An orbital mechanics question inspired by SyFy's The Expanse

Factual Questions
1

Mild Season 2 spoiler ahead:

In the TV series The Expanse, there exists an agricultural colony on the moon Ganymede. The colony consists of, among other things, large domes with plants growing within. A large mirror is placed above the domes to collect the meager sunlight available and direct it to the agricultural domes, allowing the plants to grow.

In Season 2, a space battle occurs above the Ganymede Station. In the mayhem, the mirror is destroyed. Large parts of the mirror fall onto the surface of the moon, damaging people and infrastructure. Chaos ensues.

So, now my question. The mirror has to stay in a fixed position above the station so as to provide reliable sunlight. Therefore, it must be in some sort of a sync orbit. Here on Earth, these geosynchronous orbits are quite far from the surface of the Earth. Of course, a similar orbit for Ganymede would be less far since Ganymede has less gravity. So, when the mirror is destroyed in the battle, wouldn’t the parts simply remain in the orbit where they began? I suppose a not-insignificant amount of the mirror’s mass could be propelled to the surface by the explosion or collision that led to the mirror’s destruction. In the TV show, it is repeatedly mentioned that the mirror fell. It seems to me that the real result of the mirror’s loss would be a whole lot of debris in the orbit that used to contain the mirror, some small part being pushed toward the moon, and another part being pushed to other orbits or out of Ganymede’s influence altogether.

This program (and book) goes to great lengths to present realistic physics. Did they get this one right?

2

Was any momentum transferred to the mirror when it was destroyed?

3

Regarding the highlighted premise, you might think so, but you’re overlooking an important factor.

The rotational period of the primary (Earth in geosynchronous, Ganymede in ganymeosynchronous*) controls the orbital period of the satellite.

Ganymede’s rotational period is 7 days, 9 hours. That’s a hella slow orbit, and if it were practical at all it would be stupendously huge.

*I just made this word up. I don’t know the proper adjectival prefix for the minor moons of the solar system. Fight my ignorance if you know!

4

I don’t think they got this one right. Even if the pieces were nudged towards the planet by impacts or explosions, I think they’d just go into a different orbit. If the nudge was big enough, eventually they’d fall to the surface, but it’d be very unlikely to be at the same spot that the geosyncronous orbit was above, if my of orbital mechanics is correct.

5

Spitballing here, but I don’t think the mirrors could be in true geosync orbit around Ganymede. It has a rotational period of over 7 days, so the orbital position would have to be a decent distance from the planet. I also suspect the gravitational forces from Jupiter would interfere. The moon is tidally locked with Jupiter, so unless the ag dome was on the side facing Jupiter (which I don’t think was the case), the mirrors would have both Ganymede and Jupiter pulling in the same direction.

So assuming I’m right about that, the mirrors must be kept in position with constant thrust. And when the mirror structure is destroyed, it will indeed fall.

6

Ganymede is tidally locked to Jupiter, so the geostationary points would be either the L1 or L2 libration points. However, at just over 1x10[SUP]6[/SUP] km from Jupiter and close enough to be in a coupled resonance with Io and Europa, I don’t think it would be possible to maintain a stable orbit for any significant period of time without regular orbital maintenance. It might be possible to do this with magnetic propulsion stationkeeping, especially since Ganymede has its own magnetic field, but it seems more likely that it uses some version of The Expanse universes’ inexplicably efficient Epstein Drive (according to some source of unknown canonicity, the drive has a specific impulse of 1.1x10[SUP]6[/SUP] s) to maintain position. Even at that, at the orbit of Jupiter the Sun’s irradiance is only 3%–4% of that at Earth, so a mirror structure would have to be gigantic to collect and concentrate enough light for even a relatively modest farm. It would probably be more feasible to have a solar collector network somewhere inside of the orbit of Jupiter and beam power to Ganymede station to convert into UV for hydroponics than to collect and shine sunlight directly through a transparent dome.

Stranger

7

:smack: Of course. It’s the period that matters, not the mass of the planet (or moon).

So, if you wanted to put a mirror above an agricultural outpost on Ganymede, how would you do it? Constant thrust seems like it would consume a huge amount of energy. Of course, the device is collecting sunlight. Perhaps it can retain some of that sunlight for use in keeping itself aloft.

Would you even need your mirror aloft at all? Why not just build your mirror on the surface of Ganymede? If I understand it correctly, the purpose of the mirror is to collect (dim) sunlight from a large area and focus it into something more analogous to Earthly sunlight and direct it toward the plants you want to grow. So, put a big mirror on a tower above your greenhouse and you’re good to go. Or, even better, install a bunch of small mirrors.

8

Is the sunlight reflected from Jupiter itself any use?

9

FWIW, I think I computed the “hours” portion of the rotational period; the correct answer seems to be 7 days and 3 hours (per Wikipedia).

Also, I tracked down an orbital mechanics calculator that would allow me to plug in the primary’s mass and the orbital period needed, and it looks like a synchronous orbit would require a height of 45,742 km. That’s pretty dang high, all right; that’s 4% of its own periapsis with Jupiter and nearly double Earth’s.

