Author Topic: Jumping To L1 Points  (Read 5440 times)

Daryk

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Re: Jumping To L1 Points
« Reply #30 on: 14 January 2024, 09:33:19 »
I used to have an astronomy textbook that had tables that resulted in the DS&JS numbers.  It's long gone though, and when I tried looking up those tables on the internet, they didn't match DS&JS anymore.

Lagrange

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Re: Jumping To L1 Points
« Reply #31 on: 14 January 2024, 21:03:35 »
I broke out wikipedia for stellar classes and tried to work out a formula for the Zenith<->planet distance based on star mass and luminosity.

Schwarzchild geometry would suggest something like distance = C*sqrt(mass) where C is a constant. This is very wrong with an extreme case being the B0V given in Strat ops page 70.  A B0V is 17.7 solar masses, which would suggest 42 AU, but it's listed as 2318.96AU, missing by a factor of 55.

Eyeing things, distance = C*sqrt(luminosity) is closer---that gets within a factor of 5.  Fiddling a bit further, distance = C*Luminosity^0.62 gives a factor of 3.5 approximation.

Throwing in mass and luminosity together so distance = C*mass^a * luminosity^b and solving for a and b, you can get a factor of 3ish approximation using C*mass^-3.05*luminosity^1.43.  That's not much better given the effort.

In retrospect, luminosity dependence is more consistent with charging times which varies over just a 40% range.  Using the recharge times, I can get a factor of 2.4 approximation via distance = C*sqrt(luminosity)*(solcharge time/recharge time)^5.

Overall, there's no clear exact formula, but sqrt(luminosity) (~= solar power incident on the Zenith) is the closest easy approximation, with the distance somewhat longer for small stars and shorter for large stars.

Daryk

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Re: Jumping To L1 Points
« Reply #32 on: 14 January 2024, 22:27:48 »
Looks like progress to me! :)