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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).

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    $\begingroup$ What if my car was a Ferrari??? What are you proposing should set the temperature of your hypothetical Sirius B? $\endgroup$ Feb 15, 2022 at 18:53
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    $\begingroup$ 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. $\endgroup$
    – James K
    Feb 15, 2022 at 21:38
  • $\begingroup$ 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. $\endgroup$ Feb 16, 2022 at 1:19
  • $\begingroup$ @JamesK Unless the OP provides more details, we'll have to resort to spherical, zero-albedo, temperature-distributed Earth in a vacuum. $\endgroup$
    – WarpPrime
    Feb 16, 2022 at 13:46
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    $\begingroup$ This is edging towards Worldbuilding 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. $\endgroup$
    – James K
    Feb 24, 2022 at 21:03

1 Answer 1

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The effective 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 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

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  • $\begingroup$ That's a good way to provide a meaningful answer to a somewhat ambiguous question. $\endgroup$ Feb 16, 2022 at 1:30
  • $\begingroup$ could you say Sirius B is in the habitable zone then? depending on the hypothetical atmosphere $\endgroup$ Feb 16, 2022 at 1:39
  • $\begingroup$ @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. $\endgroup$
    – Thomas
    Feb 16, 2022 at 8:27
  • $\begingroup$ Is there a special kind of atmosphere that could exist that would raise the temp? $\endgroup$ Feb 16, 2022 at 16:37
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    $\begingroup$ @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. $\endgroup$
    – giardia
    Feb 18, 2022 at 4:36

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