I’ve spent a lot of time trying to answer certain questions in astronomy, where I just want a rough approximation for the purpose of a simulation, and don’t need an exact answer. These are some of the equations I’ve come up with.

### Yerkes Classes’ T/M_{v} Relations

These equations are shown as functions where x is temperature in Kelvin, and f(x) is absolute magnitude (visual). Most are valid from 2400 K to a little bit past 30000 K, the exceptions are noted. For the hypergiants and white dwarfs, the range is within an elliptical region, of which these functions define the major axis; for all others, they are a trend line along a Yerkes classification.

Hypergiants (0):

f(x) = -8.9

Supergiants (Ia):

f(x) = -0.00135x^{3} + 0.0233x^{2} + 0.0187x – 7.349

Supergiants (Ib):

f(x) = 0.00329x^{3} – 0.0962x^{2} + 0.829x – 7.209

Bright Giants (II):

f(x) = 0.00557x^{3} – 0.166x^{2} + 1.505x – 6.816

Giants (III):

f(x) = 0.0135x^{3} – 0.373x^{2} + 3.019x – 7.233

Subgiants (IV):

f(x) = -0.151x^{2} + 2.216x – 5.128 *(4450-100000 K ***only**)

Dwarfs (V):

f(x) = 0.00193x^{5} – 0.0615x^{4} + 0.742x^{3} – 4.257x^{2} + 12.439x – 12.996 *(note: this one is the least accurate)*

Subdwarfs (VI):

f(x) = 0.131x^{3} – 3.275x^{2} + 27.576x – 71.7 *(3050-6000 K ***only**)

White Dwarfs (VII):

f(x) = 0.489x + 10.01 *(4450-30000 K ***only**)

### Simple Conversions

Absolute Magnitude (visual) → Luminosity (solar luminosities):

L_{sun} = 100 * exp(-0.944 * M_{v})

Accurate between 0-10 M_{v}. Probably continues accuracy relatively well.

Main Sequence Luminosity / Mass Relation:

L_{star} / L_{sun} = (M_{star} / M_{sun})^{3.5}

L_{star} = ( 3.68 * ln(M_{star}) – 0.244 )^{e}

*(The second equation applies to all stars.)*

Mass / Lifetime Relation:

T_{years} = ( 23.4 – 2.68 * ln(M_{star}) )^{e}

*(This applies to all stars.)*

Spectral (UBVRI) Filters:

**U**ltraviolet, **B**lue, **V**isual, **R**ed, **I**nfrared.

Objects are listed in different indexes:

**U**–**V** for the hottest objects (stellar remnants, galaxies), then **B**–**V** (the majority of stars), and **R**–**I** for the coolest (LTY “stars” and below).

### Equations I no longer recommend

Provided for completeness, in case they are found to be useful.

Temperature (K) → Absolute Magnitude (visual):

M_{v} = 35.463 * exp(-0.000353 * T)

Roughly accurate between 2000-50000 Kelvin. Probably doesn’t continue accuracy at hotter temperatures. Previously this was at the top of this post, now I am not sure why (perhaps the simplicity). The Yerkes’ classifications are a better system.

B-V index (x) → Temperature (K):

T = -772.2x^{3} + 3152x^{2} – 6893x + 9500

Sorta accurate between 0-2. (This equation I am least comfortable with, and don’t plan to use.)