Questions of Scale (Deconstructing The Expanse, part 1)

[wrog]

(other titles:)

How to do Solar-System-Travelog SF and Not Get It Completely Wrong

How Magical is The Expanse's "Epstein Drive" Anyway?

Why Nuclear Fusion Sucks and We Really Need Those Antimatter Cells

What Part of "Rockets Are Stupid" Did You Not Understand?

Just to get something out of the way up front:

I am now mostly convinced that, barring unexpectedly early, lucky results to our terraforming experiments, colonizing the solar system will for a long time remain an absurd enterprise that will only make sense if we manage to screw up the Earth really, really, really bad — at which point we've probably already gone extinct — and that SF premised on this should be regarded as a variety of steampunk (i.e. seeing what stories we can make out of improbable combinations of technology).

But never mind that. I do eventually expect an assortment of random human-crewed research/mining-supervision/etc stations scattered about needing to engage in commerce of a sort. E.g., just as today we maintain South Pole Station at fantastic expense and there's no way in hell anybody expects that to turn into a colony any time soon (or ever, or, at least, not until after the Antarctic ice-sheet has completely melted), but there will always be a few nutjobs wanting to live there. They may never comprise more than an infinitesimal percentage of Earth's population, but it will be sufficient to make the rest of this post/sub-series not entirely useless.

Having finished a re-watch of (the good parts of) The Expanse, I have to say, I really appreciate how they evidently did give thought to the solar system being way, way bigger than people give it credit for and are actually rather successful in getting this across in ways previous shows completely punted on — the Star Trek: TNG opening that zips by Mars, Jupiter, and Saturn in a matter of seconds being one of those "No, Just No" moments.

While I'm on the subject of good things, I also liked

• the effort put into depicting 0g and classical mechanics correctly, though, I think, now that we have a generation raised on Mass Effect and similar video games, the old Star Wars X-wings doing WW2-movie banked turns in a vacuum were just never going to be acceptable anymore.
  
  
• their pointing out exactly how miserable life in space (or on Mars) would be, even if they are still sugar-coating it. Though on the bright side, I strongly expect there will be far less need (read nearly zero) for human manual labor in space, if only because the mining and powersat construction I envision happening will be essentially impossible without automation, including automated repairs, and once we have it, the cost of maintaining an army of human laborers there will make no economic sense.
  
  (To be sure, I do not know how soon we'll have our act together on automation. I like watching the Boston Dynamics robot dogs jump around, but I'm guessing self-driving cars are at least another decade off. Then again, the Self-Driving Car Problem is much easier if you don't have to worry about passengers or pedestrians who can sue the shit out of you.)

As a matter of general principle, I also really like it when trying to get things right fails in interesting ways.

The biggest mistake they make — perhaps intentionally since, of course, Having a Good Story trumps everything else — is in how, after all that effort, they end up shrinking the solar system after all.

I get why they wanted to have a magic Epstein Drive in order not to have to wait years to get anywhere in the outer planets. But the actual numbers are completely brutal. It is not simply a question of making our current rockets "more efficient". There's tech we need that we're not going to have for a long time, if ever, and if the Belter folks actually had it, Earth and Mars would be treating them a lot more politely.

So, let's do a perhaps not so brief guide to getting it vaguely right:

The Problem with Depending on Gravity

First, let's start with the Before picture, i.e., the technology we have today and for the immediate future: Shitty expensive rockets (liquid hydrogen+oxygen or hydrazine [or maybe ion drive, but for now that's only for really tiny craft]) and shitty energy sources (rocket fuel or radioisotope batteries, depending), the consequence being that we're doing as little propulsion as we can get away with, using gravity tricks everywhere, because we simply do not have the energy to be doing anything else.

Primarily using gravity means we are essentially in the same boat that the planets themselves are. Meaning a good rule of thumb for figuring out long it'll take to get someplace is: Look at how long it takes the planets to get there; that will be pretty much your answer, at least to within an order of magnitude. Examples:

1. You want to get from Low Earth Orbit (LEO) to the Moon. The Moon takes about 13 days to do a half orbit, so you can be sure your trip will take multiple days to get there and not hours or minutes. (Yes, the actual answer is around 5 days [below], and Apollo 11 did it in 3. Again, we're just going for order of magnitude here.)
   
