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I'm creating a D&D campaign which takes place on a Mercury-sized planet, orbiting a Proxima-Centauri style red dwarf. It is tidally locked.

I would like it to make physical sense as much as possible, and only use magic or hand-waving if there is absolutely no alternative.

I would also like the sun to appear to be absolutely massive in the sky. At least 10 degrees in angular diameter, 20 if possible. This would correspond to the orbital radius of the planet to be between 5 and 11 solar radii, which is insanely small (earth's orbit is approximately 230 solar radii for comparison).

The problem is, it appears to me that it's absolutely impossible for a star to have a habitable zone this close to it. If the star is cold enough that liquid water can exist that close to it, it will be too cold to radiate in the visible. This can be fudged with a high albedo, but the trade-off there is that you won't be able to see the sun if the albedo is high enough to be in its habitable zone.

The thing is, we always model stars as blackbodies, but what would it look like if a star had a very low emissivity? This way, it could be hot enough to radiate in the visible, but its habitable zone could be extremely close. Would there be a conceivable reason/mechanism for such a thing, and would it be physically possible?

(The other concern I've glossed over here is the Roche limit, but I'm happy to say that I did the math and it's not a problem. For a star with the mass and radius of Proxima Centauri, and a very dense planet orbiting it -- sufficiently dense to be very small but have Earthlike surface gravity -- the Roche limit is only 4 solar radii)

EDIT: Oh boy, I just realized a big problem I hadn't considered, and that's that at these distances, at the surface of the planet, the gravitational force towards the planet would be LESS than the gravitational force towards the sun. I'm going to have to do some soul-searching here.

EDIT 2: Wow, thanks for all the feedback! This has metastasized to the spreadsheet stage, where I'm calculating whatever I can for red dwarfs, brown dwarfs, red giants, even white dwarfs and neutron stars (both complete nonstarters).

Yet another problem I hadn't considered until today was the actual luminance, i.e., how visibly bright the sun would appear, as opposed to the total energy the sun would be heating the planet up with. Putting all of these factors together - gravitation, heat, and luminance, makes it pretty tricky to find a solution to all of these, if I want the planet to be 5 solar radii from the sun.

Orbiting close enough for to a red dwarf, you'd be pulled towards the sun with 2.5 Gs. It would be about as bright as the Sun, but it would be receiving 340 times as much energy total.

With a brown dwarf, it would only be 0.4 Gs pulling you towards the sun, which you could deal with, and even jump twice as high as you could here, but it would be a significant game mechanic I don't want. Furthermore, it's only 5% as bright as the Sun, but it would still be 75 times as hot.

A red giant like Aldebaran would be MUCH better with respect to gravity - it has almost no effect there. And it's also visibly as bright as the sun. But it's still 350 times as hot.

So there's not really an existing star on which this would make sense. I'll take some time playing with numbers to see if I can find a temperature, mass, and radius that does let me do what I want and decide if that makes sense. Otherwise, I'll probably just fudge it with an atmosphere that's VERY reflective in all frequencies except for the visible. Or just magic, that's always cool.

EDIT 3: In response to @pluckedkiwi's comment, I'll use one specific example, in which my planet is orbiting around a red dwarf. The planet has a radius of 2500 km, and a mass m of about 10^24 kg. The red dwarf has a mass M of 10^30 kg, and the planet is in a circular orbit with a semimajor axis a of 700,000 km.

My conjecture: Orbital mechanics don't matter very much close to the surface of the planet, as you can predict what will happen to within a degree of error by using a rotating coordinate system. On the surface of this planet, you appear to be in a Cartesian coordinate system with the sun directly overhead. Plugging the numbers above into Newton's laws, your acceleration towards the planet's surface is 10.67 m/s/s. Your upwards acceleration, towards the sun, is 136/m/s/s. So you'll be falling upwards at a rate of 126 m/s/s.

Once you get more than a few hundred kilometers up, that very small and dense planet will be far enough away that that coordinate system doesn't hold up very well, and you'll model your movement as a keplerian orbit around the sun. From that perspective you'll be in a similar, but perturbed, orbit as that of the planet. You still have basically the same amount of tangential velocity/angular momentum as you did before, so you won't fall into the sun, but the planet's surface won't be pulling you downwards sufficiently to keep you on it. So the real way to look at it is you and the planet are in your own orbits around the sun. You're both falling into it at the same speed, but you won't feel much of an attraction to the planet at all. I think?

