Suppose we want to create a star and a planet to orbit it that supports life. Then we want the
star to not be hot (blue) or cold (red) but somewhere in between (yellow). Then by the
relationship of mass to luminosity, it has to have a mass and a luminosity given by the mass-
luminosity relationship:!
!
Where L stands for luminosity and M for mass. This is the sun and it does satisfy this equation.
By the inverse square law, the habitable zone of a star with such a luminosity is determined by
a distance that allows for water to exist in its liquid phase. !
!
This is the earth. Let us now say we think intelligent life on this planet will when they invent
their mathematics divide a circle into 360 degrees so that it is nicely divisible by 30, 45, 60, 90,
120, which are angles in special and important triangles, because they are dynamic, and we
want that their planet orbits their star at one degree per day. Then this is about 360 days for
their year equal to the their 360 degrees for a circle. This is the Earth and its 365 day year is
close enough to this.!
But let us say we want to let the inhabitants of this planet to know of our presence, so we
place a moon of the right size and distance from their planet that it eclipses their star (The Sun)
nearly perfectly when it passes between them and their star. To do this let us say we want their
moon to complete an orbit about every 30 days because as such they will be able to create the
idea of months for which there will be about 12 in this scheme because the orbital period T
squared is proportional to the orbital radius r cubed:!
!
This is the earth-moon-sun system and it does satisfy all of these equations while maintaining
these characteristics, and this works well because 12 of the 12 month year is the most divisible
number for its size because it is divisible evenly by the integers that precede it 1, 2, 3, 4, 6.
That is, 1+2+3+4+6=16>12. !
Click here to go to the homepage: https://eanbardsley.github.io/source/index.html
L
L
sun
=
(
M
M
sun
)
3.5
S
0
=
3.9 × 10
26
4π (1.5 × 10
−11
)
2
= 1370
wa t ts
m
2
T
2
∝ r
3
