now it’s personal

Okay brace yourself because this isn’t going to be about science or about gaming.

Queen_The_Game
The sharp reader will note that I was 15 when this came out. It’s not an album from that summer but there were a couple of summers.

I fell in love for the first time forty years ago. It was summer and I was 14 and I met a girl a grade ahead of me (to be fair I already knew her, but I fell for her that year) and we spent the whole summer together. Shopping, talking, listening to music, and making out. It was a sexual awakening with no sex and it shaped my life forever. Kelly’s still out there and we still talk and she’s still on my mind. Chatting with her tonight I had a bit of a revelation about that and about exactly how it impacted me.

Ever after I lost partners (well one, anyway) because I wasn’t interested in sex. Well, that’s not quite right. I was interested but I also wanted my romance to be that same clunky romance I had at 14: I loved kissing and knowing it was not going (much) further. I wanted that to happen forever. And it doesn’t — I had an intuition that sex would change everything and I was right but I put it off for as long as possible. I wanted adolescent fumbling for as long as I could get away with it.

We would normally say “she broke my heart” but I think it’s unfair to put that on Kelly. She didn’t break my heart. We wanted different things and what I wanted was her and so I broke my heart and frankly it was a … great feeling? Not that. It was awful, it was agonizing, it was tear-my-hair out horrible but there is also a certain joy in that heartache. When you feel so much so hard and it’s all about you, all about your pain, about your loss, it’s kind of addictive. And, I think, extraordinarily selfish after a certain point. You’re allowed your pain but it’s a little weird to cling to it.

And I think for a long time afterwards that was my model for romance: infatuation and heartache. And kissing. Those were basically my romantic goals for what seems like decades but was in fact only one (at most). Why does the short time in our youth seem so expansive and the later years tick by like seconds? It feels like I spent almost all my life between 14 and 24, pursuing heartache.

elvis_costello_the_attractions_-_this_year_s_model_base
Oh Elvis. You’re so broken but you spoke to my own broken.

My musical tastes tracked this (this was the thing I realized while chatting with Kelly this evening). Before that summer I listened to the Beatles and Queen and I can’t even remember what else. Afterwards I moved to early David Bowie and then Elvis Costello. Elvis was lyrically in the same space I was — clearly in love with his angst, with his heartache, with his bitterness. And he made it angry, which was kind of vindicating. It would be many years before I could see the degree of selfishness needed to make a heartache all about yourself. Enough to be angry rather than just sad. So it resonated — it was how I felt and the message was that I could keep that pain for as long as I liked. And I liked it.

The_Cure_-_The_Top
Around the time I found the Cure I was spending my angst dancing. A lot. Not necessarily with anyone.

I wasn’t unhappy, mind you. Just in constant pursuit of heartache. I wanted that summer back, the strongest feelings in that summer, and one of those was the heartache. I still kind of love it. It’s not very different from falling in love. The ending and the start have the same clutch and pull. Being in love for me was a constant joyous terror that it was all going to end at any point. Is that a kind of masochism or does everyone feel that? Well if it’s unusual then clearly that summer was a defining moment for me, because that pain still brings a kind of joy. I like to feel hard. I cry at a well-crafted commercial. I’m cool with that.

Tom_Waits-Heartattack_and_Vine
Tom Waits was part of my recovery period. I wasn’t craving the heartache any more. I was enjoying a deeply flawed stability.

I won’t go through the relationships up until now. There was a pattern and then there wasn’t. I hurt some people and yet I loved every one of them dearly. I wanted each relationship to last forever unchanged and I wallowed in each ending. I fell in love with people who didn’t even like me, possibly so I could skip straight to the heartache. It was a strange decade. I behaved badly but, at least, earnestly. If I could find all those people I’d apologize but finding people who are now in their 50s is surprisingly difficult. And stalkery. So I’m sorry. You know who you are.

I put a paragraph in there about music because this period of my life has a soundtrack and it’s important: the music triggers the feelings. If I’d figured this out earlier I could have just replayed one heartache over and over with a song or an album or an artist instead of inventing impossible relationships to agonize over. And maybe I still do that to some extent. Maybe we all do.

There is no gaming content here and no rocketry. I contain multitudes, as they say. You get all of it. I can’t pick and choose what I write.

Well, I choose not to anyway.

…in space!

Usagi_02I remember my wife bought me a copy of Space Usagi in the distant past and I was very excited — after all, I love science fiction and I love Usagi Yojimbo! And I read it and I was bitterly disappointed.

