My father Daniel Richards Allen and I wondered this in the early 1980s. It was probably near Thanksgiving, and we had driven to the top of Mount Hamilton. It was cold and clear. We could see the 8844 foot Half Dome in Yosemite very clearly with binoculars, but could we see Mount Whitney as well?
First we had to determine distances and angles. Second we had to consider the curvature of the earth, and finally years later, I have taken refraction into consideration. Here are the basic distance and angle calculations, which I did originally with an HP-41 calculator, but now I do with a navigation tool I have written in C.
Distance to Half Dome from Mount Hamilton: % nav 37~20.516 121~31.633 37~44~46 119~31~59 Trip: N37.34193° W121.52722° to N37.74611° W119.53306° GC: 112.68 mi, 97.92 nmi, 75.05° (E) Ellips: 112.99 mi, 98.19 nmi, 75.09° (E) Rhumb: 112.68 mi, 97.92 nmi, 75.66° (E) Distance to Mount Whitney from Mount Hamilton: % nav 'Mount Hamilton' 'Mount Whitney' Mount Hamilton, CA (N37°20.516' W121°31.633') Mount Whitney, CA (N36°34.633' W118°17.550') Trip: N37.34194° W121.52722° to N36.57722° W118.29250° GC: 186.10 mi, 161.72 nmi, 105.50° (E) Ellips: 186.60 mi, 162.15 nmi, 105.46° (E) Rhumb: 186.11 mi, 161.73 nmi, 106.48° (E)Second, we determine how far one can see an object. The relevant equations are:
distance in mi = sqrt(height in feet) * 1.22 (no refraction) or distance in mi = sqrt(height in feet) * 1.32 (with refraction)We will use the equations that factor in refraction and we come up with:
For the Mount Hamilton to Mount Whitney case, one adds 85+159: 244 miles is the maximum distance apart for two such objects to be visible one from another, and since they are only 186 miles apart, it is possible!
Googling this topic I found a short article written in 1909, about 73 years earlier than our observation. It was published in the Publications of the Astronomical Society. Here is the article:
So my father and I were not the first people on Mount Hamilton to consider this observational challenge! Try it yourself on a cold clear winter's day. Mount Hamilton is a hidden gem in the San Francisco Bay Area.
Created: 18 Aug 2016 Modified: 10 Dec 2016