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After what feels like forever and after asking several questions (like this, this and this), I believe I may have decided upon a suitable orbital system for my world:


$M_{S}=2.272\;571\;144\;5 \times 10^{30} = 1.142\;857$ $\color{blue}{\underline{M_☉}}$
$M_{P}= 1.898\;2 \times 10^{27} = 1 $ $\color{blue}{\underline{M_J}}$
$M_{M}= 2.272\;686\;259\;599\;33 \times 10^{25} = 3.806\;844 $ $\color{blue}{\underline{M_⊕}}$
$D_P = 324,936,410.689\;212 $
$D_M = 14,596,597.842\;622\;8 $
$AD_S \approx 1929\; \mathrm{arcseconds} $
$AD_{P\,min} = 2374.8 \; \mathrm{arcseconds} $
$AD_{P\,max} = 2879.4 \; \mathrm{arcseconds} $

where $M_S$ is the mass of the sun in kilograms; $M_P$ is the mass of the planet my world orbits in kilograms; $M_M$ is the mass of my world (it's an Earth-like moon) in kilograms; $D_P$ is the average distance (semi-major axis) from the planet to the sun in kilometers; $D_M$ is the average distance from the moon to the planet in kilometers; $AD_S$ in the angular diameter of the sun (as viewed from the planet) in arcseconds; $AD_{P\,min}$ is the minimum angular diameter of the planet (as viewed from the moon) in arcseconds; $AD_{P\,max}$ is the maximum angular diameter of the planet (as viewed from the moon) in arcseconds;

One year in my world is defined at the amount of time it takes the Earth-like moon to orbit around the planet, which should be equal to about 360.3126455 real-life Earth days. The amount of time it takes for the planet to orbit around the sun is about 1093.734343 real-life Earth days.

I have calculated the radius of the planet's Hill Sphere in this system as 21217756.17 km, which allows my Earth-like moon to orbit at the desired orbital period and distance.


The problem

My main issue here is the sun. The distance from the planet to the sun is a little further than Mars is to our own sun. If I am not mistaken, under normal circumstances, this would place the planet outside of the habitable zone where life can form.

What kind of sun can have a mass of 1.142 solar masses and have a habitable zone 324,936,410 km away?

For bonus points, I'd like to have my sun have a similar angular diameter when viewed from the planet as our real-life sun, which is approximately 1929 arcseconds.


NOTE: I have re-read this question very carefully to ensure I only use the term 'planet' to refer to the body in direct orbit of the sun. Similarly, 'Earth-like moon' or just 'moon' is used to refer to the main setting of my world, which is actually a moon orbiting a larger Jupiter-like planet.


UPDATE: It might not be possible with these numbers

I'm looking for a habitable zone that is large enough to accommodate the distance between the planet and the moon. So the Earth-like moon should never leave the habitable zone.

How far from the sun can I place the planet, where there is a type of star that might be feasible for the majority of the requirements above?

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    $\begingroup$ It seems this is simply a question of solar irradiance. As stars age and consume fuel, their irradiance changes. So maybe it's more about how old your star needs to be? Also, is there room for a closely orbiting binary star system to get your higher irradiance, or does it absolutely have to be a single star? Our own sun will increase in diameter and burn hotter when it starts fusing helium in a couple billion years. $\endgroup$ – Vogon Poet Nov 14 '19 at 0:01
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For a star of that mass, you are looking at a G0V to F9V main sequence star. It's luminosity, depending on age, is probably around 1.2 sol, from which you can calculate the bounds of the habitable zone.

The inner edge of the zone is around 1.04 AU.

The comfortable outer limit is around 1.5 AU.

The maximum outer limit is around 1.86 AU.

Your planet's moon, at a distance of 2.17 AU, is uninhabitable for Earth-like conditions.

However, as stars age, they become more luminous. It is entirely possible that at some point before the star reaches the end of its main sequence lifespan, luminosity will be high enough for the maximum outer edge of the habitable zone to reach 2.17 AU.

Estimates of circumstellar habitable zone limits from Kasting et al. 1993, Kopparapu et al. 2013

