NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Stuart
Date: 2019 Jun 24, 06:08 -0700
The weekend has passed and there were no takers on dip problem arising out of Frank’s Yogurt Sky problem.
Altair and d Aquilae (at about 4 o’clock from Altair) are separated by 8.52° and 143 pixels in the image giving a scale of 0.05946 degrees/pixel. The Earth in the image is 180 pixels in diameter and therefore subtends 10.70°.
The dip of the horizon is 90° – 10.70°/2 = 84.65°.
We can’t use the standard formula involving square roots to extract the height of the eye from the measured dip of the horizon as it assumes small angles and contains an adjustment to radius of the Earth to account for refraction. It’s not difficult to derive the exact formula
1 + h/R = sec(dip)
where h is the height of the eye and R is the Earth’s radius. The left hand side is the observer’s distance from the centre of the Earth measured in Earth radii and comes out to be 10.72.
Robin Stuart
