Posts Tagged ‘Eratosthenes’

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.


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.

10/13/2015 – Ephemeris – Columbus was wrong!

October 13, 2015 Comments off

Ephemeris for Tuesday, October 13th.  The Sun will rise at 7:55.  It’ll be up for 11 hours and 6 minutes, setting at 7:02.   The Moon, 1 day past new, will set at 7:35 this evening.

Yesterday I recounted that Christopher Columbus was able to extort supplies from the native Jamaicans by using an eclipse table to predict a lunar eclipse.  But let’s face it Columbus was lost.  He wasn’t in India as he thought.  He based his voyage on the erroneous belief that the Earth was less than 19,000 miles in circumference, when it’s actually 25,000 miles, which was the prevailing view of the day.  That the Earth was round was known from the 3rd century BC, and measured quite accurately by Eratosthenes.    Of course with the varieties of distance units of the day it was no wonder an error of that magnitude could be made.  Of course did anyone think to remeasure the circumference of the Earth?  Apparently not.  Nowadays no scientist thinks of taking only one measurement. Columbus was lucky a continent was here, or no one would have heard from him again.

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


1474 map of the Atlantic Ocean

A map of the western ocean (Atlantic Ocean) by Paolo dal Pozzo Toscanelli about 1474 which may have influenced Columbus. North America is superimposed at the proper longitudes. Credit: A literary and historical atlas of America, by Bartholomew, J. G. via Wikipedia.  Click to enlarge.

Note that Cathay is China and Cippangu represents Japan.  It was thought back then that the Eurasian continent spanned 180 degrees of longitude at the latitude of Spain, rather than 130 degrees it actually does  Japan was thought to be bigger and farther off the Chinese coast.  The phantom island of Antillia seems to date back to stories from Spain of the 8th century.