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 Math / Science
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, F0 is the solar constant (1361 W/m2), the flux of light from the sun at Earth's distance from it (1 AU = 1.5x1011 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:
- dmin: The inner radius of the Goldilocks zone
- dmax:The outer radius of the Goldilocks zone
- 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.
Exoplanet Functions:
- 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