# Calculating solar mass using luminosity

• zircher
In summary: M=L^(1/3.5)In summary, the conversation revolves around finding the mass of a star (M) given its luminosity (L) using the formula L=M^3.5. The discussion also touches on using a scientific calculator or logarithm table to solve for M, as well as the possibility of finding a list of stellar masses for reference. The goal is to use this information for creating a fictional but realistic star atlas for sci-fi games. There is also mention of using the TAZM formula, but it is unclear which units are being used for M and L in this case. The conversation ends with the question of whether there is a more updated version of Accrete, a solar system modeling program, available to
zircher
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?
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TAZ

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.

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.
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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.
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TAZ

## 1. How is solar mass calculated using luminosity?

The solar mass can be calculated using the formula: M = L / (4πGσ), where M is the solar mass, L is the luminosity, G is the gravitational constant, and σ is the Stefan-Boltzmann constant.

## 2. What is luminosity and how is it measured?

Luminosity is the total amount of energy emitted by a star per unit time. It is measured using a photometer, which measures the intensity of light emitted by a star over a specific wavelength range.

## 3. Can the solar mass be calculated for any star?

Yes, the solar mass can be calculated for any star as long as its luminosity and distance from Earth are known. However, this calculation may be more accurate for stars that are similar to the Sun in terms of size and temperature.

## 4. What are the units of solar mass and luminosity?

Solar mass is typically measured in units of kilograms (kg), while luminosity is measured in units of watts (W). However, in astronomical calculations, solar mass is often expressed in terms of solar masses (M☉) and luminosity is expressed in terms of solar luminosities (L☉), where 1 M☉ is equal to the mass of the Sun and 1 L☉ is equal to the luminosity of the Sun.

## 5. Why is it important to calculate the solar mass using luminosity?

Calculating the solar mass using luminosity allows scientists to determine the mass of stars that are too far away to be measured using other techniques. It also provides important information about the internal structure and evolution of stars.

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