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`d = ((L*F_0)/(4\sigma T^4)(1-a)(1+(3/4)\tau))^(1/2)`

0.589

1.1

0.511

The **Goldilocks Zone** calculator returns the orbital range around a star where habitable life, as we know it, is possible.

**INSTRUCTIONS**: Choose units and enter the following:

- (
**L**) Star's Luminosity - (
**a**) Average Planetary Albedo - (
**τ**) Infrared Optical Depth of Planetary Atmosphere- (0 = no atmosphere; 0.8 = Earth's atmosphere)

**Goldilocks Zone Range (d)**: The calculator returns the minimum and maximum semi-major axes (approximate radii) in astronomical units. However, this can be automatically converted to compatible distance units via the pull-down menu.

The **Goldilocks Zone** calculator estimates the minimum and maximum distance from a star in which you can place a habitable planet. It's based on the idea that the mean planetary temperature must be between the freezing point of water (0° C = 273 K) and the boiling point of water (100° C = 373 K). The formula used inverts the one in the Planetary Temperature calculator to find the minimum and maximum distances. In the formula given above, F_{0} is the solar constant (1361 W/m^{2}), the flux of light from the sun at Earth's distance from it (1 AU = 1.5x10^{11} m).

The formula for the Goldilocks Zone is:

`d = ((L*F_0)/(4\sigma T^4)(1-a)(1+(3/4)\tau))^(1/2)`

The parameters you input are:

**d**= mean distance from the center of the star (approximate semi-major axis of the orbit)**T =**the temperature. Max distance uses (0° C = 273 K) and the min distance uses boiling point of water (100° C = 373 K).**L =**the luminosity (brightness) of the star, in units where the sun's luminosity is 1**a =**the average planetary albedo (the fraction of light that the planet reflects in the visible region of the spectrum)**τ =**the infrared optical depth of the planetary atmosphere (a measure of how much heat the planet traps due to the Greenhouse effect) (0 = no atmosphere; 0.8 = Earth's atmosphere)

The calculator's outputs are:

**d**: The inner radius of the Goldilocks zone_{min}**d**The outer radius of the Goldilocks zone_{max}:**W**: The width of the zone

By default, the answers are given in astronomical units, but you can convert them into any units of distance you want.

- Separation from Mass and Period
- Speed of Circular Orbit
- Mass of Exoplanet from Mass and Speed of Star and Planet Speed
- Mass of Exoplanet from Stellar Mass and Radius around barycenter and planetary orbit radius
- Mass from Period and Separation
- Mass from Speed and Separation
- Radius from Speed and Period
- Speed from Delta Lambda and Lambda
- Distance from Apparent and Absolute Magnitude
- Flux Ratio from Magnitudes
- Planetary Temperature
- Goldilocks Zone