<p>The <a href="https://en.wikipedia.org/wiki/Effective_temperature#Blackbody_temperature" rel="nofollow noreferrer">effective blackbody temperature</a> of a planet is given by the formula</p>
<p><span class="math-container">$$T_P=\left (\frac{L(1-a)}{16 \pi \sigma D^2} \right )^{1/4} $$</span></p>
<p>where <span class="math-container">$L$</span> is the luminosity of the star, <span class="math-container">$D$</span> the distance of the planet, <span class="math-container">$a$</span> its albedo (reflectivity) and <span class="math-container">$\sigma$</span> the Stefan-Boltzmann constant.</p>
<p><em>(in principle one would have to use a <a href="https://en.wikipedia.org/wiki/Effective_temperature#Surface_temperature_of_a_planet" rel="nofollow noreferrer">slightly more complicated formula</a> that incorporates rotation and atmospheric effects for a real planet, but as the question here is for an Earth-like planet (and we know the actual temperature of the Earth) these factors effectively drop out and we can use the simpler formula instead, adjusting only the luminosity and distance to obtain the corresponding temperature).</em></p>
<p>The luminosity <span class="math-container">$L$</span> of the star is given by the Stefan-Boltzmann law</p>
<p><span class="math-container">$$L=4\pi R^2 \sigma T_S^4$$</span></p>
<p>where <span class="math-container">$T_S$</span> is the effective (black body) temperature of the star.</p>
<p>Now since <span class="math-container">$T_S$</span> is about a factor <span class="math-container">$1.7$</span> higher for Sirius A compared to the Sun, and the radius is also a factor <span class="math-container">$1.7$</span> higher, this means that the luminosity <span class="math-container">$L$</span>  of Sirius A is <span class="math-container">$24$</span> times higher than the Sun's luminosity. On the other hand, the distance <span class="math-container">$D$</span> to Sirius B is <span class="math-container">$8.2$</span>-<span class="math-container">$31.5$</span> times that of the Earth's distance from the Sun. Inserted into the first equation, this means that an Earth like planet (same albedo <span class="math-container">$a$</span>) would have a temperature <span class="math-container">$0.77$</span> timess that of the earth at the closest distance to Sirius A and <span class="math-container">$0.39$</span> times at the furthest point, which, taking the Earth's temperature as <span class="math-container">$300 K$</span>, translates into <span class="math-container">$232 K$</span> and <span class="math-container">$118 K$</span> respectively</p>

CC BY-SA 4.0
2022-02-16T01:30:22.087Z
That's a good way to provide a meaningful answer to a somewhat ambiguous question.
GrapefruitIsAwesome
CC BY-SA 4.0
2022-02-16T01:39:06.817Z
could you say Sirius B is in the habitable zone then? depending on the hypothetical atmosphere
Thomas Blobaum
CC BY-SA 4.0
2022-02-16T08:27:28.967Z
@ThomasBlobaum Habitable zone is defined as the zone in which liquid water could exist. At the temperatures as calculated above (corresponding to about -40 C to -150 C) no liquid water could exist.
Thomas
CC BY-SA 4.0
2022-02-16T16:37:53.540Z
Is there a special kind of atmosphere that could exist that would raise the temp?
Thomas Blobaum
CC BY-SA 4.0
2022-02-16T22:20:10.573Z
@ThomasBlobaum In theory, the maximum temperature would be achieved if all the incoming radiation is absorbed i,e, if the albedo $a=0$. With the earth's albedo about $1/3$, setting $a=0$ instead in the first equation above would only increase the temperature by about $10$%. So the maximum temperature  would still be about $255 K = -17C$, which would be still too cold for liquid water to exist.
Thomas
CC BY-SA 4.0
2022-02-18T04:36:35.623Z
@ThomasBlobaum You could raise the temperature using the greenhouse effect: letting stellar energy in through an atmosphere transparent in the visible, and trapping infrared energy emitted from the planet's surface in the atmosphere. Various things affect the strength of the greenhouse effect, like the absorbing efficiency of the atmospheric gases, the temperature profile in the atmosphere, and the total column density of atmosphere.
giardia
CC BY-SA 4.0
2022-02-18T11:50:13.123Z
@Thomas The temperature of a planet's *surface* can be higher, because when an atmosphere is present, the planet's photosphere (the approximate region where most of the outgoing IR flux is emitted and where the temperature will be approximately what you compute) is not necessarily the same as the surface. This is the case for the Earth and (even more so) for Venus. A zero-albedo Venus (in the Solar System) would have an effective temperature of $\sim 330$ K; its actual surface temperature is about 740 K.
Peter Erwin
CC BY-SA 4.0
2022-02-18T19:04:12.257Z
@PeterErwin Yes, you are right, I got my argument with the black body the wrong way around in my comment (now deleted) to giadia's comment. But the latter is not applicable here anyway as the OP's question clearly implies an Earth-like planet not a Venus-like one.
Thomas
CC BY-SA 4.0
2022-02-24T20:54:21.943Z
@Thomas it could be Earth-like or Venus-like. After reading your answer I'm just curious about any combination of variables and observation that could make Sirius B into a habitable planet with liquid water, etc.
Thomas Blobaum
CC BY-SA 4.0
2022-02-24T22:43:54.700Z
@ThomasBlobaum There is no combination of variables that could do so, because Sirius B _isn't_ a planet, habitable or otherwise. It's a white dwarf with a surface temperature of approximately 25,200 K.
notovny
CC BY-SA 4.0
2022-02-25T08:13:23.610Z
@notovny He was referring to a planet with the orbit of Sirius B
Thomas
CC BY-SA 4.0
2022-02-25T19:00:11.997Z
@ThomasBlobaum The problem is the high eccentricity of the orbit which results in a variation of the distance to Sirius A by a factor 4.  As you can see from the formula in my answer, this would result in a temperature variation of a factor 2 (in degrees Kelvin). This is a massive variation, making it impossible to be habitable over the whole orbit (and you can't just sit this out, as a year in this orbit lasts over 100 Earth years). It is practically impossible for any kind of life as we know it to develop in these conditions. You really need an orbit with small eccentricity to start with.
Thomas
CC BY-SA 4.0
2022-02-15T23:13:20.930Z
2022-02-18T22:26:13.160Z
2022-02-18T22:26:13.160Z
Thomas
<p>If Sirius B was a planet like Earth and not a white dwarf star what would the temperature be on the surface of Sirius B at its nearest and furthest distance? 8.2 AU to 31.5 AU</p>
<p>EDIT: I want to know if there is any combination of variables that would make Sirius B out to be the perfect distance for a habitable planet of certain specifications (and I'm not sure what those specs are).</p>

