Thanks for reading Scientific American. Create your free account or Sign in to continue. See Subscription Options. Go Paperless with Digital. Key concepts Mathematics Geometry Circumference Angles Earth's equator Introduction If you wanted to measure the circumference of Earth, how long would your tape measure have to be? He could measure the angle of the shadow cast by a tall object in Alexandria.
He knew the overland distance between Alexandria and Syene. The two cities were close enough that the distance could be measured on foot. The only unknown in the equation is the circumference of Earth! Materials Sunny day on or near the spring or fall equinoxes about March 20 or September 23, respectively Flat, level ground that will be in direct sunlight around noon Meterstick Volunteer to help hold the meterstick while you take measurements Or, if you are doing the test alone, you can use a bucket of sand or dirt to insert one end of the meter stick to hold it upright.
Stick or rock to mark the location of the shadow Calculator Protractor Long piece of string Optional: plumb bob you can make one by tying a small weight to the end of a string or post level to make sure the meter stick is vertical Preparation Look at your local weather forecast a few days in advance and pick a day where it looks like it will be mostly sunny around noon.
You can try again. Look up the sunrise and sunset times for that day in your local newspaper or on a calendar, weather or astronomy Web site. Go outside and set up for your materials about 10 minutes before solar noon so you have everything ready.
Procedure Set up your meter stick vertically, outside in a sunny spot just before solar noon. If you have a volunteer to help, have them hold the meterstick.
For example, if a kitchen unit is mm wide to the nearest 10 mm, it could actually be any width from mm up to mm — so it might not fit into a gap that is exactly mm wide. To describe all the possible values that a rounded number could be, we use lower and upper bounds.
The lower bound is the smallest value that would round up to the estimated value. The upper bound is the smallest value that would round up to the next estimated value. We looked up the distance between the two locations. Also, we used a common time so that we could find the difference between our local noons. Check out Chad's more detailed post at Uncertain Principles. He even has some nice graphs. I guess I should include my time-lapse video, just in case. View Iframe URL. The more I think about this, the more I like this experiment.
Redoing classic experiments with a modern twist. Really, we could have done better. What if we used the moons of Jupiter or something to synchronize our times instead of using official time. Instead of looking up the distance between the two locations, we could use short wave radio and time how long it takes for a pulse to go there and back.
Parallax is an important rung in the cosmic distance ladder. If a star is too far away to measure its parallax, astronomers can match its color and spectrum to one of the standard candles and determine its intrinsic brightness, Reid said. For example, if you project a one-foot square image onto a screen, and then move the projector twice as far away, the new image will be 2 feet by 2 feet, or 4 square feet. The light is spread over an area four times larger, and it will be only one-fourth as bright as when the projector was half as far away.
If you move the projector three times farther away, the light will cover 9 square feet and appear only one-ninth as bright. If a star measured in this manner happens to be part of a distant cluster, we can assume that all of those stars are the same distance, and we can add them to the library of standard candles. Its main purpose was to measure stellar distances using parallax with an accuracy of 2—4 milliarcseconds mas , or thousandths of an arcsecond.
Another application of parallax is the reproduction and display of 3D images. The key is to capture 2D images of the subject from two slightly different angles, similar to the way human eyes do , and present them in such a way that each eye sees only one of the two images.
For example, a stereopticon, or stereoscope, which was a popular device in the 19th century , uses parallax to display photographs in 3D. Two pictures mounted next to each other are viewed through a set of lenses. Each picture is taken from a slightly different viewpoint that corresponds closely to the spacing of the eyes.
The left picture represents what the left eye would see, and the right picture shows what the right eye would see.
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