These preliminary observations show that the elevation angle formula yields approximately what is observed, although there are a few things to point out: (1) The observed elevation angle of Haleakala of 0.54 deg is off by from the predicted 0.657 degrees. (2) The relative heights of Haleakala peak and the peak on the island of Lanai agrees well with the predicted ratio. The Haleakala peak is observed to be ~1.5 times the Lanai peak. The predicted ratio is 0.657/0.438 ~ 1.5. Thus, observed ratio is as expected. (3) Note that the calculated elevations angles for both Mauna Kea and Mauna Loa (Big Island) are negative indicating that these peaks are not viewable from this viewing location. As expected, neither Mauna Kea or Mauna Loa can not be been seen at any time from this location even under the best seeing conditions. (4) During these observations both the Molokai cliffs and the Molokai mountain peaks were obscured by clouds and therefore not visible. Because of this, comparisons of these objects with the elevation angle formula could not be made.
In conclusion, the disagreement with the Haleakala peak is probably
within the uncertainty of the observations. Overexposure of the Sun’s
image may also have been a contributing factor. The fairly good
agreement with the relative sizes of the Haleakala peak and Lanai are
also a good indication of the validity of the elevation angle formula.
I have gone back and checked all small angle approximations made in
order to derive the elevation angle formula and have verified that
these approximations are valid for typical distances and heights
discussed. Further observations will certainly be necessary to verify
the elevation angle formula.
Observer | Mountain/ | Distance | Height | Lambda |
Height(ft) | Island | (miles) | (feet) | (deg) |
400 | Haleakala | 100.0 | 10023 | 0.675 |
400 | Lanai Peak | 61.2 | 3366 | 0.438 |
400 | Mauna Kea | 174.7 | 13796 | -0.077 |
400 | Moana Loa | 183.0 | 13679 | -0.182 |
400 | Molakai Cliffs | 27.0 | 1350 | 0.541 |
400 | Molakai Peak | 53.5 | 4970 | 0.894 |
400 | West Maui Peak | 76.0 | 5788 | 0.574 |