# Habitable zone of a star

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Hi !

I need your help to find a formula to calculate the habitable zone of a star ... I searched and searched without having the answer ...

I found this calculation:
But it just defines a radius. I would like to calculate the lower limit of the ZH and its upper limit. I found other calculations with Boltzman's law, but I can not find results that work.

So if you have an idea I'd be happy

Thanks (sorry for my english)

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I'm not sure how you are defining habitable zone, in our solar system both Venus and Mars are within the habitable zone but both have atmospheres that prohibit life.

I know this is not an answer but I want to see what others have to say and I'll do a bit of digging too..

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17 hours ago, Moontanman said:

I'm not sure how you are defining habitable zone, in our solar system both Venus and Mars are within the habitable zone but both have atmospheres that prohibit life.

I know this is not an answer but I want to see what others have to say and I'll do a bit of digging too..

I think (but I'm not sure) that the albedo (so the composition of the atmosphere) is not taken into account to define the habitable zone. But I can be wrong...

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Is the 'habitable' zone usually defined as the min and max orbits around a star where temps are such that water is in a liquid state ?
I don't think atmospheres are considered.
( water would not be liquid on a planet with no atmosphere at 70 deg C )

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14 minutes ago, AXdlv said:

I think (but I'm not sure) that the albedo (so the composition of the atmosphere) is not taken into account to define the habitable zone. But I can be wrong...

This seems reasonable. Otherwise you could have planets assumed to be outside the habitable zone of a star like the Sun, orbiting at 93,000,000 miles from it, with other planets, both closer and further, considered in the zone simply due to their make up.

I think the habitable zone, assuming there is one, says more about the star than the individual planets.

Edited by J.C.MacSwell

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3 minutes ago, MigL said:

Is the 'habitable' zone usually defined as the min and max orbits around a star where temps are such that water is in a liquid state ?
I don't think atmospheres are considered.
( water would not be liquid on a planet with no atmosphere at 70 deg C )

With no atmosphere the earth would be freezing cold much like the moon at night, the average temp of a body in earth's orbit would be below freezing..

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I would define "habitable zone" as distance from the star in which planet is receiving 1370 Watts per square mater of surface +- couple (or couple dozen) percent tolerance.

1370 W/m^2 is measured radiation of the Sun, and by applying reverse of inverse-square law, we can calculate total power of the Sun.

$P=\frac{P_0}{4 \pi r^2}$

$P_0 = P * 4 * \pi * r^2$

$P_0 = 1370 * 4 * 3.14159265 * (150*10^9)^2 = 3.8 *10^{26} W$

So, if we will use +-10% tolerance, star must deliver (approximately) 1200 W/m^2....1500 W/m^2.

You should be able to calculate min and max radii for this range by yourself now.

Carbon-based organic life requires water. Water must be able to exist in liquid form. Which is in temperature range 0 ... 100 C (at standard pressure). Too large radiation from the star, and water will vaporize, like on Venus. Too low radiation, and it'll freeze.

There are existing super cold stars which emit fraction of energy which is emitted by the Sun. So distance between such super cold star and planet would have to be very small. e.g. star which has 1% of power of the Sun, must have planet located at distance ~15 mln km.

Edited by Sensei

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True, but we are only just now developing the means to detect extra-solar atmospheres.
Previously the only definition would have involved distances from the parent star where enough radiation is received to keep water liquid.
I'm assuming, of course.

X-posted with Sensei

Edited by MigL

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4 minutes ago, Sensei said:

I would define "habitable zone" as distance from the star in which planet is receiving 1370 Watts per square mater of surface +- couple (or couple dozen) percent.

1370 W/m^2 is measured and by applying reverse of inverse-square law, we can calculate total power of the Sun.

$P=\frac{P_0}{4 \pi r^2}$

$P_0 = P 4 \pi r^2$

$P_0 = 1370 * 4 * 3.14159265 * (150*10^9)^2 = 3.874*10^{26} W$

So, if we will use +-10% tolerance, star must deliver 1200 W/m^2....1500 W/m^2.

You should be able to calculate min and max radii for this range by yourself now.

