Bob Moler's Ephemeris Blog

Tuesday, May 10th.  The sun rises at 6:20.  It’ll be up for 14 hours and 36 minutes, setting at 8:57.   The moon, at first quarter today, will set at 2:46 tomorrow morning.

The ancient Greek astronomers had great success in actually calculating the distance to the moon.  They came up with 60 earth radii.  Yes, they knew the earth was round and even measured its circumference to great accuracy.  The distance they got for the moon lies within the range of the actual moon’s distance.  They next tried to measure the distance from the sun.  To do this, they tried to observe the moon and the sun at the exact time the moon was at first quarter.  At this time the earth, sun and moon make a right triangle.  Theoretically the actual angle between the sun and the moon would give the distance to the sun.  The answer they got was that the sun was 20 times the moon’s distance.  That’s way short, the sun is 400 times the moon’s distance away.

* Times are for the Traverse City/Interlochen area of Michigan.  They may be different for your location.

Addendum

How the ancient Greeks tried to calculate the distance to the sun.

To the right is my take on the Greek sun measuring experiment.  Using their guy Euclid and his geometry they knew that the sum of the angles of a triangle equal 180 degrees.

Having an exactly quarter moon, first or last, they knew the Sun-Moon-Earth angle was 90 degrees, so if they could measure the Sun-Earth-Moon angle from observation, they knew the other angle at the sun.

They had already calculated the moon’s distance, so they could calculate the other leg, the Sun-Moon distance using trigonometry.  The first trig tables were invented by Greek astronomer Hipparchus.

Ah yes, Trig tables.  I don’t suppose you kids use them anymore, with your electronic calculators.  Back in my high school days my calculator was a slide rule.  Sorry, old guy grousing.