Under the section about the distance to the Sun, FEW mentions Rowbothams experiment, described in Ch5 of TENG involving the observed altitude of the Sun at two separate locations, London Bridge and Brighton. I thought I would carry out a little investigation of my own on this.

The idea is simple. A triangle is formed from three points.  The Sun, the observers position and the point on the Earths surface where the Sun would be taken to be directly overhead, if the surface was flat.

Two different observation points are considered. L is London Bridge in London, B is the coastal town of Brighton on the south coast of England. It is stated that L and B are situated around 50 statute miles apart.

From point L the Sun is observed at noon on 13th July 1870 to be at an altitude of 61 degrees above the horizon. At the same time the Sun is observed from Brighton to be at an altitude of 64 degrees.
I have used Starry Night Pro Plus (v8) software to simulate these observations. Rowbotham gives an angle of elevation for the Sun as seen from London Bridge at 12pm of 61 degrees. Starry Night gives a value of 60d 19m. Within 1d. From Brighton at the same time, Rowbotham states the elevation of the Sun to be 64d. Starry Night gives a figure of 61d 1m. So the difference is bigger for Brighton but still within a couple of degrees of the computer simulated altitude. 

Given that these measurements were taken about 140 years ago with no mention made that Rowbotham had use of a telescope on a leveled alt azimuth mount with degree graduated scales allowing an accurate measurement to be taken, some errors in measurement are allowable.  In summary we can say that Rowbothams observations provide us with a classic 60/30/90 degree right angle triangle scenario.

We now go back to the mention by Rowbotham that the distance between London Bridge and Brighton is approximately 50 statute miles. If a line is drawn to represent the line of sight between the observer and the Sun from both London Bridge and Brighton, the angular difference in the Suns altitude that Rowbotham quotes gives us two distinct lines. The intersection of these lines, (LS and BS) define a point S in Fig 58 which is the physical location of the Sun.

With Points L and B and S now known it is a simple matter to extrapolate the distance between L and B to give us point D which is the point on the Earths surface where the Sun should be observed to be directly overhead. Using a pair of compasses, Rowbotham gives this distance to be 400 statue miles.

If Rowbothams reasoning is correct and the Earths surface is flat then the Sun should be observed to be directly overhead when observed at 12pm 400 statue miles south of London Bridge. Starry Night has already shown Rowbothams elevation measurements of the Sun from London and Brighton to be quite accurate so let us now set Starry Night to a location 400 miles south of London at 12pm on 13th July 1870. Continuing the line from London Bridge directly through Brighton this takes us to just a few miles east of Cognac, near Saintes in W France. 

With the Sun due south at noon from this location, Starry Night gives the altitude of the Sun as only 66.14 degrees. According to Rowbothams diagram though the Sun should now be directly overhead. 24 degrees difference is quite a large discrepancy - 48 times the Suns visible disk diameter. In reality over a distance of 400 miles, the Suns elevation has changed by only about 6 degrees.

Now using the celestial coordinates of RA and Dec used in astronomy, the Suns declination on 13th July is +21d 50m. RA and Dec are simply a projection onto the sky of longitude and latitude on Earth. Based on RET then, the Sun should be directly overhead at local noon as seen from a location with a latitude corresponding with the declination of the Sun.

Once again I have set Starry Night to a location on the same longitude line as London Bridge but with a latitude of 21d 50m N. Setting the date to 13th July 1870 at local noon, the Sun is seen to have an altitude or elevation of 89.5d.

The same section of FEW talks about 'later researchers' reaching a figure of 3000 miles for the height of the Sun above the surface of the Earth. However unlike the above method which is described in detail and hence I can investigate that, no explanation is given about how those 'later researchers' reached that figure. It has to be said that 700 miles compared to 3000 miles is quite a difference. Where no explanation is given you could to all intents and purposes simply think of a number.
« Last Edit: February 06, 2019, 04:07:01 PM by manicminer »