1. What is the Radius Calculation Formula?

The formula calculates the radius of the sun/star based on the mean distance between the sun and planet, total solar irradiance, and effective surface temperature using the Stefan-Boltzmann law.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r \) — Radius of the sun (Meter)
• \( L \) — Mean distance between sun and planet (Meter)
• \( G_s \) — Total solar irradiance (Watt per Square Meter)
• \( \sigma \) — Stefan-Boltzmann Constant (5.670367×10⁻⁸ W/m²K⁴)
• \( T_s \) — Effective surface temperature (Kelvin)

Explanation: The formula derives the solar radius by balancing the total energy output (based on Stefan-Boltzmann law) with the solar energy received at a given distance.

3. Importance of Solar Radius Calculation

Details: Calculating the solar radius helps astronomers understand stellar properties, verify theoretical models, and study the energy balance in planetary systems.

4. Using the Calculator

Tips: Enter mean distance in meters, solar irradiance in W/m², and temperature in Kelvin. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the Stefan-Boltzmann constant?
A: The Stefan-Boltzmann constant (σ) is a physical constant that relates the total energy radiated per unit surface area of a black body to the fourth power of its temperature.

Q2: Why is the distance squared in the formula?
A: The energy received decreases with the square of the distance from the source (inverse square law for radiation).

Q3: What is typical solar irradiance value for Earth?
A: The solar constant for Earth is approximately 1361-1363 W/m² at the top of the atmosphere.

Q4: What is the effective surface temperature of the Sun?
A: The Sun's effective temperature is approximately 5778 K (or about 5505°C).

Q5: How accurate is this calculation method?
A: This method provides a good estimate but assumes the sun is a perfect black body radiator, which is an approximation.