Help with orbital mechanics for an unusual alien planet

[Bandersnatch]

Yeah, I'd say the "don't worry about it too much" approach is the best you can take. So what if there's going to be some Bad Stuff[TM] happening some few million/billion years in the future? Your story doesn't care.

The only thing I'd maybe(but not very strongly) suggest doing, is not to chose a satellite setup that's got a very regular orbit - that'd suggest a long history of tidal stabilisation. Make the orbit a bit eccentric, with the moon not always showing the same face to the planet, and it'll be perfectly plausible for a (geologically-speaking)recently captured satellite that never had much time to engage in tidal magic.


Seriously, why I also like to think about this stuff, I don't think I'd ever bother with that much detail as far as writing a book goes. Who's going to notice anyway?

 

[AotrsCommander]

Yeah, I'd say the "don't worry about it too much" approach is the best you can take. So what if there's going to be some Bad Stuff[TM] happening some few million/billion years in the future? Your story doesn't care.

Yes. But I think it was important for me to at least make the attempt to confirm that the results would be within a plausible ball-park.

The only thing I'd maybe(but not very strongly) suggest doing, is not to chose a satellite setup that's got a very regular orbit - that'd suggest a long history of tidal stabilisation. Make the orbit a bit eccentric, with the moon not always showing the same face to the planet, and it'll be perfectly plausible for a (geologically-speaking)recently captured satellite that never had much time to engage in tidal magic.

According to my calculations, the tidal forces on the Andorlaine moon are about seven times that of Earth's on the moon, so it's fairly possible that even it could be tide-locked already.

(My estimates from above (and assuming +2 milliseconds/century) suggest that the tidal effects on Andorlaine from the moon would extend the day length by only a couple of days (on what would be a really slow rotation) - so if the moon was captured two or three billions years ago, the acceleration would be small and it could be tide-locked.)

So I may or may not go with a tide-locked moon. I'll have to think about it: at this stage, plausible says either way, so I can go with "what will give me the most narratively interesting result."

Seriously, why I also like to think about this stuff, I don't think I'd ever bother with that much detail as far as writing a book goes. Who's going to notice anyway?

This is unfortunately a symptom of my "must Get It RIGHT" syndrome. (I blame my engineering upbringing.) I am always deeply against "magic did it" or the MST3K mantra (and anything other than a joke) or "it's just a story." I like to at least see the author has actaully thought about it. Granted, I am just a huge pendant. I reckon that a good 90% of my world-building for my campaing worlds goes unseen and unnoticed by my PCs... But it matters to me that it's right!

 

[AotrsCommander]

So, I had another think... It occurred to me that a rotating moon could be usefully used. If there is a large, dark feature (perhaps an impact crater or old volcanic activity) on the surface, we could the "the eye of the moon" which could have all sorts of interesting implications. (Also, it provides a get-out clause either way on the moon rotation, ebcause you could say it was either still rotating from the capture, or because of the impact.)

Further, if it's a fairly slow rotation, that could be used as the basis for the Andorlaine equivilent of "year" (I (somewhat arbitarily) 184 orbits (@ 6 earth-days) which gives you 1104 days = roughly three years).

Granted, I was considering something that a multiple of six (because I still want to use hours/minutes ("day") so that a) my players don't go too mad and b) I don't have to re-write too many rules!). (Then, you see, six becomes a number of importance (6 x 10 secons in a minute, 6 x 10 minutes in an hour, a sixth of a moon orbit is a day (itself 6 x 4 hours) and then 6 x [something] is a "year". (And 6 x 6 x 10 degrees in a circle...!)

But on the other hand, I try not to make things too neat, so I'm still thinking about that one.

180 (orbits to 1 rotation, so 1080 Earth-days to one rotation) would probably be the most significant number it could be without being too long, but like I say, I think that might be slightly too neat? What do you think? Would that seem to be pushing credibility a bit to have the rotational speed synch that neatly?

Still need to fix the density of the moon, though (while trying to keep the albedo pretty high - need to have a look and see if there's any other at not-ice moons with a fairly high albedo otherthan Luna.)



I've also had another look at global temperatures. I looked up a few analysis of what would happen to a tide-lcoked Earth (I found one or two) and the temperature ranges (which were not identical) where about 60-80 degress (K or ºC) between the hot and cold poles, with a bit of a bias towards the hot-side.

