Embedded Files
Astronomy and geometry have been studied since ancient times. Over the course of many years, evidence began to suggest that the Earth was round, even if it might appear flat to a naïve observer.
For example, tall ships disappear bottom first over the horizon as if they are going over a hill. When they approach, they appear top first.
Around 240 BCE, a Greek mathematician named Eratosthenes devised a way to measure the size of the Earth. A city in Egypt happens to fall on the Tropic of Cancer, which means the sun is directly overhead there on the summer solstice.
This was important for two reasons. First, the summer solstice is an astronomically significant day, so you could know with certainty that two observations are being made under the same astronomical conditions, even if they are made years apart.
Second, it simplifies the geometry. If the sun is directly overhead, then the sunbeam lines up with the Earth’s diameter at that point. If you measure the sun’s zenith angle at another location on the same day, then you've measured the angle of latitude between those locations.
Combined with the distance between those locations (the length of the circular arc subtended by the angle), it is possible to solve a proportion to find Earth's total circumference.
While it may be inspiring to learn about this historical experiment, it's also frustrating. Most of the world lives far away from the Tropic of Cancer, and many students are not in school on the summer solstice. How can we do this ourselves?
- Choose a different day
The solstice may not work, but the equinoxes (spring and fall) often both happen while students are in school. On those days, the sun is directly over the equator instead of one of the tropics.
This also means that the latitude angle will simply be a location's geographic latitude, since that is measured from the equator anyway!
2. Use different math
2. Use different math
While simple geometry was enough for Eratosthenes' method, it will be necessary to use more sophisticated tools to calculate Earth's size with measurements made this way.
This requires spherical trigonometry, but it makes it so that anyone can conduct this experiment from anywhere in the world!
This experiment is fundamentally collaborative. It is impossible to do this project by yourself because the calculations must be made between pairs of observers. The more distant the observers, the better! This experiment seeks to bring people from all over the world together to work towards a common goal. Students, amateurs and professionals from across the globe can meaningfully work together on a shared project to celebrate our shared planet.
Page updated
Google Sites
Report abuse