Mean Distance Between Sun Or Star And Earth Or Planet Calculator

Formula Used:

\[ L = \sqrt{\frac{r^2 \times \sigma \times T_s^4}{G_s}} \]

Radius Of The Sun/Star:

meters

Effective Surface Temperature:

Kelvin

Total Solar Irradiance:

W/m²

Mean Distance Between Sun/Star And Earth/Planet:

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1. What Is The Mean Distance Calculation?

The mean distance between a sun/star and earth/planet is calculated using the relationship between the star's radiative properties and the received solar irradiance. This formula helps determine the orbital distance based on stellar characteristics.

2. How Does The Calculator Work?

The calculator uses the following formula:

\[ L = \sqrt{\frac{r^2 \times \sigma \times T_s^4}{G_s}} \]

Where:

\( L \) — Mean distance between sun/star and earth/planet (meters)
\( r \) — Radius of the sun/star (meters)
\( \sigma \) — Stefan-Boltzmann constant (5.670367 × 10⁻⁸ W/m²K⁴)
\( T_s \) — Effective surface temperature (Kelvin)
\( G_s \) — Total solar irradiance (W/m²)

Explanation: The formula derives from the balance between the star's total radiative output and the solar irradiance received at the planetary distance.

3. Importance Of Distance Calculation

Details: Calculating the mean distance is crucial for understanding planetary orbits, habitable zones, and the energy balance between stars and their planetary systems.

4. Using The Calculator

Tips: Enter the radius of the sun/star in meters, effective surface temperature in Kelvin, and total solar irradiance in W/m². 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: How accurate is this calculation?
A: This calculation provides a theoretical mean distance based on ideal radiative transfer. Actual distances may vary due to orbital eccentricities and other astronomical factors.

Q3: Can this be used for any star-planet system?
A: Yes, this formula can be applied to any star-planet system where the stellar parameters and received irradiance are known.

Q4: What is total solar irradiance?
A: Total solar irradiance (solar constant) is the amount of solar energy received per unit area at the top of a planet's atmosphere.

Q5: How does temperature affect the distance calculation?
A: Higher surface temperatures significantly increase the calculated distance due to the T⁴ relationship in the radiative output.