This is in contrast to where we are now, at 1 AU from the sun. The difference is much greater here, where the sun pulls us towards it with an acceleration of about 6 millimeters per second squared. If we were just two solar radii from it like in the scenario I describe here, that acceleration would be closer to 70 m/s/s. Our intuition breaks down because we're so much closer to the sun. It just looks like there isn't really a possible way to be this close to any sun relative to its radius, without your mechanics just completely breaking down on the planet's surface, unless the sun is very, very not dense, as in the case of a red giant.

Of course there's a lot of speculation in this and it's entirely possible I haven't thought it through enough.

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    $\begingroup$ Welcome To Worldbuilding, FrankHarris, two suggestions. You might consider replacing the star with a brown dwarf. This will lower the mass of your primary star. Another solution to the gravity problem is give the planet rotation. Everybody will need to keep moving to stop falling upwards. They stay in the dark & it adds an extra frisson of danger. Powered flight would be easier on the dayside, but aircraft will have to work hard not to fly too high. Good to see you've worked out some of the problems with your world already. Have fun! $\endgroup$ – a4android Nov 22 '19 at 0:42
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    $\begingroup$ Have you considered a red giant instead of a red dwarf? You'd have to crunch the numbers to be sure, but they're pretty huge, so it'll probably take up a lot of the sky when viewed from the habitable zone. $\endgroup$ – Arkenstein XII Nov 22 '19 at 1:06
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    $\begingroup$ Orbital mechanics is certainly not my area of expertise, but I wouldn't worry about the gravity of the star on an individual. Presumably the planet is in orbit around the star, as would be the people on it. I'm having difficulty conceptualizing a jump being sufficient power to alter their own orbit around the star that the pull of the planet is overcome from that single impulse. Being that orbiting is already "falling into the star", they shouldn't worry about jumping too high unless you are proposing some kind of fixed cosmology where the star and planet are magically fixed in place. $\endgroup$ – pluckedkiwi Nov 25 '19 at 17:43
  • $\begingroup$ @ArkensteinXII I've basically gone with that route. The way I've been thinking about it is, the chunk of the sky taken up by the sun is a factor of your distance from it, in units of solar radii. For instance, if you're 2 solar radii from the sun, it will have an angular diameter of about 20 degrees, big enough that you can't cover it with both hands at arms length. $\endgroup$ – Frank Harris Nov 26 '19 at 18:16
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Instead of a red dwarf, use a brown dwarf.

Brown dwarfs can be nearly the size of a red dwarf but because they are no longer doing hydrogen fusion and just slowly cooling down, you can make them arbitrarily less hot and of lower emissivity. Really old ones might not glow much at all.

Your world would be something like a Jovian moon, if Jupiter glowed.

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  • $\begingroup$ Brown dwarfs don't have high enough mass to ever have sustained hydrogen-to-helium fusion, but the lighter ones (13+ Jupiter masses) are believed to fuse deuterium, and the heavier ones (65+ Jupiter masses) are believed to also fuse lithium). Not that this changes the validity of your answer. :-) $\endgroup$ – Klaus Æ. Mogensen Nov 22 '19 at 9:13
  • $\begingroup$ There may be a problem with habitability, according to Wikipedia: "Habitability for hypothetical planets orbiting brown dwarfs has been studied. Computer models suggesting conditions for these bodies to have habitable planets are very stringent, the habitable zone being narrow and decreasing with time, due to the cooling of the brown dwarf. The orbits there would have to be of extremely low eccentricity (of the order of 10^−6) to avoid strong tidal forces that would trigger a greenhouse effect on the planets, rendering them uninhabitable." $\endgroup$ – Klaus Æ. Mogensen Nov 22 '19 at 9:16
  • $\begingroup$ @KlausÆ.Mogensen - do you have any idea how orbital characteristics could produce a greenhouse effect? I am at a loss. $\endgroup$ – Willk Nov 22 '19 at 13:15
  • $\begingroup$ An elliptic orbit that close will heat the planet because of tidal forces. The planet will stretch and contract a bit with every orbit (which may only be a few hours), and this leads to heating. I assume that is what could lead to a greenhouse effect. $\endgroup$ – Klaus Æ. Mogensen Nov 22 '19 at 14:31
  • $\begingroup$ Brown dwarfs definitely have their appeal. The problem is they're just too dark for their heat. If I were to make a brown dwarf with an emissivity of 0.2 and a temperature of 2600 K, at 5 solar radii from the star, you'd be receiving fifteen times as much energy as the sun provides, but only 1% the visible light (candelas per meter squared). Being outside would be the equivalent of sitting in a dark room in front of a brightly lit monitor. $\endgroup$ – Frank Harris Nov 22 '19 at 20:42
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If I have this right, what you want is the effect of a large body looming over the visible side, and perpetual daylight.

