be 5% farther from 1.0. In normal air, the index is 1.0003, so if the air is 5% denser, the index would be about 1.000315. Using these indices and assuming that the ray is incident on the front at an angle of 45 degrees, I find a deflection of the light ray away from the zenith of just about 3 seconds of arc towards the east (the ray deflects west, the apparent image deflects east). That's small, but measurable. OK so far?
Now let's add a few more stars. Picture a small 'cross' composed of five stars at the observer's zenith. One star is directly overhead. The other four stars are each one degree away from the zenith towards the four points of the compass. How would the above weather front affect the positions of these stars in the sky? It is not hard to continue the analysis above and show that each star's apparent position would be shifted towards the east by nearly 3 seconds of arc. The star on the east side of the cross is being deflected away from the zenith. The stars north and south remain at about the same distance from the zenith. The star on the west side is deflected towards the zenith. Of course each of these stars is also experiencing a small amount of "standard" refraction towards the zenith for the usual reasons; their light rays are passing through the atmosphere at a slight incline to the otherwise parallel layers and so their images are all pushed slightly towards the zenith. At 89 degrees altitude, this effect, standard refraction, is about 1 second of arc. So the net refraction (standard plus the weather front) is 4" of arc TOWARDS the zenith on one side of the zenith and 2" of arc AWAY from the zenith on the other side.
Make sense?
Why would this almost never be of concern for a navigator? Well, most of these substantial changes of air density are accompanied by something else... clouds. The fair weather and mostly clear skies that are required by celestial navigation would usually not be accompanied by serious deviations from a "plane parallel" model of the atmosphere. Also, it's only a couple of seconds of arc. It's not a big angle even for the most demanding of celestial sights.
Frank R
[ ] Mystic, Connecticut
[X] Chicago, Illinois
