DEFINITION
The Goldilocks zone, also known as the habitable zone in a planetary system is defined as that volume around the primary star in which life (as we know it) might exist.
Currently this is defined as the volume in which the surface temperature of a planet will lie between the freezing point and the boiling point of water.
This is not a well defined region of space for any planetary system as it depends on the atmosphere around a planet and the consequent amount of greenhouse effect a planet experiences.
"Not too hot, not too cold, just right."
CALCULATING PLANETARY TEMPERATURES
If we know the luminosity of a star and the distance of a planet from that star it is possible to calculate the theoretical mean surface temperature of the planet providing it is rapidly rotating. This is done by assuming the energy received from the Sun is equal to the energy radiated by the planet out into space.
The stellar flux at a distance r from a star is S = Ls / ( 4 π r2 ) where Ls is the luminosity of the star in watts (ie the energy radiated from the star in Joules per second or watts. S then has the units of W / m2. This is often called the solar constant for the specified planet.
The energy received by the planet is then S π R2 where R is the radius of the planet.
The energy radiated back out into space is given by the Stefan-Boltzmann equation and is equal to 4 σ π R2 T4 where T is the mean planetary surface temperature and σ is a constant ( σ = 5.67 x 10-8 ).
Equating energy received to energy radiated we can calculate the planetary surface temperature as:
Note that this temperature depends only on the distance of the planet from its star and not on its size.
THE GREENHOUSE EFFECT
As seen in the last section it is possible to calculate the theoretical mean surface temperature of a rapidly rotating planet at a given distance from the Sun. However, this assumes that the planet has not atmosphere and that it is rapidly rotating. If neither of these assumptions is valid, the calculated temperature will be in disagreement with the measured value.
The table below shows the respective mean temperatures of Venus, Earth and Mars:
Mercury is not included in this table because it not only doesn't have any atmosphere but it also doesn't rotate rapidly. Any atmosphere would be boiled off by the Sun. Mercury has a surface temperature variation from about 100 to 700K.
The disparity between the theoretical and observed mean temperature is due to the presence of an atmosphere – a process known as the “greenhouse effect”. This is due to the fact that much more of the shorter wavelength solar energy reaches the planet surface, whereas the atmosphere only allows a small portion of the surface long wavelength reradiation to escape back to space.
Mars, which has only a small atmosphere has very little greenhouse effect. Earth, which has a moderately dense atmosphere, has a moderate greenhouse effect, and Venus, which has a super dense atmosphere appears to suffer from a super-greenhouse effect. However, Venus only absorbs 2.5% of the incident solar energy, so internal heat transport may be important.
GOLDILOCKS IN THE SOLAR SYSTEM
In the solar system the habitable zone is believed to include the planets Earth and Mars as shown in the diagram at left. If Venus had a much less dense atmosphere it might also lie in the Goldilocks zone.
It can be seen that the extent of the habitable zone in the solar system has been adjusted using a knowledge of the actual surface temperature of the planets. For most exoplanets (planets around other stars) we will not have this knowledge and so any attempt to draw a goldilocks zone in these systems will be subject to large error.
Australian Space Academy