Measuring the Sun's position above the horizon

Simplified evaluation procedure

If you find two observation sites the direct connection of them is contained in a plain which also contains the direction of the sun light deriving the earth's radius is a plane problem. In this case, the central angle α corresponding to the arc between the both sites (that is a great circle on the earth's surface or a "orthodrome") is simply the difference between the simultaneously measured altitudes h_1,2 of the sun.

If the observers live on different hemispheres (to be more exact: north and south of the sub-solar point) this equation must be replaced by

Now, if the distance s is known the radius can easily be calculated:

In praxis, there are only two realistic possibilities for such a situation:

The both observers live on the same longitude and measure the position of the sun exactly at local noon.
If one of the sites is the sub-solar point the simple situation is true for any other site on earth. That's the reason for refering to a well-known sub-solar point.
In this project, the sub-solar points for the three points of time are given. If you would like to repeat this experiment later you can determine the actual position (φ_ss,λ_ss) of this point for the time t₀ by measuring your actual noon data (t_M,h_M):
Obviously, you must know your own geographical position (φ,λ).

In all other cases, the situation is skew and a more sophisticated method is necessary for which we wrote a little program. We describe the algorithm in the document attached to this program.

back to the project page

Udo Backhaus

last change: last update: 2020-03-03