Tauragės „Versmės“ gymnasium
Moon’s diameter calculation
Justinas Jorudas IIIe
2012
Introduction
The moon is Earth's closest celestial neighbor. It has a huge influence upon our lives,
governs the tides and is responsible for eclipses. The moon lies, on average, 384,400 km
(238,900 miles) away and takes 27.3 days to orbit the Earth. Strange as it may seem, its rotation
period is exactly the same as its orbital period, something that scientists call tidally locked.
Therefore, one half is always facing the Earth while the other half is always facing away.
Objective
To calculate moon diameter using DIY tools and simple math.
Tools
DYI cross-staff, tripod.
Cross-staff
Cross-staff is a simple device, used centuries before the invention of the telescope to
determine the angular separation between two objects, or the angular size of a single object. If
you are measuring single object, cross-staff can be use to determine its linear size or distance.
The cross staff consists of meter stick and a crosspiece attached at a right angle. All you have to
do is sight an abject along the stick and slide the crosspiece back and forth until the apparent or
angular size of the crosspiece matches the apparent or angular size of the distant object.
Since we are only going to measure the diameter of the moon, we can make a very
simple device.



Take a small empty rectangular box. Then cut a slot at the bottom of the middle of each
of the longer sides. Make these slots the same size as the height and width of a meter
stick that you happen to have (If done right, you will have something that slides
smoothly up and down meter stick.)
Take a thin piece of a cardboard and make a nice, neat hole in the center of it. (5-7mm)
Tape this to the box bottom that slides up and down meter stick.
In my case, I manufactured everything from wood.
My slider:
Meter stick:
My cross-staff:
To do
 Make a Moon measuring device, as described above.
 Using a millimeter ruler, as accurately as you can measure the diameter (d’) of your hole
that will be used for sighting.
 Now go outside on a reasonably clear night, when the Moon is up and match moon size
with your sighting holes size, while cross-staff is up against your cheekbone. Make sure you
write down the distance from meter stick’s end (from that end which you were looking) to
sighting hole. This distance will be D’.
Calculation
Using properties of similar triangles, we can measure distance to the moon if we know
diameter or vice versa.
𝒅′
𝑫′
𝒅
=𝑫
In this formula d’ is diameter of your sighting hole, D’ is distance you wrote down earlier
from your sightings, d - is diameter of Moon, D – distance to Moon.
I know that distance to Moon is 385304 km. (according to Wofram|Apha data).
So:
𝒅=
𝒅′ × 𝑫
𝑫′
𝒅=
𝟖𝒎𝒎 × 𝟑𝟖𝟓𝟑𝟎𝟒𝟎𝟎𝟎𝟎𝟎𝟎 𝒎𝒎
𝟖𝟗𝟎 𝒎𝒎
𝒅 = 𝟑𝟒𝟔𝟑, 𝟒𝟎𝟔 𝒌𝒎