So I've revised my really, really ballpark figure of average temperatures to +20 over global average at the poles (as before, so about 40º C) to -40 at the cold pole (thus about -20ºC). There is a suggestion that the surface of the sea may not be frozen, due to convection (and or salinity). Not sure on that one.

 

[snorkack]

So, I had another think... It occurred to me that a rotating moon could be usefully used. If there is a large, dark feature (perhaps an impact crater or old volcanic activity) on the surface, we could the "the eye of the moon" which could have all sorts of interesting implications. (Also, it provides a get-out clause either way on the moon rotation, ebcause you could say it was either still rotating from the capture, or because of the impact.)

Further, if it's a fairly slow rotation, that could be used as the basis for the Andorlaine equivilent of "year" (I (somewhat arbitarily) 184 orbits (@ 6 earth-days) which gives you 1104 days = roughly three years).

Slow rotation is going to be problematic because of tidal torques. Moon, for example, has free libration period of 1056 days.

Still need to fix the density of the moon, though (while trying to keep the albedo pretty high - need to have a look and see if there's any other at not-ice moons with a fairly high albedo otherthan Luna.)

Vesta is rocky, and pretty bright. But also dense - slightly denser than Moon.

 

[AotrsCommander]

Slow rotation is going to be problematic because of tidal torques. Moon, for example, has free libration period of 1056 days.

Why is that a problem for slow rotation specifically (as opposed to fast rotatation or tide-lock)? Other than inducing some eccentricity to the length (but ones that most primitive civilisations are probably either not going to notice, or if they are appeciably skilled astronomers (like the Mayans or something), add in the odd leap-time-unit to keep their calendar synched to the moon like we do?

Vesta is rocky, and pretty bright. But also dense - slightly denser than Moon.

Still a bit low, really needs to be at least 0.3 to be as bright as luna from the surface (according to my apparent magnitude calculations spread sheet).

So, I think here we can cheat a bit, since there's really no way to get a high albedo without ice (and as Bandersnatch rightly pointed out, at those temperatures. it ain't happening) or an atmosphere; which opens a whole host of other problems I'm not sure I want to tackle! I'm having enough trying to work out what Andorlaine's wind patterns are going to be like, seeing as there is suggestions that it might have a Venus-like pattern and/or a huge hurricane on the substellar point...!)

So, we'll say that the surface has a particularly high concentration of magnesium (which may have been desposited from being dissolved in surface water/ water ice before the moon spiralled inwards got captured, and thus left behidn when the water photodissociated. As magnesium (well, magnesium oxide) has a high albedo (0.96 diffuse), I can say there's enough to raise the albedo to say, 0.4, especially there's also a high concentration of silver (as my very early thoughts had gone to) as well. We'll call the overall denisty 3650 (higher than Io), which puts the tidal acceleration at 98% of Luna. (Which, as we established, isn't going to significantly un-tide-lock the planet.)

 

[snorkack]

Why is that a problem for slow rotation specifically (as opposed to fast rotatation or tide-lock)? Other than inducing some eccentricity to the length (but ones that most primitive civilisations are probably either not going to notice, or if they are appeciably skilled astronomers (like the Mayans or something), add in the odd leap-time-unit to keep their calendar synched to the moon like we do?

Imagine a pendulum with a rigid stick, not string for suspension. Furthermore imagine that the fixed end of the stick is affixed so that it can perform a full circle.

As you increase the amplitude of the pendulum, its period does NOT stay constant. Its period increases - and can be increased to infinity.
But the period is large for a very narrow range of pendulum speeds at bottom.
As you increase the speed of pendulum at the bottom, there is a certain speed at which the pendulum comes to full stop exactly balanced at the top. But this is unstable balance. If the pendulum is very slightly slower, it comes to a full stop almost, but not quite, at the top, and slows down for a long time before eventually falling back. If the pendulum is very slightly faster, it almost stops, but does not quite stop, at the very top, passes through the top at a slow speed, then speeds up again on falling forward.

Thus, slow rotation is low probability activity for an unbalanced rotator in a tidal field.

Low probability, but one that can and must happen. You could have a previously freely but slowly rotating body become tidally locked with nearly 90 degree amplitude of free libration during the events of your story.