CC BY-SA 4.0
2022-02-15T18:53:51.367Z
What if my car was a Ferrari??? What are you proposing should set the temperature of your hypothetical Sirius B?
AtmosphericPrisonEscape
CC BY-SA 4.0
2022-02-15T21:38:52.207Z
This is not answerable, as it written.  I think you mean "what would the temperature be on a planet that orbits an A0V, absolute magnitude 1.42 star at a distance of 8.2 AU. But consider Venus.  You can't predict the temperature on the surface of a planet unless you know something about its atmosphere, albedo, rotation, etc.
James K
CC BY-SA 4.0
2022-02-16T01:19:57.323Z
To make this an answerable question the specifics of the planet  would need to be better defined.  Even if we were to place Earth at that location I'm not sure we could make a vary good guess without some sort of climate model. Also, should this be a mean temperature?  Planets don't typically have a uniform temperature.
GrapefruitIsAwesome
CC BY-SA 4.0
2022-02-16T13:46:04.103Z
@JamesK Unless the OP provides more details, we'll have to resort to spherical, zero-albedo, temperature-distributed Earth in a vacuum.
WarpPrime
CC BY-SA 4.0
2022-02-18T18:39:44.447Z
I disagree with the above comments. The question is perfectly and accurately answerable if one just reads it carefully enough (see my own answer below).
Thomas
CC BY-SA 4.0
2022-02-24T21:03:22.703Z
This is edging towards [worldbuilding.se] After all, there *isn't* a habitable planet that orbits Sirius at the same distance as B.  There are lots of variables you could tweek, but, fundamentally this is a question about a planet that doesn't exist.
James K
<star><planet>
What would the temperature be on the surface of Sirius B
Thomas Blobaum
# What would the temperature be on the surface of Sirius B

(Asked by: username_0 on 2022-02-15)

If Sirius B was a planet like Earth and not a white dwarf star what would the temperature be on the surface of Sirius B at its nearest and furthest distance? 8.2 AU to 31.5 AU

EDIT: I want to know if there is any combination of variables that would make Sirius B out to be the perfect distance for a habitable planet of certain specifications (and I'm not sure what those specs are).

**Tags:** star, planet
> **Comments:**
> **username_1**: What if my car was a Ferrari??? What are you proposing should set the temperature of your hypothetical Sirius B?  
> **username_2**: This is not answerable, as it written.  I think you mean "what would the temperature be on a planet that orbits an A0V, absolute magnitude 1.42 star at a distance of 8.2 AU. But consider Venus.  You can't predict the temperature on the surface of a planet unless you know something about its atmosphere, albedo, rotation, etc.  
> **username_3**: To make this an answerable question the specifics of the planet  would need to be better defined.  Even if we were to place Earth at that location I'm not sure we could make a vary good guess without some sort of climate model. Also, should this be a mean temperature?  Planets don't typically have a uniform temperature.  
> **username_4**: @JamesK Unless the OP provides more details, we'll have to resort to spherical, zero-albedo, temperature-distributed Earth in a vacuum.  
> **username_5**: I disagree with the above comments. The question is perfectly and accurately answerable if one just reads it carefully enough (see my own answer below).  
> **username_2**: This is edging towards [worldbuilding.se] After all, there *isn't* a habitable planet that orbits Sirius at the same distance as B.  There are lots of variables you could tweek, but, fundamentally this is a question about a planet that doesn't exist.  