You could have your world be a moon of a large gas giant, tidally locked in L1 position between the planet and its star. The "Sun" in the sky would then actually be the gas giant.

Given a high enough albedo for the latter, and some magic to stabilize L1 for geological periods, it could be doable and would also solve your gravitation problem.

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    $\begingroup$ The L1 position would put the 'moon' planet too far from the gas giant to achieve the desired visible size of the 'sun'. The L1 point between Earth and the Sun is about 1 million miles from the Earth. The Earth seen from this point would be little larger than the Moon in the sky. Since your gas giant is bigger, than Earth, the L1 point would be farther from it (unless the sun is far bigger than our or much closer to the planet; both of which has issues). $\endgroup$ – Klaus Æ. Mogensen Nov 22 '19 at 9:25
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If the point is to have a large body looming in the sky all the time, you might want to use a moon orbiting a gas giant, as LSemi suggests, but not in the L1 point between the sun and the gas giant, since that would put the moon-planet too far from the gas giant to achieve the desired visual size.

Put your moon-planet in a fairly close orbit to a gas giant a bit outside the habitable zone of the sun, tidally locked so that one face always faces the gas giant. Your moon-planet will receive additional heat from radiation from the gas giant as well as reflected sunlight when it is day on the gas giant, so it is possible to place the gas giant somewhat outside the habitable zone.

The sun will be visible at day, but the gas giant will eclipse it during midday. This will be the only time you can see stars, since it is night on the gas giant when it is day on the moon-planet, and vice versa. In fact, the terminator (day-night boundary) on the gas giant will work as a giant clock for people on the moon-planet.

The side of the moon-planet facing away from the gas giant will be colder, since it doesn't receive the benefit of reflected light and radiation from the gas giant. However, you would want a fairly thick atmosphere to shield from radiation (which also helps keeps the moon-planet warm), which will distribute the planetary heat better than on Earth. A thicker atmosphere will make airships and flying creatures/craft more efficient than on Earth, e.g. making huge dragons more realistic.

For dramatic effect, give your gas giant a ring like Saturn, perhaps slanted to make it more visible.

This isn't exactly what you are asking for, but might fulfill your purpose, while adding some cool details, like a short, deep night in the middle of every day and a ring around the huge gas giant in the sky - which might also have cool weather patterns like Jupiter, clearly visible at nighttime when the surface of the gas giant is lit.

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    $\begingroup$ Thanks Klaus. The problem is, it's pretty crucial that it be locked to the sun and not a planet; that's more important than the Sun's size, really. Both hemispheres of the planet are supposed to be inhospitable due to extreme temperatures. Really good thought though! $\endgroup$ – Frank Harris Nov 22 '19 at 21:12
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Have you considered artificial stars?

There are several ways to crate an artifical star whose parameters you can tweak with great precision. The YouTube channel SFIA made a video on Making Suns a while back. While these solutions require some really extreme engeneering, they get you around gravitational, thermal and tidal issues. From sane to wacky my suggestions are fusion planet, penrose, stellar flashlight, penrose star and a kugelblitz. Let's take a look at each of them

  • fusion planet Build a planet of deuterium and helium-3 under 13 jupiter-masses (to prevent deuterium fusing with itself). Use orbital rings to build a mega-earth around it, place fusion reactors on the inside of the shell and whatever you consider practical for illumination purposes on the surface. This surface can be much bigger than the planet (fuel source) itself.

  • fusion flashlight Basically a fusion plant, but we just illuminate the planet. Since we go for a much more elaborate illusion, we can cut down on the brute force. Maybe a slightly bigger "planet" which your planet orbits like a double planet would be sufficient.

  • penrose star This one is similar to the first two with respect to the external structure, but insted of fusion, we dump hydrogen into a black hole and produce energy via the Penrose Process. This video is about the colonisation of black holes and might be of interest.

  • Kugelblitz The Kugelblitz is another way of using a black hole to harvest energy. It is a very small black hole which evaporates within a few billion years. It gives of Hawking Radiation which you can absorb and use to generate the light you need.

Additionaly keep in mind that you don't really need a tidally locked planet, one whose rotation has been matched to its orbital period by other means will get you the same results.

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  • $\begingroup$ I had not considered artificial stars! The extreme engineering part of it could actually be fine because magic. I was playing with the idea that the planet would have been magicked into its current state, from a previously normal orbit with days and seasons. But just creating one from scratch has some interesting applications too. I'll definitely be considering this concept moving forward. Thanks! $\endgroup$ – Frank Harris Nov 24 '19 at 20:00

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