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# How can I calculate the size and rotation of the earth using the movement of the stars?

For my philosophy class we're supposed to spend time watching the sky. I wanted to try and use some rudimentary equipment and techniques to try and estimate the size of the earth and how fast it rotates on it's own axis. If anyone could help with this it would be greatly appreciated.

Thanks

### 3 Answers

- Anonymous1 decade agoFavorite Answer
For the size of the Earth, you can replicate Eratosthenes' (276 BC – c. 195 BC) measurement using a meter stick and a car (unless you prefer to walk several miles). Read the first website below for a general description of the calculations--pay attention to the diagram at the bottom. If you can't make it to the equator, it'll take a bit of trigonometry work to figure out the angles. The basic process is to measure the length of shadows cast at high noon at two different locations that are directly north-south of each other. The difference in their length will allow you to calculate the radius of the Earth. To simplify calculations, assume the suns rays are parallel.

When I was studying at UCLA, I did this measurement with a meter stick and a trip to Las Vegas and obtained a value with less than 1% difference from the accepted value.

As for how fast the Earth rotates, I can think of two ways: slow and easy, or fast and tricky.

The first way is simply to time how long it takes for the sun to return to its previous location in the sky. For example, start a clock when the sun first touches the horizon and stop when it touches the horizon again (make sure to observe from the same location both times). You'll need a stop watch that can handle times up to 24 hours.

The second way is to time how long it takes for the sun to disappear after touching the horizon, then calculate the angular size of the sun. From this data, you know how long it takes the Earth to rotate across the angular size of the sun. It's a simple multiplication to get how long it takes the Earth to rotate 360°. The tricky part is figuring out the angular size of the sun (I would assume you wouldn't cheat by looking this up or looking up the size and distance of the sun).

Source(s): http://www.uh.edu/engines/epi1457.htm - Anonymous1 decade ago
Autumnal equinox, Sept. 20th is a magical date.

A stick in the ground, carefully set vertical.

Shadow length at noon is straight to pole (N-S line) and shortest length. Note angle of sun's rays to create shadow.

Set your clock for 12:00

Wait for sunset dead west at right angles to the N-S line

Note time, should be 6:00. Keep clock running.

Earth rotates 90* in six hours, or 15* per hour.

Get in jet plane and travel 690.53 miles due south or north.

Set same stick in ground, same way, wait for noon again.

Measure sun angle of stick and shadow again. Note difference of angles (about 10*). Multiply distance 690.53 x 36 to get 24,859 miles circumference of Earth. Divide that number by 24 to get speed of rotation at the equator.

Source(s): The Greek-Egyptian astronomer and philosopher Eratosthenes http://answers.yahoo.com/question/index?qid=200808...