Was the mirror satellite portrayed as a solid mass? If I were engineering a space solar collection mirror, I’d use superthin reflective film. Damage would just punch holes in it, except for the more substantial bits to hold the film taut, provide stationkeeping, control cabin, etc. I wouldn’t think that would be catastrophic if it crashed to Ganymede.

10

Actually, it’s only slightly more than Earth’s at 42,303 km. That’s from center of mass of course.

11

A mirror would have to have an enormous collecting surface; for every hectare of growing area, you’d need 25 to 30 hectares of Sun-facing surface aspect not accounting for any other loses. A ground-mounted mirror could only have an aspect facing the Sun consistent with how much it could articulate, and of course a ground-based mirror cannot capture light over the horizon so for half the orbital period of ~7 days it would collect no light at all.

Jupiter has a Bond albedo of 0.343. I’m not sure what the albedo is in the UV and near-UV range but I expect that the gaseous atmosphere tends to absorb the UV wavelengths, so I would assume that reflected light from Jupiter is less than 1% of solar irradiance at Earth orbit. And of course, Ganymede would only see reflected sunlight half the time, and only at the angle of incidence to Jupiter. In short, a ground-mounted mirror array would be almost completely worthless for illuminating any significant growing area.

Because of tidal effects and the need for stationkeeping and orientation, there would need to be some kind of thrust structure which would be substantial. And objects falling from a quasi-orbit are going to have at least a couple thousand meters per second of speed with no attentuation due to the non-existent atmospheric drag, so even relatively lightweight structure is capable of doing damage comparable to a hypervelocity rifle bullet.

Stranger

12

Inexplicably, I’ll say. The theoretical maximum specific impulse using a photon rocket is only 30,000s or so.

Dennis

13

Would a mirror array at L4 or L5 work? Are those points less stable due to the influence of the other moons? (Leaving aside the fact that an attack on a mirror at L4 or L5 would probably not result in much debris landing on Ganymede.)

14

The L4 and L5 points are the same distance from Ganymede as Jupiter: about 1 million km.

15

It goes to great lengths to present realistic physics when it can, and flat out ignores it for the many, many situations where realistic physics prevents telling interesting sci-fi.

16

The L4/L5 points at 60° ahead and behind Ganymede in its orbit, are points of stable equilibrium about which objects can orbit, provided they aren’t being perturbed by another body. However, the proximity of the other Galilean moons, which are sufficient to pull Ganymede into a resonance orbit, would certainly perturb a kilometers-long solar array and certainly put large fluctuating stresses on it.

Which is really true of pretty much any space-based science fiction. It just isn’t possible within existing physics, medicine, and propulsion technology to travel quickly to other planets or engage in exciting space battles. Even stories like The Martian, which is pretty firmly rooted in a plausible extrapolation of near-term technology, has to take a number of liberties with fact to make an exciting story and still permit the protagonist to survive. The Expanse’s “Epstein Drive” is a literary conceit without any real-world basis but necessary to make travel and colonization of the asteroid belt physically and economically plausible. Ditto for drugs that almost instantaneously repair damage from exposure to massive amounts of radiation, compact power sources that permit large habitable ships without massive radiating surfaces to eliminate waste heat, and indefinite exposure to freefall conditions without the attendant physiological degradation we know does occur.

When humanity does develop the capability to support a sustained crewed presence in space, the technology will look about as much like our present imagination of it as a modern computing cluster looks like a steam-powered mechanical difference engine. And instead of running around in jumpsuits with funny haircuts and magnetic boots, people will probably look different, too, in order to adapt to the conditions and hazards of a non-terrestrial environment.

Stranger

17

Bear in mind that , at 60 degrees away in the orbit, these two points are a LOT farther away. They’re as far from Ganymede as it is from Jupiter. So they’d have to be an awful lot bigger.

I agree that gravitational perturbations from the other moons would probably mess up the stability. You could maybe overcome that with active measures, but the depth of that well of stability of the L4 and L5 points is pretty shallow. things at such Trojan Points tend to follow kidney bean-shaped orbits. In regards to the OP’s question, if the mirror were destroyed, the parts wouldn’t necessarily remain there – they’d very likely overcome their very slight potential well wall and wander. (And getting trapped at these points isn’t all that easy, either. Objects headed towards them would more likely have their path affected, but wouldn’t be trapped. You’d need just the right combination of velocity and direction. I suspect the number of objects trapped at such points through the solar system is more a sign of how much space debris there is, than to the awesome trapping power of the Trojan points. When a gravity well pulls you into a planet or moon, you tend to hit something and stay there. But the only thing to hit at a Trojan point is the other trapped debris. You’re more likely to pass through or to skip out, like a penny pitched into a dish in one of those carnival booths.)

18

So, Ganymede is a bust. The other Jovian moons probably are not good, either.

So, you’ve got a couple million colonists in the Asteroid Belt. Water is coming from ice found in the Belt. You need to feed the colonists. For logistical and political reasons, depending on food from Earth is not a good plan.

