### Luminosity Calculator:

Enter Star radius in R☉, Star temperature in K, Luminosity L☉, Absolute magnitude, Distance in pcs and Apparent magnitude. Then our calculator calculates the Luminosity values.

This luminance calculator is a handy tool, This allows us to calculate the energy emitted by stars and how bright they appear from Earth. The absolute and apparent magnitudes of stars can also be determined. Luminance is a measure of the energy emitted by a substance,

For example, a star or constellation. For main-sequence stars, luminosity is directly related to their temperature—the hotter a star is, the more luminous it is.

Cooler stars, on the other hand, emit less energy—so, spotting them in the night sky is more challenging.

- Check the star’s radius and temperature
- Divide the stellar radius by the Sun’s radius.
- Divide the stellar temperature by the sun’s temperature.
- Find the square of the two values and multiply them.
- Multiply the result by the Sun’s luminosity to get the output.

Luminance is the absolute measure of radiant electromagnetic energy or radiant energy emitted by a light-emitting material. It depends on the temperature and radius of the object.

### Luminosity Equation:

Luminosity of the star L_{(w)} in watts and divided by the is the luminosity of the sun LΘ_{(w)} in watts is equal to the star radius R _{(km)} in kilometer and divided by the radius of the sun RΘ_{(km)} in kilometer and multiply the star temperature T_{(k)} in Kelvin and divided by the the star temperature T_{(k)} in Kelvin and divided by the temperature of the sun TΘ_{(k)} in Kelvin.Hence the Luminosity equation can be written as

L_{(w)} / LΘ_{(w)} = (R _{(km)}/RΘ_{(km)} )^{2} * (T_{(k)} /TΘ_{(k)})^{4}

Where

L = is the luminosity of the star

LΘ = is the luminosity of the sun and is equal to 3.828 *10^{26}w

R= is the star radius

RΘ = is the radius of the sun and equal to 695700km

T = is the star temperature

TΘ = is the temperature of the sun and it is 5778k

Absolute magnitude is a away of finding luminosity.It uses a logarithm scale to calculate it

The formula of absolute magnitude is M =2.5 * log_{10} (L /L_{o})

Where

M = is the absolute magnitude of the star

L_{0} = is the zero-point luminosity and its value is 3.0128 *10^{28 }w

Apparent magnitude is used to measure the brightness of stars when seen from Earth.It equation m= M-5+5log_{10} (D)

Where

M= is the apparent magnitude of the star

D = is the Distance between star and Earth

### Example:1

Find the luminosity of a star having the radius 57893 km and temperature is 225k

### Answer:

Given that

Radius of the star R =57893 km

Temperature of the star T =225K

The luminosity of star formula is L / LΘ = (R /RΘ )^{2} * (T /TΘ)^{4}

L=3.828 *10^{28} (57893 /695700)^{2} * ( 225 /5778)^{4}

M=-2.5 *log_{10} (6095368342.972829 /3.828 *10^{28} )

Luminosity (L) =6095368342.972829 Gw

Absolute magnitude (M) =24.2349258

### Example:2

Find the luminosity of a star having the radius 500 km and temperature is 150k

### Answer:

Given that

Radius of the star R =500km

Temperature of the star T =150k

The luminosity of star formula is L / LΘ = (R /RΘ )^{2} * (T /TΘ)^{4}

L=3.828 *10^{28} (500 /695700)^{2} * ( 150 /5778)^{4}

M=-2.5 *log_{10} (89809.61140426056 /3.828 *10^{28} )

Luminosity (L) =89809.61140426056 Gw

Absolute magnitude (M) =36.31511871355258 w