---

## 1 answers

### Answer by username_5 on 2022-02-15. Score: 8 | Accepted answer

The [effective blackbody temperature](https://en.wikipedia.org/wiki/Effective_temperature#Blackbody_temperature) of a planet is given by the formula

$$T\_P=\left (\frac{L(1-a)}{16 \pi \sigma D^2} \right )^{1/4} $$

where $L$ is the luminosity of the star, $D$ the distance of the planet, $a$ its albedo (reflectivity) and $\sigma$ the Stefan-Boltzmann constant.

*(in principle one would have to use a [slightly more complicated formula](https://en.wikipedia.org/wiki/Effective_temperature#Surface_temperature_of_a_planet) that incorporates rotation and atmospheric effects for a real planet, but as the question here is for an Earth-like planet (and we know the actual temperature of the Earth) these factors effectively drop out and we can use the simpler formula instead, adjusting only the luminosity and distance to obtain the corresponding temperature).*

The luminosity $L$ of the star is given by the Stefan-Boltzmann law

$$L=4\pi R^2 \sigma T\_S^4$$

where $T\_S$ is the effective (black body) temperature of the star.

Now since $T\_S$ is about a factor $1.7$ higher for Sirius A compared to the Sun, and the radius is also a factor $1.7$ higher, this means that the luminosity $L$ of Sirius A is $24$ times higher than the Sun's luminosity. On the other hand, the distance $D$ to Sirius B is $8.2$-$31.5$ times that of the Earth's distance from the Sun. Inserted into the first equation, this means that an Earth like planet (same albedo $a$) would have a temperature $0.77$ timess that of the earth at the closest distance to Sirius A and $0.39$ times at the furthest point, which, taking the Earth's temperature as $300 K$, translates into $232 K$ and $118 K$ respectively

> **Comments:**
> **username_3**: That's a good way to provide a meaningful answer to a somewhat ambiguous question.  
> **username_0**: could you say Sirius B is in the habitable zone then? depending on the hypothetical atmosphere  
> **username_5**: @ThomasBlobaum Habitable zone is defined as the zone in which liquid water could exist. At the temperatures as calculated above (corresponding to about -40 C to -150 C) no liquid water could exist.  
> **username_0**: Is there a special kind of atmosphere that could exist that would raise the temp?  
> **username_5**: @ThomasBlobaum In theory, the maximum temperature would be achieved if all the incoming radiation is absorbed i,e, if the albedo $a=0$. With the earth's albedo about $1/3$, setting $a=0$ instead in the first equation above would only increase the temperature by about $10$%. So the maximum temperature  would still be about $255 K = -17C$, which would be still too cold for liquid water to exist.  
> **username_6**: @ThomasBlobaum You could raise the temperature using the greenhouse effect: letting stellar energy in through an atmosphere transparent in the visible, and trapping infrared energy emitted from the planet's surface in the atmosphere. Various things affect the strength of the greenhouse effect, like the absorbing efficiency of the atmospheric gases, the temperature profile in the atmosphere, and the total column density of atmosphere.  
> **username_7**: @Thomas The temperature of a planet's *surface* can be higher, because when an atmosphere is present, the planet's photosphere (the approximate region where most of the outgoing IR flux is emitted and where the temperature will be approximately what you compute) is not necessarily the same as the surface. This is the case for the Earth and (even more so) for Venus. A zero-albedo Venus (in the Solar System) would have an effective temperature of $\sim 330$ K; its actual surface temperature is about 740 K.  
> **username_5**: @PeterErwin Yes, you are right, I got my argument with the black body the wrong way around in my comment (now deleted) to giadia's comment. But the latter is not applicable here anyway as the OP's question clearly implies an Earth-like planet not a Venus-like one.  
> **username_0**: @Thomas it could be Earth-like or Venus-like. After reading your answer I'm just curious about any combination of variables and observation that could make Sirius B into a habitable planet with liquid water, etc.  
> **username_8**: @ThomasBlobaum There is no combination of variables that could do so, because Sirius B _isn't_ a planet, habitable or otherwise. It's a white dwarf with a surface temperature of approximately 25,200 K.  
> **username_5**: @notovny He was referring to a planet with the orbit of Sirius B  
> **username_5**: @ThomasBlobaum The problem is the high eccentricity of the orbit which results in a variation of the distance to Sirius A by a factor 4.  As you can see from the formula in my answer, this would result in a temperature variation of a factor 2 (in degrees Kelvin). This is a massive variation, making it impossible to be habitable over the whole orbit (and you can't just sit this out, as a year in this orbit lasts over 100 Earth years). It is practically impossible for any kind of life as we know it to develop in these conditions. You really need an orbit with small eccentricity to start with.  

---

