Luminosity Calculator

Formula

To calculate the luminosity of a star:

\[ L = 4 \pi R^2 \sigma T^4 \]

Where:

\(L\) is the Luminosity (watts)
\(R\) is the Radius of the Star (meters)
\(\sigma\) is the Stefan-Boltzmann constant (5.670 \times 10^{-8} W \cdot m^{-2} \cdot K^{-4})
\(T\) is the Temperature (Kelvin)

What is Luminosity?

Luminosity is defined as the radiant energy or power given off by a star. It is a measure of the total amount of energy emitted by the star per unit of time. The luminosity of a star depends on its radius and temperature.

Example Calculation 1

Let's assume the following values:

Radius of the Star (\(R\)) = 6.96 \times 10^8 meters
Temperature (\(T\)) = 5778 Kelvin

Using the formula:

\[ L = 4 \pi (6.96 \times 10^8)^2 (5.670 \times 10^{-8}) (5778)^4 \]

Calculate the intermediate steps:

\(R^2 = (6.96 \times 10^8)^2 = 4.84 \times 10^{17}\)
\(T^4 = (5778)^4 = 1.11 \times 10^{15}\)

Plugging in the values:

\[ L = 4 \pi (4.84 \times 10^{17}) (5.670 \times 10^{-8}) (1.11 \times 10^{15}) \]

\[ L \approx 3.828 \times 10^{26} \, \text{watts} \]

The Luminosity is approximately \(3.83 \times 10^{26}\) watts.

Example Calculation 2

Let's assume the following values:

Radius of the Star (\(R\)) = 1.39 \times 10^9 meters
Temperature (\(T\)) = 6000 Kelvin

Using the formula:

\[ L = 4 \pi (1.39 \times 10^9)^2 (5.670 \times 10^{-8}) (6000)^4 \]

Calculate the intermediate steps:

\(R^2 = (1.39 \times 10^9)^2 = 1.93 \times 10^{18}\)
\(T^4 = (6000)^4 = 1.296 \times 10^{16}\)

Plugging in the values:

\[ L = 4 \pi (1.93 \times 10^{18}) (5.670 \times 10^{-8}) (1.296 \times 10^{16}) \]

\[ L \approx 5.671 \times 10^{27} \, \text{watts} \]

The Luminosity is approximately \(5.67 \times 10^{27}\) watts.