Numerological relations between masses of Sun, Earth and Moon

In their book "Who built the Moon" Alan Butler and Christopher Knight indicated to the interesting relations between differend quantities, concerning Moon, Earth and Sun.

http://www.whobuiltthemoon.com

The most remarkable fact of the beforementioned book was that visible disc sizes of Moon and Sun are equal, but there were much more interesting numerological "coincidences".  Best of all is to read the book.

Beside that I think there are many unnoticed relations between physical quantities, concerning this triple system.

At first let us concider MASSES.

Moon mass: 7.349 * 10**22 kg (10 with 22 zeroes)

http://en.wikipedia.org/wiki/Moon

Earth mass: 5.972 * 10**24 kg  

http://hypertextbook.com/facts/2002/SamanthaDong2.shtml

Sun mass: 1.98855 * 10 **30 kg

http://en.wikipedia.org/wiki/Solar_mass

If we divide mass of Earth by mass of Moon, then we get 81.3

Mass(Earth)/Mass(Moon) = 81.3

It is quite close to 81, error only 0.4 %

But 81 = 3 to 4 power

81 = 3**4

If we divide mass of Sun by  mass of Earth, we get:

Mass(Sun)/Mass(Earth) = 332978

 This is VERY close to 333000 (error only 0.006%)

This number is written with 3 threes and 3 zeroes in (and only in) decimal system.

If we divide mass of Sun by mass of Moon, we get:

Mass(Sun)/Mass(Moon) = 27058783

This is very close to 27000000, error only 0.2%
But this is equal to 300 to 3 power:

300**3 = 27 000000

If we take under the consideration the other remarkable "coincidences" from the book "Who 
built the Moon", it seems that these relationships are not coincidential but rather causal.

Medieval mystics, for example Cornelius Agrippa, knew, that the magic number of Moon is 9 (81=9**2)
and magic number of Sun is 666.

But 333000  = 666000/2
But Cornelius Agrippa lived before Newton, so he did not know nothing about masses and gravitation.

It is interesting, that gravitational force on Moon is 6 times weaker, then on Earth and
gravitational force on surface of Sun is 27 times stronger, then on Earth.
6 is also a magic number and 
27 = 3**3