   
2. Jupiter's orbit has two asteroid groups, the Greeks and the Trojans at the L4 and L5 points — I'd say respectively except I forget which is which. You want to travel between the two, and it's a distance that Jupiter itself takes 4 years to cover, so if somebody's claiming to be able to do this in a month or a week without having the Very Special Engine, you need to call bullshit.

For a benchmark on this, I'll use Hohmann Transfer, the dirt-simplest of the gravity maneuvers to calculate. It works like this:

• If, say, you want to go from Earth to Mars, you fire your engine to increase your velocity around the Sun, changing your own orbit from being nearly a circle (Earth's orbit, green in this diagram I stole from wikipedia) to one where you're at the bottom of an ellipse (at perihelion, closest approach to the sun). As you accumulate kinetic energy, the top of your ellipse (aphelion) moves farther out. When it reaches the Mars orbit distance, you can turn off your engine and coast the whole way there (along the yellow line).
  
  
• The other piece of the puzzle is your having timed things so that, when your ship reaches the Mars distance, Mars will be there catching up with you. You'll be going slower, but then you fire your engine once more -- now that you're at the top of your ellipse, increasing your velocity has the effect of moving the bottom end of your orbit outwards until it, too, reaches the Mars distance, at which point your own orbit around the sun is again a circle (red line), your relative velocity with respect to Mars has gone to zero, and now Mars' gravity can catch you.

Everything gets accomplished in those two short burns. It's marvelously cheap; probably the best you can do that doesn't involve stealing momentum from other planets. (To be sure, the ITN trajectories are way cheaper, but also tend to take much longer, never mind being way more complicated to calculate.)

Here is how long it takes and how much it costs:

Hohmann Transfer flight plans

Trip	Distance (major axis)	Travel Time		Total ΔV	Mass Cost
LEO ⟶ Moon	1.3s		4d 23h	4.0 km/s	13.30 g/t
Earth ⟶ Venus	860s		146d  2h	5.2 km/s	17.35 g/t
Earth ⟶ Mars	1259s		258d 21h	5.6 km/s	18.66 g/t
Earth ⟶ Ceres	1879s	1.3y	471d 21h	11.2 km/s	37.27 g/t
Earth ⟶ Jupiter	3094s	2.7y	997d  2h	14.4 km/s	48.15 g/t
Earth ⟶ Neptune	15499s	30.6y	11176d 11h	15.7 km/s	52.40 g/t
Earth ⟶ Saturn	5258s	6.0y	2208d  4h	15.7 km/s	52.48 g/t
Earth ⟶ Uranus	10071s	16.0y	5854d 17h	15.9 km/s	53.17 g/t
Earth ⟶ Mercury	692s		105d 12h	17.1 km/s	57.19 g/t

Column explanations:

• Distance:  This is actually the major axis (larger diameter) of the (yellow) ellipse we're traveling along, and as such is merely a representative distance, not the actual distance traveled, but still the same order of magnitude, which is good enough for comparisons.
  
  That "s" stands for "seconds", meaning light-seconds, 1 second being roughly 300,000 km. Yes, normal people would use kilometers. There is also the Astronomical Unit — preferred by astronomers, surprisingly enough, — 1 AU being the average Earth-Sun distance or, roughly 150 million km = 500 seconds. But I wanted to include the moon distance on here and so needed something intermediate.
  
  Also this makes it easy to know what the communication time delay will be or what magic FTL ships would be able to do, if we could have those (which we can't). Or if, say, we have a flight plan where (spoiler alert) the ship coasts most of the way at (1/n)-th of the speed of light, then you just multiply the seconds distance by n to get the travel time.
  
  Two takeaways from this column:
  1. Mars is 1000 times farther away than the Moon, just in case you were getting too excited about us having Mars expeditions/colonies any time soon.
  2. Comparing with the travel times (next column), you can see we are no way no how getting anywhere near the realm where Relativity matters.
     
     
• Travel Time:  For interplanetary missions, it's multiple months, or, for the outer planets, years to get there, and there's nothing you can do about this if you're mostly relying on gravity.
  
  
• ΔV = Total of all of the velocity changes needed — the only number you really need to get the fuel cost. In this case, there are just the two burns and we're adding them together.
  
