Moon Angular Size

Back to Sunset and Moonset on Flat Earth

Flat Earth

The calculated angular size varies from 15.30 Minutes at moonrise to 36.70 Minutes in the middle of its transit and back to 15.30 Minutes at moonset.  The calculated angular size of the moon varies over 200% throughout its transit and is different for all locations on the earth.  This is a major difference and is easy to test with a basic camera on a phone.

Spherical Earth

During the moon’s perigee, the predicted angular size varies from 29.357 Minutes at moonrise to 29.774 Minutes in the middle of its transit and back to 29.357 Minutes at moonset.

During the moon’s apogee, the predicted angular size varies from 33.493 Minutes at moonrise to 34.102 Minutes in the middle of its’s transit and back to 33.493 Minutes at moonset.

The predicted angular size of the moon varies by about 1.4% throughout its transit.  It varies less for locations not on the equator.  This is a very small change, it is difficult to measure this small amount of change without high-quality instruments.  It would probably be difficult to accurately measure any difference on a basic camera on a phone.

Calculations

Flat Earth

  • Moon diameter: 32 miles
  • Moon elevation 3,000 miles

The largest angular size would be when the moon is directly overhead, the smallest will be at moonrise/moonset. Directly overhead the distance is 3,000 miles. There are several different values from different people. Substitute your preferred numbers if you want. The online angular size calculator has just 2 values to enter: the size of the moon and the distance to the moon. I am guessing that on the flat earth the moon will also pass close to directly over the tropic of cancer on the northern solstice, if anyone has clear guidance for this please let me know.

Havana, Cuba is very nearly on the tropic of cancer, at 23.13 N, 82.28W. I am guessing that moonset will be about 90 degrees farther along at 23.13N, 172.28W. The flat earth calculator gives a distance of 6,534 miles. Using that distance and an elevation of 3,000 miles the Pythagorean theorem gives a distance of 7190 miles at moonset, the distance the other direction for moonrise will be the same distance.

This gives the most conservative numbers favoring the flat earth. The numbers for southern locations will be significantly smaller as the moon is farther away.

Directly overhead distance: 3,000 miles -> 36.70 Minutes

Moonset distance: 7,190 miles -> 15.30 Minutes

Spherical Earth

  • Earth radius: 3959 miles
  • Moon diameter: 2158 miles
  • Apogee distance center earth to the center moon: 252,700 miles
  • Perigee distance center earth to the center moon: 221,500 miles

Numbers are for the equator to give the largest variance.

  • Distance from moon at moonrise/moonset at apogee: 252,700 miles -> 29.357 Minutes
  • Distance from the moon at the middle of transit at apogee: 249,161 miles -> 29.774 Minutes
  • Distance from moon at moonrise/moonset at perigee: 221,500 miles -> 33.493 Minutes Distance from moon at middle of transit at perigee: 217,541 miles -> 34.102 Minutes

To calculate the moonrise/moonset distance, take the center-center distance and subtract the radius of the earth.

Angular Size formula: a=2arctan(g/2r)

  • g = size of the object
  • r = distance to the object
  • a = angular size

Notes:

I used Walter Bislin’s flat earth distance calculator to calculate the distance on the flat earth.  If there is a different way to measure the distance between points on the flat earth, let me know: mctoon@mctoon.net.

Angular calculator: http://www.1728.org/angsize.htm

This experiment measured the angular size of the moon to vary from 29.94 arc minutes to 33.66 arc minutes: http://homepages.wmich.edu/~korista/moon-illus.html