Calculating solar mass using luminosity

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Discussion Overview

The discussion centers around calculating the solar mass using luminosity, specifically through the formula L=M^3.5. Participants explore how to manipulate this formula to solve for mass (M) given luminosity (L), while also considering the applicability of the formula to different types of stars beyond main sequence stars. The context includes both theoretical calculations and practical applications for creating a star atlas for science fiction games.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about solving for mass (M) using the formula L=M^3.5 and requests assistance, particularly in Visual Basic syntax.
  • Another participant suggests that a scientific calculator can find the 3.5th root of luminosity and proposes a potential rearrangement of the formula.
  • A different participant recommends using logarithm tables to simplify calculations involving powers and roots.
  • Further clarification is provided on the logarithmic approach, indicating a method to derive M from L using logarithmic functions.
  • One participant notes the need for a comprehensive list of stellar masses due to the large number of solar systems being populated, while acknowledging the utility of existing lists for verification of calculations.
  • Another participant presents the formula M=L^(1/3.5) and inquires about the units for mass and luminosity being used.
  • A participant mentions that the mass of the Sun (Sol) and its luminosity are both set to 1 for reference, explaining the implications of absolute magnitude on brightness relative to the Sun.

Areas of Agreement / Disagreement

Participants express various methods for calculating mass from luminosity, but there is no consensus on the best approach or the applicability of the original formula to different star types. The discussion remains unresolved regarding the most effective formula for non-main sequence stars.

Contextual Notes

Participants have not fully clarified the assumptions regarding the units for mass and luminosity, nor have they resolved the limitations of the formula for different types of stars.

Who May Find This Useful

Individuals interested in astrophysics, particularly those involved in stellar modeling or creating fictional star systems for games, may find this discussion relevant.

zircher
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Okie dokie, I searched the web and found L=M ^ 3.5 (luminosity equals mass to the power of 3.5). But, I'm pretty clueless on anything beyond Algebra I. How do I solve for M if I know L? [If the answer can be expressed in Visual Basic syntax, all the better.]

I also read several caveats that said the above formula works best for main sequence stars. Does anyone know of better of formula for sub-dwarfs, dwarfs, giants, and super giants? I'm pulling my numbers from a sub-set of the Hipparcos data. So, from absolute magnitude, I can calculate luminosity, but I get stuck after that.

My goal is to calculate solar mass and plug that into Accrete so I can create a fictional but semi-realistic star atlas for hard sci-fi games.

Along a similar line, I've seen some sites that says Accrete is fairly dated as far as solar system modelling goes. Has anyone written a successor to Accrete that is available to the public?
--
TAZ
 
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A scientific calculator should be able to find the 3.5th root of luminosity without difficulty. I would imagine that the formula would be something along the line of L^-3.5=M, but I'm not a Visual Basic user. I also suspect that you could simply find a direct list of stellar masses in any number of references.
 
Use a logarithm table. Powers and roots are simple when working with log values.
 
Good point Chronos. So you would start with X=Log(L)/3.5
Then M=INV LOG(X).
 
Thanks for the prompt replies, guys. I'll give them a try. The list of stellar masses has merit, but I need to populate 59,000 solar systems and most lists only have a handful of stars. But, I can use them to check my math now that I have something to work with.
--
TAZ
 
M=L^(1/3.5)

But what units are you using for M and L?
 
Mass of Sol = 1 and Luminosity of Sol = 1. So a star with an Absolute Magnitude of zero whould be 100 times brighter than Sol.
--
TAZ
 

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