Carbon-based organic life requires water. Water must be able to exist in liquid form. Which is in temperature range 0 ... 100 C (at standard pressure). Too large radiation from the star, and water will vaporize, like on Venus.

I think this is a good start, but different atmospheres should be able to maintain higher temperatures with the same energy balance as our Earth.

Could a rogue planet (OK, non planet) with no star to orbit sustain life? It would need to  be of sufficient size to maintain a substantial atmosphere, and have enough radioactivity to keep it warm...but not too warm. If the answer is yes that could mean almost anywhere could be habitable.

But the range you suggest seems most reasonable.

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1 hour ago, J.C.MacSwell said:

I think the habitable zone, assuming there is one, says more about the star than the individual planets.

..and stage of life of particular star..

In the future of solar system, also the Earth will be outside of habitable zone, when energy emitted by the Sun will be too high for living organisms on the Earth. Temporary *) solution could be building of cosmic-scale remote-controlled network of mirrors between the Sun and the Earth, that will reflect photons in different directions, reducing radiation reaching Earth's surface.

*) temporary for millions of years.

Edited by Sensei

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2 hours ago, Sensei said:

I would define "habitable zone" as distance from the star in which planet is receiving 1370 Watts per square mater of surface +- couple (or couple dozen) percent tolerance.

1370 W/m^2 is measured radiation of the Sun, and by applying reverse of inverse-square law, we can calculate total power of the Sun.

P=P04πr2

P0=P4πr2

P0=137043.14159265(150109)2=3.81026W

So, if we will use +-10% tolerance, star must deliver (approximately) 1200 W/m^2....1500 W/m^2.

You should be able to calculate min and max radii for this range by yourself now.

Carbon-based organic life requires water. Water must be able to exist in liquid form. Which is in temperature range 0 ... 100 C (at standard pressure). Too large radiation from the star, and water will vaporize, like on Venus. Too low radiation, and it'll freeze.

There are existing super cold stars which emit fraction of energy which is emitted by the Sun. So distance between such super cold star and planet would have to be very small. e.g. star which has 1% of power of the Sun, must have planet located at distance ~15 mln km.

Thank you for this calculation ! In the solar system, the habitable zone is between 0.95 UA and 2 AU. I do not find these values if I use your calculation ... Is it because the Earth is not in the middle of this zone ?

What are the minimum and maximum "P" for a temperature between 0 ° C and 100 ° C? (I mean Pmin=1200 W/m^2 and Pmax=1500W/m^2 ? or is it another value)

Edited by AXdlv

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1 hour ago, AXdlv said:

In the solar system, the habitable zone is between 0.95 AU and 2 AU. I do not find these values if I use your calculation ...

3.828*10^26 W / ( 4 * PI * ( 150*10^9 * 0.95 )^2 ) = 1500 W/m^2 (0.95 AU).

So inner edge is at least "right"..

It is several times mentioned on Wikipedia, in "Solar System estimates" section:

I picked up +- 10 % of power tolerance as an example values, which are acceptable for human.

in "Solar System estimates" section, we can see there is no general consensus between scientists, how to estimate it. They make predictions which require e.g. special non-Earth-like atmospheres, with significantly different pressures.

4 hours ago, Sensei said:

Water must be able to exist in liquid form. Which is in temperature range 0 ... 100 C (at standard pressure).

I would like to fix it a bit. The majority of Carbon-based living organisms will be dead at temperatures above 46 C, because their proteins will be denatured..

Edited by Sensei

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14 hours ago, Sensei said:

3.828*10^26 W / ( 4 * PI * ( 150*10^9 * 0.95 )^2 ) = 1500 W/m^2 (0.95 AU).

So inner edge is at least "right"..

It is several times mentioned on Wikipedia, in "Solar System estimates" section:

I picked up +- 10 % of power tolerance as an example values, which are acceptable for human.

in "Solar System estimates" section, we can see there is no general consensus between scientists, how to estimate it. They make predictions which require e.g. special non-Earth-like atmospheres, with significantly different pressures.

I would like to fix it a bit. The majority of Carbon-based living organisms will be dead at temperatures above 46 C, because their proteins will be denatured..