  Multiply this by 1.7 to get the number of minutes of burn time, assuming you're happy with accelerating at 1g. That's just under 7 minutes for the Moon trip, 9 minutes for the Mars trip — out of 146 days, — and so on.
  
  We are really not doing a whole lot of propulsion here.
  
  
• Mass Cost:  Here is where the fun starts. This is how much mass gets expended per unit of payload mass to accomplish that ΔV, i.e., assuming we have the ideal rocket configuration that can convert that mass into momentum (mc) with 100% efficiency, or, equivalently, convert it completely into energy (mc²), capturing all of it to power the 100%-efficient Big Ass Laser so that we can send it all out as photons in the right direction, … ignoring for now that this is impossible; I just want to have a Useful Number for comparisons.
  
  Here the units are all in grams per metric ton (1000kg), which you can feel free to read as " ×10⁻⁶ ".
  
  Example:  If we want to get the 10 ton Winnebago from LEO to the Moon, we need to burn 133 grams of matter+antimatter. This will be a lower bound on the mass-energy we need no matter what tech we use.
  
  Recall that "burning" an entire kilogram gives us that 21 megaton explosion that wipes out Rhode Island. But this, at least, will be "only" 2.8 megatons, and the stupider tech options will only ever be burning a teentsy fraction of this (hint: an exploding Saturn V will not destroy Rhode Island)
  
  And if you're trying to reconcile this with my previous post where I said this cost was 327 g, that was for starting from rest on the surface of the Earth rather than LEO, which is a big difference.
  
  Similarly for the other rows, we're only giving the cost of switching orbits around the Sun, and not what it takes to deal with the planetary gravity wells. However,
  1. This doesn't change the overall travel times that much.
  2. We're just trying to get a lower bound, here.
  3. There can be ways to evade some of that extra cost, e.g., if, when landing, you have an atmosphere you can use to slow down without using any fuel…
     
     

Rows are ordered by cost, and if it looks weird, that's not your imagination:

• Somewhere just short of Uranus is where the mass cost for Hohmann Transfer hits a maximum, so getting to Neptune is indeed cheaper than getting to Saturn.
  
  (Best way to think of this: the first burn increases as you go farther out, but is always less than what it takes to get to solar escape velocity; the second burn goes to zero, and at some point you can expect the 2nd effect to catch up with the first).
  
  
• … and Mercury is indeed the most expensive planet to reach with this method (why Mariner 10 was so late in the game [1973], and even then they had to do it as a slingshot off of Venus).
  
  Briefly: If you're in a circular orbit, canceling your velocity to fall into the Sun is always more work than escaping — just in case you were wondering why all solar probes go to Jupiter first (to get a backwards gravity assist) rather than being sent directly — and then the 2nd burn in closer to the sun is always larger.

Gravity is weird. In the next installment, I will need to discuss "Slingshots"

After that, we'll do an excursion to Fantasy Land.

Comments

[nosrednayduj]

Did you also read the books? They spend more time dorking around in their spaceship waiting to get to their next destination than they do in the series, because TV has to be more action-packed.

Note: I have only read the first 3 books, and I only watched one season. Eventually I'll probably read the rest of the books, but probably won't watch the rest of the TV.

[wrog]

Did you also read the books?

sadly, not yet; they're still on the stack. Meaning everything I'm going to complain about it is based on the TV series. Which is perhaps unfair, but nobody put guns to their heads and said they had to sign the TV deal.

I also have this sense the TV folks really were trying to be faithful for at least for the first two seasons, that they do try to follow the first two books, though I'll admit I'm not yet in a position to judge how well they did that.

[nosrednayduj]

I thought they did a pretty good job of sticking to the first half of book 1 for season 1. I considered paying for season 2 in order to watch the second half of the book as well, but haven't got around to that yet. I only watch TV when I'm running on the elliptical, and I usually try to exercise outdoors if possible, so there's really not a lot of TV watching for me. (I watched it on VUDU, because that doesn't require you to pay a monthly fee, but you can just pay for individual episodes and watch them at your leisure.)

[wrog]

I get it via Amazon Prime, which has all of the seasons. If you liked season 1, you'll probably like season 2 and the first 7 episodes of season 3. After that, it's different.

[rmd]

YAY! I do enjoy your nerdy posts like this.