1. What is the Stellar Radius Equation?

The stellar radius equation calculates the radius of a star based on its luminosity and surface temperature, using the Stefan-Boltzmann law. This fundamental relationship helps astronomers determine the size of stars from observable quantities.

2. How Does the Calculator Work?

The calculator uses the stellar radius equation:

Where:

• \( R \) — Stellar radius (meters)
• \( L \) — Luminosity (Watts)
• \( \sigma \) — Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²·K⁴)
• \( T \) — Surface temperature (Kelvin)

Explanation: The equation derives from the relationship between a star's luminosity, temperature, and surface area, where luminosity is proportional to the fourth power of temperature.

3. Importance of Stellar Radius Calculation

Details: Knowing a star's radius is essential for classifying stars, understanding stellar evolution, and determining physical properties like density and surface gravity.

4. Using the Calculator

Tips: Enter luminosity in Watts and temperature in Kelvin. Both values must be positive. For solar values, use L☉ = 3.828×10²⁶ W and T☉ = 5778 K.

5. Frequently Asked Questions (FAQ)

Q1: How does this relate to the Stefan-Boltzmann law?
A: The equation is derived from the Stefan-Boltzmann law which states that a star's luminosity equals its surface area times σT⁴.

Q2: What are typical stellar radius values?
A: Stellar radii range from ~0.01 R☉ (white dwarfs) to >1000 R☉ (supergiants). Our Sun has R☉ ≈ 6.96×10⁸ m.

Q3: Can this be used for all stars?
A: This works well for main sequence stars, but may need adjustments for very compact or inflated stars.

Q4: How accurate is this calculation?
A: Accuracy depends on precise measurements of L and T. Errors in these inputs propagate to the radius calculation.

Q5: What if I know the radius and want to find luminosity?
A: The equation can be rearranged to solve for L = 4πR²σT⁴.