So, what do you do for locally sourced food?

[In Season 1, much is made about how humans have changed to adapt to the lower gravity found on asteroids. People born in the Belt are taller and have spindly limbs. Traveling to Earth is torture for them; the gravity and the sunlight are oppressive. In Season 2, a contingent of Martians visit Earth. They can function in the gravity, but they tire easily. The sunlight and heat on their skin is unpleasant for them. One character is obsessed with seeing the ocean while they visit. So, the physical and cultural changes that occur due to extended occupation of space is addressed, though not dwelled upon.]

19

Of course, if they are discussing real physics, I seem to remember that the large Jovian moons are well inside the intense radiation belts that would make them uninhabitable (and kill any crops) unless buried under tremendous shielding (and ignoring how humans travel there through that radiation).

Jupiter is 10 times as far as earth from the sun, so sunshine is 100 times weaker. to illuminate a dome to the same as the earth, you need a mirror with 100 times the area. As mentioned the L4 and L5 points would work, but then the reflector would have to be fairly accurately flat to ensure proper illumination; and aim - you are talking about an aim of 1km in 1Mk; and as mentioned, the best design would be a collection of independently aimed mirrors, rather than one large structure.

IMHO the better design would be a series of smaller mirrors in a close orbit (less disruption by other moons) and have each aim as necessary as they pass over the dome. If a number of domes are placed around the globe, the mirrors would aim at each dome in turn as they pass over. Put multiple mirrors at different orbit altitudes and they would provide the necessary light as long as they don’t block each other.

20

Ganymede isn’t necessarily “a bust” just because of the distance from the Sun; as I noted before, a better scheme would be to collect energy from solar radiation using solar orbiting satellites, beam the power on microwave frequencies to Ganymede (or another airless moon), and then convert the power into the UV and near-UV that plants need. However, there are a number of other issues with habitation on Ganymede, chief among them are the low surface gravity (0.146 g, slightly less than Earth’s moon), the high radiation environment around Jupiter, and a powerful magnetosphere that may interfere with normal navigation and communication tools. Unless some practical way of dealing with these hazards is found it would not be feasible to base human settlements on any of the Jovian moons regardless of food production and energy issues.

There is an assumption that comes strictly from science fiction that developing in low gravity or freefall environment will just result in taller and weaker people. However, while we have only a modest amount of experience with humans in long duration freefall and none in fractional gravity except for the short stays on the surface of the Moon, the experiments we have run with small mammals and other animals in freefall and centrifuge as well as before-and-after examinations of astronauts in mission durations of six months to a year indicate that there are far more fundamental problems besides the obvious issues of loss of muscle tone and skeletal decalcification. Humans operating for an extended period in freefall or in gravity much less than that of Earth (and the cosmic radiation environment that no reasonable amount of shielding will protect occupants from from) are likely to suffer from a variety of physiological problems including immune system dysfunction, disruption of circadian rhythms affecting endocrine and neurotransmitter systems, changes to the brain and other organs due to fluid dislocation, balance and proprioception issues resulting from adaptation to freefall, et cetera, as well as the known psychological issues from isolation, confinement, and elevated stress levels.

In reality, the notion of creating fixed bases using moons or planets as “ports” makes little sense and is essentially a trope adopted from the Age of Sail narratives of exploring the high seas and finding riches and bountiful produce in exotic distant lands. Given access to resources in the asteroid belt and other small objects such as Jupiter’s Trojan asteroids (those collected around the Jupiter-Sun L4 and L5 points), Hildian asteroids, centaurs, SDOs, et cetera, it makes far more sense to construct sizeable thick-walled habitats using natural materials such as water ice and silicates reinforced with long fiber overwraps, spun to simulate Earth-normal gravity, and with a deep inside layer of water upon which habitable and arable “islands” of low density icy pumice would float (which also provides a radiation environment comparable to that of Earth’s surface), with a large solar collector/sunshield at one end pointing to the Sun and a long anchor deployed the other direction using orbital tidal forces to maintain stability and orientation. Such a habitat could be moved (slowly) to rendezvous with resource-rich asteroids or long period comets and extract the resources for agriculture and manufacturing, and maintenance and expansion of the structure.

However, agriculture in the conventional sense is not really feasible for long term space habitation outside the orbit of Saturn where incident sunlight drops to less than 1% of solar irradiance at Earth orbit. If civilization is to exist indefinitely at that distance or to engage in direct interstellar exploration, it would require developing methods of synthesizing nutrients and probably eliminating the wasteful and complicated system of animal digestion entirely in favor of some nutrient delivery system that doesn’t require the mess and costs of agriculture, which would also require a massive retooling of the human form into something more like an organic machine. Space inhabitants of the future aren’t likely to look very ‘human’ because the human form is not readily adaptable to the space environment, and the enormous effort and energy to create a simulation of a terrestrial environment could be put to better use than growing food in the same way we have for the last twenty-odd thousand years.

Stranger