Circumference & Radius of Earth
In order to evaluate radius and circumference of Earth it was chosen to measure the shadow of sun from gnomon on September, 17th. The length of the shadow was approximately 39.8 cm
We can find the angle ? using simple trigonometric formula for arcos.
A arcos (30.3/50)
Since we know that sun angle for Sep. 17th in New Mexico site is equal to 57.19 (degrees) we can evaluate the radius of Earth.
R= (L*360)/(?*2?), where L=518 kilometers (distance between Denver, CO and site in New Mexico)
References give the following data for Radius of Earth
R=6356,755 kilometers (polar radius)
R=6378,140 kilometers (equatorial radius)
So we can evaluate our result, since both locations are closer to equator then to North Pole we should take equatorial radius for estimation:
error is equal to ?=|6378,140-6610,075|/6378,140
Circumference of earth using my measurements is equal to L= 2?R which is L=2*3.14159*6610,075 kilometers or L=41532.291 kilometers
Why did you have to do this at local solar noon, that is, when the Sun is due South in the sky?
The length of shadow at local solar noon is the shortest which presents the most accurate value for the Sun angle, as measurements in site of NM were also done at local solar noon the calculations will give the most accurate result with the least error.
If you had done this significantly too early or too late, what kind of error would there have been your shadow length?
The shadow length would have a bigger value as sun’s angle would have been smaller.
If you had done this significantly too early or too late, what kind of error would there have been your circumference value?
Such measurement would have given smaller sun angle value for the location, which would have been resulted in greater value of angle ?. In calculations greater value of ? wouls result in smaller value of estimated radius since its inversely proportional to angle ?.
4) Could astronauts on the Moon or Mars use this technique to determine the circumference of those objects?
Yes., such technique can be used to any astronomic objects which rotate around Sun.
The Circumference & Radius of Earth