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I want to know how big the earth is. I have heard of double sun set experiments, but it appears that you need to know you latitude, which I do not. I want to do this without using any outside measurements or values. What I can do is measure lengths and times. I can't be in more than one place at once. I can be near a large body of water. I also know the basics of astronomy (the earth is a round thing going around another giant round thing.) and trignometry are correct. Any formulas need to be explained though, no magic internet formulas.

(If you want a reason for why I might want to do this, maybe I think the airline industry has bribed all scientists everywhere to say that transcontinental flights are longer than they actually are to increase fares, but mathematicians have remained uncorrupted/I went through and checked all the proofs and believe the axioms.)

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    $\begingroup$ Simply walk/swim in one direction until you arrive where you started. You can measure lengths, so there you have it, you know the circumference of the Earth. $\endgroup$ – Joshua Lin Feb 14 '15 at 3:02
  • $\begingroup$ @JoshuaLin You sir, are a genius. You should post a video demonstrating the experiment. $\endgroup$ – PyRulez Feb 14 '15 at 3:03
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    $\begingroup$ More reasonably get a sextant and chronometer (or modern equivalents which are cheaper), shoot some star night after night until you can predict its position to within the accuracy of your instruments; travel a well metered distance in a straight line and re-shoot the star. Comparison of prediction to measurement will tell you the angle through which you have traveled. $\endgroup$ – dmckee Feb 14 '15 at 3:17
  • $\begingroup$ Take a transcontinental flight on a clear night. If your hypothesis is correct, the plane will have to circle over and over to make what should be a brief twenty minute trip turn into an agonizing twenty hour flight, making the stars appear have a rather wonky motion to them. If the airplane industry are right (and going back a bit further in time, the ancient Greeks), the stars won't exhibit that wonky behavior. $\endgroup$ – David Hammen Feb 14 '15 at 3:31
  • $\begingroup$ @DavidHammen The answer to Mach's principle. The airline industry controls the stars. $\endgroup$ – PyRulez Feb 14 '15 at 3:33
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When you say you don't know your latitude - then why don't you measure that first?

Measure the maximum altitude of the same (assumed very distant) astronomical object from two different places on the Earth's surface on the same day of the year. Measure the length between the two places. The method was used by Eratosthenes.

A variant, used by Islamic scholars in the 9th Century, was just to measure the latitude of two different places and the distance between them.

I think the latter two methods are only sensitive to the north-south distance, so that's where your clock would come in to check the longitude variation.

An alternative: Get a team of people to help you. Pick 3 points on the surface of the Earth and construct "straight lines" that join them. Measure the sum of the angles in the triangle. Calculate the radius of the Earth (assuming it is spherical).

Alternative 2: Build a tall tower on a beach. Measure its height above the high tide mark. Take a buoy out to sea at high tide. Measure how far you have to take it before it disappears from sight over the horizon to an observer at the top of the tower. Calculate the radius of the Earth.

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