[SPACE] Tidal braking

[dataweaver]

For the record, the means of determining how long it would take to get from one rotational period to another is:

A = 62.5 * [(P2 - P1)] / [P1 * P2 * M/D^5 * (S1 - S2)]
A: time needed in billions of years
P1: initial rotational period in hours
P2: final rotational period in hours
M: mass of planet in Earth masses
D: diameter of planet in Earth diameters
S1: sum of squares of tides from sun and satellites with orbital periods greater than P1
S2: sum of squares of tides from remaining satellites.

For multiple satellites:

First Step:
P1 is randomly determined
P2 is the longest satellite orbital period in hours (multiply days by 24)

Subsequent Steps (skip to end if S2 >= S1):
P1 is the previous step's P2
P2 is the next longest satellite orbital period in hours (multiply days by 24)

repeat until you run out of satellites

Last Step (skip if S2 >= S1):
P1 is the previous step's P2
P2 is the planet's orbital period in hours (multiply years by 8766)

For one satellite:

First Step:
P1 is randomly determined
P2 is the satellite orbital period in hours (multiply days by 24)

Last Step (skip if S2 >= S1):
P1 is the previous step's P2
P2 is the planet's orbital period in hours (multiply years by 8766)

For no satellites:

P1 is randomly determined
P2 is the planet's orbital period in hours (multiply years by 8766)

Again, keep a running total of the A's; stop and interpolate the current rotational period if the running total equals or exceeds the system's age.

(Oddly enough, the only equation I'm having trouble with is the interpolation of the current rotational period; and that's simple Algebra. Need sleep...)