To get a better understanding of the Earth, Moon and Sun spatial relations, the Greeks applied their geometry to this investigation. Aristarchus of Samos (310-230 B.C.) was one of many who were involved in this, and its at his efforts we will now look.
Aristarchus believed that the Earth and all of the planets revolved around the “central fire” (Sun), He thought that the paths which the planets followed were circular. These ideas predate by 1500 years the calculations of Copernicus (1540 A.D.). Aristarchus had a plan. Here I will directly quote Carl B. Boyer who wrote
A History Of Mathematics
“Aristarchus made the observation that when the moon is just half-full, the angle is less than a right angle by one-thirtieth of a quadrant. This would mean in the language of today that the ratio of the distance of the moon to the Sun (the ratio ME to SE) is Sin 3 degrees. From this he derived the conclusion that 1/20 sin 3 degrees 1/18.” What this basically said is that the Sun distance is at least 18 times the distance from the Earth to the Moon but less than 20 times this distance. The diagram, which follows, will show a geometric representation of this idea.
Figure available in printed form
Aristarchus’ “results‘’ were more accurate than the ideas of the day which had put the distance at no less than 9 no more than 12 these distances. His geometry was good but his observations were bad. The angle he thought was 87° should have been 89.5°. Artistarchus did manage to lay the ground work for future observations. He work was designed to measure the relative distances between the Sun, Earth and its moon. Some of today’s techniques mimic these early attempts.
In our attempt to monitor and measure global change we use modern tools. We now have in place a project called LARGOS (laser geophysical satellite). This is a 900 pound satellite with a 2 foot diameter. It has been fitted with 426 corner reflectors. This satellite now circles the globe in a geosynchronous orbit. Space laboratories from all over the globe shoot laser beams at it. These laser “shots’’ are then timed and measured and plotted and published. When this data is examined we should be able to tell if any movement of continents has taken place.
Figure available in printed form
In another similar way we have targeted a quasar (as our deep space “largos”), which for all practical purposes is a fixed point in space. By taking readings off of it from many points on earth it is hoped that we will be able to detect minute changes which take place between continents. As a point of interest the Moon is moving away from the Earth at the rate of 4 centimeters a year.
Figure available in printed form
There are other attempts to measure great distance which should be immeasurable because of our small base line (the diameter of our planet). Modern man has overcome this detail with a little bit of cleaver thinking. By making observations at the extreme ends of our elliptical orbit we are able to extend our base line and make more accurate readings on distance objects in space.
Figure available in printed form