Estimating the relative radius of the Moon by lunar eclipse observation

lunar eclipse 2008 total Feb 21

The total lunar eclipse of 2008 Feb 21, at 02:24 UT
binoculars 10x70, digital camera



Moon relative radius lunar eclipse		 Assumptions:
 - the diameter of the Earth and it's shadow are equal,
 - the line connecting the edges of the illuminated cusps passes
   the center of the Moon.

r2 = h (2R-h)
R = radius of the Earth
r = radius of the Moon

r2 = 2Rh - h2 ≈ 2Rh

r/R ≈ 2 h/r

Estimate the ratio x=h/r, then the relative radius of the Moon is:

r/R ≈2 x
radius moon earth ratio
Result:

x ≈ 0.15

r/R ≈ 0.3

Moon: 1737 km, Earth 6371 km

r/R=0.273