OK thanks a lot! So, if I understood correctly, in our solar system, we did not define the HZ. So, this representation is correct ?

In fact, I'd like to do a program that says (with the mass of the star, is luminosity and the distance between the planet and the star using Kepler's law) if the planet is or isn't in the habitable zone... So if I understood I must take our actuel delimitation for the solar system and transpose it to another system.

(3,8*10^26)/4*PI*(0,95*1,49*10^11)^2 = 1500 W.m^-2

(3,8*10^26)/4*PI*(2,4*1,49*10^11)^2 = 236 W.m^-2

And I take Kepler 452 with P = 1,2 * 3,8 * 10^26 W

Outer : ((1,2*3,8*1026 )/(4*PI*236))1/2 = 3,9 * 1011 m

Inner : ((1,2*3,8*1026 )/(4*PI*1500))1/2 = 1,55 * 1011 m

For Kepler from 1,55*10^11 to 3,9 * 10^11 m is "habitable" ?

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Do these calculations assume a planet identical to Earth?

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31 minutes ago, Moontanman said:

Do these calculations assume a planet identical to Earth?

According to my research, I saw that the size of the planet is not very important. But obviously, the mass has an impact on the presence of an atmosphere, so on the temperature.
But I just wanted to know how the habitable zone was calculated, this zone says more about the star than on the planet, as it was said before.

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2 minutes ago, AXdlv said:

According to my research, I saw that the size of the planet is not very important. But obviously, the mass has an impact on the presence of an atmosphere, so on the temperature.
But I just wanted to know how the habitable zone was calculated, this zone says more about the star than on the planet, as it was said before.

Ok, thanks for the clarification, I have been following Sara Seager, who works for NASA and her take on the habitable zone is a bit more complex. Also it should be noted that the Earth with no atmosphere would have an average temp below freezing.

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8 minutes ago, Moontanman said:

Ok, thanks for the clarification, I have been following Sara Seager, who works for NASA and her take on the habitable zone is a bit more complex. Also it should be noted that the Earth with no atmosphere would have an average temp below freezing.

Thank you for the name. I knew Sara Seager for her "Drake equation". Is it this calculation ? https://arxiv.org/pdf/1304.3714.pdf

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Just now, AXdlv said:

Thank you for the name. I knew Sara Seager for her "Drake equation". Is it this calculation ? https://arxiv.org/pdf/1304.3714.pdf

That is one of them, she also says the habitable zone could extend out to as far as Jupiter with the right planetary atmosphere..

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On 12/22/2018 at 4:18 PM, Moontanman said:

I'm not sure how you are defining habitable zone, in our solar system both Venus and Mars are within the habitable zone but both have atmospheres that prohibit life.

I know this is not an answer but I want to see what others have to say and I'll do a bit of digging too..

the habitability of earth is defined but the tilt at which we are at.23.5 degrees. mars tilts at 25 degrees which allows the sun to cook it. Mars used to look like earth,but was cooked because of tilt.Venus tilts at 3 degrees,thus it is very hot and uninhabitable.

Edited by peglerbc

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26 minutes ago, peglerbc said:

the habitability of earth is defined but the tilt at which we are at.23.5 degrees. mars tilts at 25 degrees which allows the sun to cook it. Mars used to look like earth,but was cooked because of tile.Venus tilts at 3 degrees,thus it is very hot and uninhabitable.

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16 minutes ago, Moontanman said:

I apologize,the tilt affect the seasons.if the earth were to tilt slightly the it would change seasons.

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13 minutes ago, peglerbc said:

I apologize,the tilt affect the seasons.if the earth were to tilt slightly the it would change seasons.

The Earth's axial tilt varies between 22.1 and 24.5 degree over a 41,000 yr cycle.  While this does have an effect on the seasons to some degree, it doesn't on the overall habitability of the Earth.

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4 minutes ago, Janus said:

The Earth's axial tilt varies between 22.1 and 24.5 degree over a 41,000 yr cycle.  While this does have an effect on the seasons to some degree, it doesn't on the overall habitability of the Earth.

yeah i was thinking differently of axial tilt.it was a flaw it my better judgment.