Some of their ways to use the sun to find direction seemed a little unreliable and time consuming too. Especially in deep winter and high summer when the suns path deviates most, I would not have too much faith in the methods.
I hope this design is much quicker and adds to our knowledge base.
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Signing UpStep 1The science?
They line up the axis of rotation with the axis of rotation of the earth . Imagine a big stick going through the earth from the north pole to the south pole.
To line up with that, you tilt your axis towards the nearest pole at an angle equal to your latitude. So you end up with an axis tilted along a north south line. At the north or south pole it is pointed straight up and at the equator it is horisontal on a north south line.
The telescope is attached to this axis
Then they rotate and elevate the telescope to point the telescope at the sun or star. Then they just have to rotate the telescope to watch the sun or star all day or all night. No more elevation is necessary.
The amount they elevate is called the declination. For the sun, this amount is know for every day of the year.
So here is my thought, If we make the same angle as the earths axis, and we make an elevation the same as the declination of the sun, keep those 2 things static, and adjust the other parameters till it points at the sun, you should have the axis angle lining up north south.
So you have a compass!
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You should say "They line up the axis of rotation with the axis of the earth (EXACTLY NORTH SOUTH), then they tilt the axis of rotation at an angle equal to the location latitude, the higher end of the shaft pointing at the local pole and then rotate and elevate the telescope to point the telescope at the sun or star. "