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  • $\begingroup$ Ah crap, I thought the planet-moon distance was going to be negligible in terms of its affect on habitability. If I move the planet further from the sun (but keep the planet-moon distance), can I resolve this and choose a type of star accordingly? $\endgroup$ – overlord Nov 13 '19 at 20:26
  • $\begingroup$ @overlord-ReinstateMonica It's complicated. Due to insolation being subject to an inverse square law, the distance between the innermost and outermost points on the moon's orbit will mean less the further out the planet is. If it's close enough the be in the CHZ, the difference is much more major. My suggestion would be, develop the orbital parameters of your planet-moon system based on habitability factors and accept the visual factors that result. You are trying to force the visual factors at the expense of habitability/realism. $\endgroup$ – Arkenstein XII Nov 13 '19 at 20:32
  • $\begingroup$ My only true requirements are a habitable Earth-like moon that has an orbital period of around 360 days. All other numbers can be changed, but that one fact must remain constant. $\endgroup$ – overlord Nov 13 '19 at 20:36
  • $\begingroup$ @overlord-ReinstateMonica That can probably be done. Do you mind if I ask why you require a 360 day lunar orbit period? $\endgroup$ – Arkenstein XII Nov 13 '19 at 20:37
  • $\begingroup$ @overlord-ReinstateMonica The habitable zone will be increasingly wide with more luminous stars. However, you begin to run into the problem that more luminous stars emit horrible radiation and don't live long enough for complex life to evolve. How much of a problem is that? $\endgroup$ – Arkenstein XII Nov 13 '19 at 20:45
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Since you want your world to be a habitable giant moon of a gas giant planet in another star system, an exomoon, you should look up some of the many previous questions about moons of gas giant planets on this site.

for example, the most recent such question that I answered was this one:

If Earth Were a Gas Giant's Moon1

And you should look up this article discussing the potential habitability of exomoons:

"Exomoon Habitability Constrained by Illumination and Tidal heating" by Rene Heller and Roy Barnes Astrobiology, January 2013.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/2

If you use the search bar to search for "Habitable moons" you will find a list of questions like this one: https://worldbuilding.stackexchange.com/search?q=habitable+moons3

If you have the mass of your Sun (Ms) calculated for your solar system, and if it is a stable main sequence star that shines steadily and can have planets with life around it, then you can easily calculate the luminosity of your star, perhaps with help from someone with more astrophysical knowledge. A small change in the mass of a main sequence star will cause a much larger change in its luminosity.

Once the luminosity of your star is calculated you can compare its luminosity to that of the Sun. then you can multiply or divide the inner and outer limits of the Sun's habitable zone to find the inner and outer limits of your star's habitable zone.

Then it will be easy to see if your selected orbital distance between planet & moon and star (Dp) is within the habitable zone of your star.

Since your planet seems to be orbiting its star at a little over twice the distance between Earth and the Sun, the star will need to be a little over four times as luminous as the Sun for the planet to receive exactly enough heat from its star as Earth gets from the Sun.

Of course your habitable moon could be habitable with somewhat less heat from its star, especially if it has significant tidal heating from its planet.

The paper by Heller and Barnes, mentioned above, does mention the possibility that an exomoon could have too much tidal heating, like Io, so it should be possible in some cases for tidal heating of exomoons to contribute to making them warm enough for life.

This looks like a situation where someone should consult the Wikipedia article "Circumstellar Habitable Zone".

https://en.wikipedia.org/wiki/Circumstellar_habitable_zone4

Astronomers don't know the inner and outer limits of the Sun's circumstellar habitable zone. Instead they estimate and calculate as well as they can the distance limits within which Earth like planets or moons might have liquid surface water and thus be potentially habitable for life.

And this section:

https://en.wikipedia.org/wiki/Circumstellar_habitable_zone#Solar_System_estimates5

Has a table listing different estimates of the inner, or outer, or both, limits of the sun's habitable zone.

And you can see that those estimates are different in the sense that they were made by different scientists and also different in the sense that the inner and outer borders of the habitable zone vary widely between some of the estimates.

The estimate by Hart, et al, 1979, a commonly cited paper, gives a very narrow habitable zone.

The estimate by Kasting, et al, 1993, another very commonly cited paper, gives a much broader habitable zone.

The Innermost inner edge of the habitable zone was calculated by Zsom et al in 2013, and the outermost outer edge of the habitable zone was calculated by Pierrehumbert and Gaidos in 2011. Combined, those those two papers, if they are correct, would give a habitable zone tens of times wider than Kasting's, and hundreds of times wider than Hart's!

It would certainly be useful to know which calculations are more likely to be correct.

So you should make an effort to study the various original papers with their calculations through the links in the footnotes in the Wikipedia article.

Or maybe ask in astronomy and astrobiology sites which habitable zone limits seem most plausible.

Note that the temperature of a planet at a specific distance from its star will depend a lot on its atmospheric composition and density. Some of those calculations in the table may have been for planets with Earth like conditions where Earth animals could breathe the air and live, while other calculations seem to have included planets with more exotic atmospheres necessary to have Earth like temperatures at their distances, atmospheres which Earth land animals could not breathe. There may be a more narrow habitable zone for planets with breathable oxygen nitrogen atmospheres than for planets with more exotic atmospheres deadly to humans and similar lifeforms.

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  • $\begingroup$ So basically you think I should just do research. I tried that and couldn't find anything that helped me, hence the question. $\endgroup$ – overlord Nov 15 '19 at 20:56

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