So, we'll say that the surface has a particularly high concentration of magnesium (which may have been desposited from being dissolved in surface water/ water ice before the moon spiralled inwards got captured, and thus left behidn when the water photodissociated. As magnesium (well, magnesium oxide) has a high albedo (0.96 diffuse), I can say there's enough to raise the albedo to say, 0.4, especially there's also a high concentration of silver (as my very early thoughts had gone to) as well. We'll call the overall denisty 3650 (higher than Io), which puts the tidal acceleration at 98% of Luna. (Which, as we established, isn't going to significantly un-tide-lock the planet.)

What would be the albedo of sodium chloride?

 

[AotrsCommander]

Imagine a pendulum with a rigid stick, not string for suspension. Furthermore imagine that the fixed end of the stick is affixed so that it can perform a full circle.

As you increase the amplitude of the pendulum, its period does NOT stay constant. Its period increases - and can be increased to infinity.
But the period is large for a very narrow range of pendulum speeds at bottom.
As you increase the speed of pendulum at the bottom, there is a certain speed at which the pendulum comes to full stop exactly balanced at the top. But this is unstable balance. If the pendulum is very slightly slower, it comes to a full stop almost, but not quite, at the top, and slows down for a long time before eventually falling back. If the pendulum is very slightly faster, it almost stops, but does not quite stop, at the very top, passes through the top at a slow speed, then speeds up again on falling forward.

Thus, slow rotation is low probability activity for an unbalanced rotator in a tidal field.

Low probability, but one that can and must happen. You could have a previously freely but slowly rotating body become tidally locked with nearly 90 degree amplitude of free libration during the events of your story.

Right.

One solution, is, course to assume the world had been tidelocked, but the impact that caused the eye of the moon was sufficient to make it rotate (and it is now in the process of slowing back down to tide-lock again.)

I did also look at scrubbing that idea for the "year-length" time, and looking at what sort of timeframe the distant binary companions stars would be. I plugged inb the values for Alpha Centauri (since I could a) estimate thedistances between them) and b) Proxima is very far away. I treated the orbital period as being from one body of the combined masses (good enough abstraction for a first order pass, I think) and at an orbital distance of "only" 3000 AU, the orbital period was 100000 years - and the apparent magtudes were about -8-10. (So don't want to get them much closer with making them a lot less luminous, or they'll be as bright as the moon! I also wanted to effective make the effect on the world fairly negliable; they still might be too "close!")

In any case, that was right out of the ball-park for something you might use to measure time.
Alternatively, then what might be the sort of order of magnitude of rotational speed you might expect? (If any?)

What would be the albedo of sodium chloride?

Dunno exactly. I can't find an exact figure. The one source I found (an excerpt from the Encyclopedia of Soil Science) suggested that "dry salt cover" has an albedo of 0.5, which is well within the bound for my purpose. That certainly wouldn't hurt the situation, would it?
Edit: Hang on, have I not made a fundamental error? The moon rotation period's got to be six days if it's tide-locked, hasn't it? Can you even HAVE a system where the day is longer than the year (or month, in this case?)

 

[snorkack]

(So don't want to get them much closer with making them a lot less luminous, or they'll be as bright as the moon! I also wanted to effective make the effect on the world fairly negliable; they still might be too "close!")

You do not want stars brighter than full Moon?

Sun is about 400 000 times brighter than full Moon, so it is as bright as full Moon at about 630 AU distance.

61 Cygni B is about 25 times dimmer than Sun, so it is as bright as full Moon at about 120 AU distance... which happens to be its apoapse distance (orbital period about 680 years).

Proxima Centauri is about 18 000 times dimmer than Sun, so it is as bright as full Moon at about 5 AU distance... which happens to be the distance of Jupiter from Sun.

The Toliman AB system combined is about twice as bright as Sun, so it would be as bright as full Moon at the distance of 900 AU. At that distance, a third star with its own mass of 1 solar would have an orbital period of about 15 000 years. From the 900 AU distance, at their maximum separation of 36 AU, Toliman A and B would be over 2 degrees from each other (over 4 times the width of Moon) and one being 3/4 the brightness of full Moon, the other 1/4 of that brightness, would be easy to separate by naked eye through almost or quite all orbit. Though dazzling, too.

Edit: Hang on, have I not made a fundamental error? The moon rotation period's got to be six days if it's tide-locked, hasn't it? Can you even HAVE a system where the day is longer than the year (or month, in this case?)

Day is longer than year on both Venus and Mercury.

