[Humble B]

Step One: Establish your latitude and longitude.
Step Two: Find a pole (with a base so the pole can stand erect without additional support) of known height.
Step Three: Measure the length of the shadow cast by the erect pole.
Step Five: Go to timeanddate.com and find the distance between you and the solar noon of the Sun at the time of the measurement.
Step Six: Do the math. The distance from the base of the pole to the end of the shadow (vertex of the angle) establishes a precise relationship with the distance between the Sun and vertex of the angle.

I think you will find the height of the Sun over the flat earth lane to be approximately 5600 miles.

My advice: Do your measurements on different times on one day. One early in the morning, one at noon and one somewhere in the afternoon and all measurements will show you a different result.

Real fun you will have when you do your measurements also at the moment of sunrise and sunset, when the length of your pole's shadow will be "infinite" because the angle to the sun is zero.

If you've done so, then please share your findings with us, I am eagerly looking forward.

[Bobby Shafto]

Yesterday, I found it very difficult to find confidence in the shadow measurement of the pole since the shadow edge was kind of diffused.  So I just went out and took measurements again, but also tried a candlestick, which being smaller provided a much sharper shadow.

Before any math (though it's obvious the sun was very nearly at a 45° angle of elevation), here are measurements I just took moments ago:

Date: 9/22/2018
Time: 1500 PDT
Location: 33°N 117°W

Object 1 Height (Pole): 68 3/8" (68.375")
Object 1 Shadow: 71 to 71 1/2" (71-71.5")

Object 2 Height (Candlestick): 9 1/2" (9.5")
Object 2 Shadow: 9 7/8" (9.875")

Sun calc stuff later.

[stack]

Fog finally lifted. Got a nice crisp shadow today. Results:

Date: 9/22/2018
Time: 15:33 PDT (22:33 UTC)
Location: 37°46'09.5"N 122°27'06.8"W

Y - Object Height: 34.5"
X - Shadow Length: 41.5"
Ratio Y:X = .8313:1

Sun location at 22:33 UTC: Latitude: 0° 03' North, Longitude: 159° 51' West
X' - Ground Distance: 3519 miles
Y' - Height of Sun:  2925 miles

[Bobby Shafto]

Step One: Establish your latitude and longitude.
Step Two: Find a pole (with a base so the pole can stand erect without additional support) of known height.
Step Three: Measure the length of the shadow cast by the erect pole.
Step Five: Go to timeanddate.com and find the distance between you and the solar noon of the Sun at the time of the measurement.
Step Six: Do the math. The distance from the base of the pole to the end of the shadow (vertex of the angle) establishes a precise relationship with the distance between the Sun and vertex of the angle.

I think you will find the height of the Sun over the flat earth lane to be approximately 5600 miles.

My advice: Do your measurements on different times on one day. One early in the morning, one at noon and one somewhere in the afternoon and all measurements will show you a different result.

Real fun you will have when you do your measurements also at the moment of sunrise and sunset, when the length of your pole's shadow will be "infinite" because the angle to the sun is zero.

If you've done so, then please share your findings with us, I am eagerly looking forward.

Was going to do this myself today, taking measurements on the hour between 1000 and 1600 using my precision-built measuring instrument:


Unfortunately, it's been overcast all day.

Instead, I used TimeandDate to construct a table of elevation angles and sun zenith locations. Using that data and assuming flat earth geometry, the sun altitude rose from 2927 miles up at 10AM to a peak of 3562 miles around solar noon, and then descended to 2137 miles by 4:30pm. Extending the times and sun locations for the period of sunrise to 1000 and 1630 to sunset, the sun altitude drops rapidly to under 100 miles under 1° elevation.

Conversely, for the sun to maintain a constant altitude of around 5600 miles over a flat earth (and assuming TimeandDate.com sun locations and distances on Google earth are correct -- for today, the sun would have had to be at 41° elevation at the times of sunrise and sunset and would top out at 68° elevation at local solar noon. One need not take measurements to know that doesn't happen.