Re: Programming a calendar system

"Mark J. Reed" wrote:
> That particular Keplerian law tells you how long a planet's orbital
> period ("year") is, based on its distance from the sun.  If you express
> the period (commonly represented in equations by T for Time) in Earth
> years and the distance (commonly represented by R for Radius) in
> Astronomical Units, the constants cancel out and you are left with the
> very simple relation that T^2 = R^3.
Provided the mass of the sun is the same.  If you have an alien sun,
then the mass would likely be different than ours, and the ratio
wouldn't work.  Kepler's law is merely a simplification based on
constant mass of the actual rotational period equation:

P = SQRT((4pi^2*R^3/(MG))

where P = period (measured in seconds) M is the mass of the sun
(measured in kilograms; actually, technically, the total mass of both
objects), R is the distance between the centers of the two objects
(measured in meters), and G is the Gravitational Constant
(6.67259*10^-11)

Thus, if you have a constant mass (and the sun is so much more massive
than any planet that the differences in M between different sun-planet
pairs is negligible) it simplifies to a proportionality of OP =
SQRT(R^3), i.e., T^2=R^3.  However, quadruple the mass, and keep the
distance the same, and you'll halve the orbital period.

> Sure, on Earth the size of the week was inspired by the number of
> visible planets in the sky, and the size of the month by the phases of
> our moon,
For that matter, the 7-day week isn't even universal on Earth.  Very
many cultures have weeks of other lenghts, such as 6 days in Japan, 8
days in ancient Rome, 10 days in Egypt, 13 and 20 days among the maya,
etc.

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