The position of the Sun and the shape of the Earth

Worldwide observation of the Sun and measurement of its position above the horizon
April 24th, 2009

Nowadays, each child “knows” that the earth is a ball. But is every child convinced of that fact? Does she/he know some arguments for it?

Anyway, our own impression shows us the earth as a flat disk:

Inside view of the earth’s surface

Satellites can photograph the earth as a round disk:

Outside vision of the earth’s surface

But do those pictures really show a ball? And, even more important: Do they show our own domicile?

In this project, the shape of the earth will be discovered by the participants all around the world by paying attention to the sun, simultaneously, and by measuring its celestial position with a so called gnomon. They will observe and measure the length and the direction of its shadow on a horizontal plane as exactly as possible.

Basic idea of the project

If people simultaneously look to the sun from different locations they will observe the sun at different positions above the horizon: Most likely, the sun will be higher for one observer. Or the sun will soon set for one observer although it is still forenoon for the other.
The sun is so far from that the sunbeams meet the earth’s surface parallel to each other everywhere. If the earth were a flat disk all observers would see the sun in the same direction.
If you know that the earth is a ball you can easily understand that different observers see the sun in different directions above their horizons. Viceversa, it is possible to determine the shape of the earth by simultaneously measuring the angle between the sunlight and the surface!

At different locations, the sunbeams meet the earth’s surface with different angles.

The project

Of course, the sun is simultaneously visible only from cities on the dayside of the earth. Therefore, we have chosen such a moment that people living in as many countries as possible can take part. The project’s central point of time is

April 24^th, 2009 6.47 UT

At that moment, the sun will “see” the earth as the following picture shows:

The earth’s dayside on April 24^th, 2009, 6.47 UT

At that moment, the sun will be perceived to be directly overhead in Bangalore, India. Or: Bangalore will be the momentary sub-solar point. That is a very suitable fact because it therefore becomes easy to calculate the distance between the place of observation and the sub-solar point, an important parameter which actually should be determined by own measurements.

In order to determine the overall shape of the earth and to enable as many people to participate as possible the observations will be repeated at two additional moments:

April 24^th, 2009, 15.56 UT and 22.29 UT

April 24th, 15.56 UT	April 24th, 22.29 UT

At 15.56 UT, the sun will be perceived in the zenith of Bridgetown, Barbados. The third point of time has been chosen so that the sub-solar point is as close to and exactly south of Hawaii. In Hawaii, the sun will be observed 8.2° from the zenith. To observe the sun in the zenith of Hawaii we would have to wait until May 27^th.

Procedure

1. We ask all people interested in participating to announce their interest by emailing their email address and their geographical position to the addres given below. We will than be able to construct a map of the earth containing all locations the sun will be observed from.
2. During the days before the project, find a suitable length of your gnomon and determine the direction to south as exactly as possible. A suitable procedure is described on an additional page.
3. Let T₀ be the proposed point of time.
   On a sheet of paper containing the exact southern direction and the base point of the gnomon, mark the positions of the shadow’s top at the following moments:
   1. T₀ – 15 min,
   2. T₀ – 10 min,
   3. T₀ – 5 min,
   4. T₀,
   5. T₀ + 5 min,
   6. T₀ + 10 min und
   7. T₀ + 15 min.
4. Using these marks determine the position of the shadow’s top at the proposed point of time T₀ as exactly as possible.
5. Determine the angle a between the shadow and the northern direction and the length l_Sch of the shadow. Taking into account the gnomon’s length l determine additionally the sun’s altitude h above the horizon.
6. Possibly, photograph the sheet and send the picture (name: “Location(Observer)ddmmhhmmUT.jpg” – example: “Acity(Mustermann)30052000UT.jpg”) to .
7. Send a file with your result (same name, but with extension “.txt”). The file contains:
   • Name of location
   • Observer
   • geographical position (latitude in degrees (positive values mean northern latitudes), longitude in degrees (positive values mean positions east of Greenwich))
   • Distance to the sub-solar point (its determination will be explained later)
   • Date and time (dd.mm., hh.mm UT)
   • Azimuth a of the sun in degrees and
   • Altitude h of the sun in degrees.
8. The results will be published as a tabular. Every participant will, therefore, be able to compare the own values with those of widely distant observers and to derive an own measure of the earth’s radius.
   Possibly, we will offer a possibility to put the results into an interactive formular containing a tabular of the following form:

   24.4., 6.47 UT
   Observer	Location	Latitude in degrees	Longitude in degrees	Distance to the sub-solar point in km	a in degrees	h in degrees
   Udo Backhaus	Essen	52.3	7.0	8323	-82.63	21.95
   24.4., 15.56 UT
   Observer	Location	Latitude in degrees	Longitude in degrees	Distance to the sub-solar point in km	a in degrees	h in degrees
   Alicia Mustermann	Lissabon	38.7	-9.2	5695	74.19	38.71
   24.4., 22.29 UT
   Observer	Location	Latitude in degrees	Longitude in degrees	Distance to the sub-solar point in km	a in degrees	h in degrees
   John Smith	Calgary	51.0	-114.0	5745	59.07	38.18

9. We will describe simplified procedures for “paper-pencil-determination” of the earth’s radius by comparison between the own result and those of other observers.
10. We will publish a program making it possible to combinate the results of arbitrary observers. The used algorithm will be explained.