 

[AotrsCommander]

You do not want stars brighter than full Moon?

Sun is about 400 000 times brighter than full Moon, so it is as bright as full Moon at about 630 AU distance.

61 Cygni B is about 25 times dimmer than Sun, so it is as bright as full Moon at about 120 AU distance... which happens to be its apoapse distance (orbital period about 680 years).

Proxima Centauri is about 18 000 times dimmer than Sun, so it is as bright as full Moon at about 5 AU distance... which happens to be the distance of Jupiter from Sun.

The Toliman AB system combined is about twice as bright as Sun, so it would be as bright as full Moon at the distance of 900 AU. At that distance, a third star with its own mass of 1 solar would have an orbital period of about 15 000 years. From the 900 AU distance, at their maximum separation of 36 AU, Toliman A and B would be over 2 degrees from each other (over 4 times the width of Moon) and one being 3/4 the brightness of full Moon, the other 1/4 of that brightness, would be easy to separate by naked eye through almost or quite all orbit. Though dazzling, too.

The idea of having a binary pair comes principally from the picture (on wiki) of an artist's impression of Gelise 667Cc, which looked so awesome I thought I had to have it on the world.

So what I'm aiming for with that was to have a couple of visible bright stars. But I don't want them too bright or close (as at a distance, you can assume the graviational and solar flux effects are not great). It's also hard to have a world of twilight when the sun dims if the light from the binary stars is too bright!

I started with Alpha Centuari as a first order analysis, since I had the stats for it, but Toliman AB, from that data might be a better bet.

(Or I could even make something up, given a reason few estimates of binary pair distances to give me the right "feel".)

In both cases, though, the orbital period is going to be beyond the useful range in terms of a civilisation's time keeping, so I think that can be pushed a touch lower prioroty.

Day is longer than year on both Venus and Mercury.

Right.

I did wonder, as my next starter for ten, whether to have rotational period of three days for the moon. If my logic is right, given the orbital period of the moon of six days, this would effectively mean that, from the perspective of the planet, the eye of the moon would be the same relative facing to the planet at the mid-point sun-side and night-side, so, from the day side it would appear to "open" and "close" (i.e. rotate into and out of sight), while on the night side, it would be effectively invisible. (Because it's turning at twice the rate it's orbiting.) Yes? (It also gives me "three" being a number of significance with regard to time-keeping, rather than six.)

 

[snorkack]

The idea of having a binary pair comes principally from the picture (on wiki) of an artist's impression of Gelise 667Cc, which looked so awesome I thought I had to have it on the world.

So what I'm aiming for with that was to have a couple of visible bright stars. But I don't want them too bright or close (as at a distance, you can assume the graviational and solar flux effects are not great). It's also hard to have a world of twilight when the sun dims if the light from the binary stars is too bright!

I started with Alpha Centuari as a first order analysis, since I had the stats for it, but Toliman AB, from that data might be a better bet.

Sorry. Toliman IS the proper name of that star. (All stars which have proper names also have Bayer designations).
So how bright CAN they be for the requirements of your twilight?

In both cases, though, the orbital period is going to be beyond the useful range in terms of a civilisation's time keeping, so I think that can be pushed a touch lower prioroty.

What is the orbital period you want for timekeeping?

Right.

I did wonder, as my next starter for ten, whether to have rotational period of three days for the moon. If my logic is right, given the orbital period of the moon of six days, this would effectively mean that, from the perspective of the planet, the eye of the moon would be the same relative facing to the planet at the mid-point sun-side and night-side, so, from the day side it would appear to "open" and "close" (i.e. rotate into and out of sight), while on the night side, it would be effectively invisible. (Because it's turning at twice the rate it's orbiting.) Yes? (It also gives me "three" being a number of significance with regard to time-keeping, rather than six.)

3 days relative to what? And in which direction?

 

[AotrsCommander]

Sorry. Toliman IS the proper name of that star. (All stars which have proper names also have Bayer designations).
So how bright CAN they be for the requirements of your twilight?

Well, I figure it ought to probably a modest bit less than the apparent brightness of the Andorlaine moon (currently at about -13, so brighter than Luna (part of that idea being that there is just enough moonlight that some extremeophile flora would live on the nightside.) So I'd eyeball probably not much more than, say -11 or something.

What is the orbital period you want for timekeeping?

