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09/13/2021 – Ephemeris – The Greeks knew the size and shape of the Earth and estimated the distance to the Moon a long time ago

September 13, 2021 Comments off

This is Bob Moler with Ephemeris for Monday, September 13th. Today the Sun will be up for 12 hours and 37 minutes, setting at 7:56, and it will rise tomorrow at 7:20. The Moon, at first quarter today, will set at 11:57 this evening.

The Ancient Greeks used lunar eclipses to determine that Earth is a sphere, and worked on determining the distance to the Moon. From ancient times, the Greeks knew that an eclipse of the Moon was caused by the Earth’s shadow falling on the Moon. Since the Earth’s shadow was always circular, no matter where the Moon was in the sky during an eclipse, the Earth must be a sphere since that’s the only three-dimensional body that always casts a circular shadow. They also used the size of the Earth’s shadow to estimate the distance to the Moon. The lunar distance, on average, is 60.8 times the Earth’s radius away. The first estimates were about one third of that. Hipparchus in the 2nd century BC got much closer. It got even better from there.

The astronomical event times given are for the Traverse City/Interlochen area of Michigan (EDT, UT – 4 hr). They may be different for your location.

Addendum

Partial Lunar Eclipse showing arc of the Earth's shadow

Partial Lunar Eclipse showing circular arc of the Earth’s shadow. Taken 04:15 UT August 17, 1970. Credit: the author.

The size of the Earth was unknown until Eratosthenes did in 240 BC. He came up with the circumference of the Earth to a fairly high degree. The Circumference is equal to the radius of a sphere or circle by 2πr.

05/10/11 – Ephemeris – The Ancient Greeks and measuring the distance to the sun

May 10, 2011 1 comment

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 diatance to the sun.

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.