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In My Program called More Realistic Galaxy I include all different kinds of stars and I can look up their solar mass limits.

I also made it like a midnight blue instead of like black so that if a black dwarf evolves you can actually see it.

I have a question. Okay I am trying to calculate what the brown dwarf threshold should be given that 500 in the program is = .75 solar masses. I divided .75 by 500 to get the solar masses per unit of mass in the program and it is .0015. I multiplied that by the minimum mass for a brown dwarf which is 13 jupiter masses which is = 0.0124098 solar masses. I multiplied the solar masses per unit by the minimum mass of a brown dwarf and I got 0.0000186147 units of mass for a brown dwarf. Is something wrong with my calculations? Would every star start off as a brown dwarf this way? I mean it is in the lowest luminosity of the main sequence being L, M, and T class but still would every star start off as a brown dwarf this way and is something wrong with my calculations?

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This might be better suited to physics.stackexchange.com, but your calculations appear to be correct from a cursory glance. –  abiessu Mar 4 at 19:37
    
Well because it is related to my program I put it in computer science which is all about programming and they said it was more suitable for the math section but okay I will post it in physics and see what they say. –  caters Mar 4 at 19:40
    
You may also find that you want to use $.75\cdot 500=375$ as the in-program value for a brown dwarf; or ${500\over .75}={2000\over 3}$ as the conversion factor between in-program values and solar masses. –  abiessu Mar 4 at 19:41
    
instead of the inverse of that which leads to really small decimals. –  caters Mar 4 at 19:46
    
Why I mean .75 solar masses for every 500 units leads to solar masses per unit and multiplying that by the lower mass limit gives you the units for the program so why would I want to multiply units of mass by solar masses for 500 units? or basically divide 2000/3? –  caters Mar 4 at 21:35
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1 Answer 1

If a brown dwarf requires $0.0124098$ solar masses (label this SM), and if $500$ in-program units (label this IPU) are equivalent to $0.75$ SM, then the conversion factor from solar masses to in-program units would be used as

$$(0.0124098\text{ SM})\cdot \frac {500\text{ IPU}}{0.75\text{ SM}}=8.2732\text{ IPU}$$

You applied this conversion factor, but in the wrong direction, and you ended up with

$$0.0000186147 \frac{\text{SM}^2}{\text{IPU}}$$

(note the application of units...) The $8.2372\text{ IPU}$ value for an in-program brown dwarf makes much more sense given the ratio of SM to IPU.

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Oh I see the solar masses cancel out that way and the way I was doing it I was squaring the solar masses. Thats why I got that really small decimal so with the correct way it like simplifies to (0.0124098 * 500)/.75. So now I can correctly figure out the threshold or lower mass limit for the other types of stars in my program. Thanks. –  caters Mar 4 at 22:08
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