The nominal plan was, if one could find something that would fit in as a timescale, something that would a be rough equivilent of a Earth-year. However, it seems unlikely we're going to plausibly gets something from either the moon or the binary stars (which in hindsight, I really should have realized was never going to be in the ballpark!)

One remaining possibility might be to have the neighbouring Gas Giant's orbit, but I'd have to look hard at the plausibility.

Otherwise, I guess it'll be an artificial grouping in multiples of the month (6 days).

3 days relative to what? And in which direction?

Andorlaine's nominal moon has a orbital period of 6 days, so if it has a rotational period of three days, it would rotate 360º for every 180º it orbits around the planet, yes? So if a fixed point (the eye of the moon) was directly facing the planet at the substellar point, on the opposite side of the planet, that point would be facing away from the nightside. (Same relative direction to sun, not the planet even. I know something was off with that sentence last post!)

 

[snorkack]

Well, I figure it ought to probably a modest bit less than the apparent brightness of the Andorlaine moon (currently at about -13, so brighter than Luna (part of that idea being that there is just enough moonlight that some extremeophile flora would live on the nightside.)

Wrong order of magnitude. Extremophile plants under shadow of forest and in deep sea endure 2...3 orders of magnitude less than full sunlight, not 5...6.

The nominal plan was, if one could find something that would fit in as a timescale, something that would a be rough equivilent of a Earth-year. However, it seems unlikely we're going to plausibly gets something from either the moon or the binary stars (which in hindsight, I really should have realized was never going to be in the ballpark!)

Andorlaine's nominal moon has a orbital period of 6 days, so if it has a rotational period of three days, it would rotate 360º for every 180º it orbits around the planet, yes? So if a fixed point (the eye of the moon) was directly facing the planet at the substellar point, on the opposite side of the planet, that point would be facing away from the nightside. (Same relative direction to sun, not the planet even. I know something was off with that sentence last post!)

It would rotate 360 degrees relative to Sun, yes. But note that the moon is not visible only briefly at midnight - it is visible for the whole night and rotates through appreciable angle.

Also, in these 180 degrees orbit, how much does it rotate relative to planet? 180 degrees, or 540?

 

[AotrsCommander]

Wrong order of magnitude. Extremophile plants under shadow of forest and in deep sea endure 2...3 orders of magnitude less than full sunlight, not 5...6.

That WAS an area I was considering bovine excrementing a little bit. (Though I haven't actually got as far as serious examination of flora yet.)

It would rotate 360 degrees relative to Sun, yes. But note that the moon is not visible only briefly at midnight - it is visible for the whole night and rotates through appreciable angle.

Also, in these 180 degrees orbit, how much does it rotate relative to planet? 180 degrees, or 540?

I think it's easier for me to show, not tell!

(See attachment.)

Something like that? So when the moon completes a 360º orbit of the planet, it has completed a 720º rotation of itself.
On the subject of plants and whatnot, I ahd a read around to see what I could find out. From what I can gather (as the work here suggests it's back to beyond what I can work out myself!) R Coronae Borealis (the basis for Andorlaine's star) is a G0 supergiant. So the light reaching it is going to be not that far of Sol's, but because it's hotter (hotter than a main sequence), the light it going to be a bit more towards the blue range and less towards the red, yes? (As the investigation suggested that F-types - which a G0 is are pretty close to - would get much moe blue light.)

So, extrapolating, the planet's foilage is going to likely use slightly more blue energy ('cos it's there) and red will be less abdundant). So the photosynthetic colour might be more towards brighter green, yellow or orange (depending how much red or green light it absorbs). Possibly with an adjustment to much darker colours towards the terminator (and a bit beyond where there's backscatter, where you would assume the plants would be nearly black.

Would it be reasonable to postulate as well, that the dense cloud cover (i.e, near the substellar point with the continuous hurricanes) mean that (like seawater) less red light would penetrate through (because the deeper you go, the bluer things get) - assuming thick cloud would absorb light in a similar manner but vastly less magnitude than water, so plants nearer the substellar point would more likely to be red, since red would be lesser use? (Or have I got that backwards, in which case the plants would be bluer...?)
Edit: I actually found a formula on wiki for calculating illuminance from apparent magntiude. The Andorlaine moon puts out about 0.41 Lux (compared to Luna's 0.26 via calculation, which is about right if a very slight touch on the low side (max of 1 from other sources), so the Andorliane moon is indeed getting on for twice as bright.

