Luminosity, Radius, and Temperature Calculator

Formula

The formula to calculate the Luminosity (L) is:

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

Where:

\( L \) is the luminosity in watts (W).
\( R \) is the radius in meters (m).
\( T \) is the temperature in kelvin (K).
\( \sigma \) is the Stefan-Boltzmann constant, approximately \( 5.67 \times 10^{-8} \) W/m²K⁴.

What is the Luminosity Radius Temperature Relationship?

The luminosity radius temperature relationship is a fundamental concept in astrophysics that describes how the luminosity (total energy output) of a star is related to its radius and surface temperature. This relationship is crucial for understanding the properties and behavior of stars. The formula \( L = 4\pi R^2 \sigma T^4 \) shows that the luminosity of a star is directly proportional to the square of its radius and the fourth power of its surface temperature. This means that even small changes in temperature can result in significant changes in luminosity. This relationship helps astronomers determine the size, temperature, and energy output of stars based on observable data.

Example Calculation

Consider an example where:

Radius (R): 7 × 10⁸ meters
Temperature (T): 5800 kelvin

Using the formula to calculate the Luminosity:

\[ L = 4\pi (7 \times 10^8)^2 (5.67 \times 10^{-8}) (5800)^4 \]

This means that the luminosity for this example is approximately \( 3.95 \times 10^{26} \) watts.