Most interestinly, I ran it for the Andorlaine sun. It's about as bright as Sol normally, but if it dims by 8 magnitude (which is what RCB does) the lux goes from ≈110000 (more or less the same as Sol) down to 69! That's a pretty huge drop in brightness!

(Fortunately, among the bending due to poorly understood phenomina the IR band is not affected!) So actually, the dimming does make a big difference.

That points me to the other interesting point though. The plants - having been adapted to this - probably would have a photosynthic substance for doing long wavelength, which they might well synthesise as the light levels drop, meaning that when the sun goes dim, the plants all start changing colour (probably going quite black for the extra absorbtion), as well as there being a sort of migration (since the dimming period I've said or decades to centuries) where their range would change a bit. Possibly the growth rate might drop as well.

All of which would be terrifiying to a primitive society who had no idea what was going on. (Or even a quite advanced one. My premise is that even 21st century civilisation would have problems with that kind of change.)

 

[AotrsCommander]

I had a bit of a play with trying to get a gas giant (for orbital resonace, as suggested back on the first page).

At the moment, I have opted for a 2:3 orbital resonance (Andorlaine orbits to gas giant orbits), which puts a Jovian-sized gas giant in at about ≈ 80 AU (Andorlaine is ≈ 104).

Given the length of the orbital periods, I figured that sort of resonace (given that orbital responace cen mean a lot of things) would be good enough to say it causes some periodic irregularities on Andorlaine resulting in tectonics.

Reasonable?



I'm working on the basis that Andorlaine is probably one of the furthest planets out in the system, but has a fairly low eccentricity orbot on account of it's low initial momentum (which is what caused it to be tide-locked at a long distance).

I figure that I should maybe say there are a mid-teen amount of planets (say 14 or 15), plus other solar objects of dwarf planet or smaller that aren't that important. I reckon that could be spread out enough to fill out the gap between the sun and Andorlaine without being too crowded or too sparse.



I am also toying with the idea of whoever does the (in-character) system survey¹ has detected what they think might be some sort of body at or within the edge of the sun's corona. (With a radius of 96 sol and only 0.8 Sol mass - according to R Coronae Borealis' current estimated stats - I imagine that the density there would be quite nebulous. If SCORCHINGLY hot!) The body might be, the surveyors theorise, a planet composed of some exotic material or perhaps some articifical body left by some other stellar power in the ancient past - in either case, perhaps explaining the reason for Andorlaine's sun's unusual longevity in its super-giant form and odd burn-cycle. One should always leave a few tantalising mysteries, after all! (Especially if it means they can plaster over the bits you really can't work out.)



¹I always write my fluff material from the perspective of historian from some unspecified point in the future. Writing "in-character" in this way affords one to be able to explain to the reader in a useful way. It also, of course, gives some authorial bias, which means that as it is not written in stone, it means that not everything may be right, nor everything is completely explained. (There should always be some unsolved mysteries.) You can blame this ENTIRELY on Stewart Cowley and Spacecraft 2000-2100AD, which work is probably the single largest influence in my life.

Thus, this survey would be from a distance, so will contain things like "this phenomina is unexplained, but it it theorized that x or y", covering the bits where I lack completely concrete answers (such as the functon of the RCB star) - meaning of course, as when or if I find new data that changes the way things should be I can alway point out that those people were wrong...! I don't mind areas where you have to suspend disbelief a bit, but they should always be placed as in obtrusively as possible, and buried next to plenty of geniunely plausible stuff.

 

[AotrsCommander]

I ran out of free time over the last few months, between holidays and family problems... But I now have a surfiet of extra thinking time free again, so I am starting to look back at this again and work towards actually thinking about the fauna in more detail.

Problem, though, one gentleman pointed out on my primary forum: stellar wind.

Not something that I think has been brought up by this thread... So the question is; how much and how doe sthe planet deal with it? We are at 104 AU out, so there's that... But Andorlaine's start is very luminous and does shed all that material in dust cloud that dims it, so that might also mean the stellar wind is quite high. I have no idea! (Not have I seen an obvious way to calculate/estimate it!)

So the question is how much, and how would the planet combat it: the magnetosphere is one, but obviously without a significant rotation, that could take some doing. (Maybe something to do with the moon...?)

Thought would be welcome!