You see, what they did was just paint the science fiction on. They had ray guns and fought aliens on alien planets, but the tropes were largely the same as the non-sf version and the imagery was the same but with space-bits glued on. Japanese fortresses hovered in space. Space armour looks remarkably like samurai armour. They have laser katanas.

This felt like, well I want to say “betrayal” but that’s pretty harsh, but I did feel betrayed. We have a masterful storyteller and artist and it feels like they just didn’t put the work in to really adopt an alternate genre. They just painted the old one a new colour. There is no attention to how technology changes things. There’s no effort to understand the differences between Edo era Japan and some distant future. And so the stories are completely transplantable: there is nothing new or exciting here other than amusing new space art.

This lack of intentionality happened a lot in early popularized science fiction as well — surely we all recall mentions of technologies like “space pills” and “space wrenches”. This just lacks effort and it’s kind of insulting.

So anyway, what I never ever want is for my science fiction gaming to be that. When I choose science fiction for play I am not choosing it because I want space ships and lasers. I am choosing it because I want to explore a world impacted by the fact of space ships and lasers. It’s not enough to say you can easily change your physical body, growing a penis or a vagina at will. You have to address how this makes the place different from where we are now. And, at least as importantly, how it’s the same. Or at least how it’s relatable, how it’s an extension of where we are now. An important question I want to ask is “how did we get from here to there?”. And what were the costs?

This is why the cluster generation system of Diaspora (and the upcoming Diaspora Anabasis) is what it is: we create random solar systems with various technologies, resources, and environments and we ask at least these questions of you: what does this society look like given its attributes? How did it come to this? How does this affect its relationship with its neighbours?

My thinking was that if you start with making sense of these things — and likely making sense of apparent impossibilities like very low technology and very low environments — then your stories would necessarily start in a place that is not just a paint job over a place you know already. It might wind up caricatured that way (we all get a little lazy) but it doesn’t start that way and you are not invited to imagine it this way. You have all the cues you need to wonder about how technology affects a world (and not our world) and how it creates power imbalances and how those gradients affect every other system.

And I think this is the heart of the paint job problem: when the setting begins as something totally familiar but with lasers, there is nothing to grab on to and wonder about. If you’re even slightly lazy then you are stuck at the bottom of a false minimum, a place that’s easy to get to but not nearly the best you can do.

Thermodynamic_stability_EN.svgAnd since — oh! shiny! — we’re on to false minima…. A false minimum is a low spot on a curve that is not the lowest spot but is surrounded by increasing values, so if you are using a simplistic algorithm to try and find the minimum point on the graph, you can get stuck there. Sometimes they are stable (there is no easy way out) and sometimes they are unstable (a minimal effort would need to be put in to find a lower minimum. So you have points that are “metastable” (in thermodynamics, anyway) which are false minima — you need a lot of energy applied in a direction you don’t want in order to get free. You have points that are unstable (curvature around them slopes flat or down) and require only a small amount of energy to go one way or another. And you have stable points where there is no lower to go no matter how much energy you spend.

We think of low as bad but low here is good.

The reason this gave me an oh shiny moment is because it might be the case that our universe is in a metastable vacuum state — that is, the vacuum of space might be at a very low energy state but not at the lowest possible energy state. We call this a false vacuum because the real one is at the lowest energy state. If this is the case, that we are in a metastable universe, then it is possible for changes in local energy to push us out of that trough to plummet down to a lower energy state — possibly a stable one but also possibly just another false minimum. If this happens then we get “bubble nucleation” and the laws of physics may change (a little or a lot) in a bubble that expands from that point at the speed of light. And at the speed of light means there’s nothing you can do about it — you will literally only know about it when it happens to you.

The effects of a shift from a low vacuum energy to an even lower vacuum energy are speculated to vary between unnoticeable (which may have happened before) to survivable (which also may have happened before) to catastrophic. A bubble nucleation could end not only life, but the very form matter takes.

Now that’s exciting!

solar sails

Okay, there’s more ∆v out there for free: photons from the sun!

To understand these slow but sure space ships we need to understand two things: how orbits work in a bit more detail, and where momentum comes from. So first, orbits.

Okay, let’s say you’re in a nice circular orbit with altitude r (for radius).

orbit 1

Now let’s say you want to leave here and go somewhere else. You need to expand this orbit. What you do is accelerate along your path of travel (a tangent to the orbit). We’ll show this acceleration with, of course a vector. We’re not showing the vector for your existing velocity (which is in the same direction) and the gravity vector. But they are there. What we’ll show instead is how your increased vector changes your orbit.

orbit 2

As you burn, your orbit begins to elongate (and widen, but mostly elongate) on the opposite side of the orbit from your burn.

orbit 3

Let’s say you continue this burn and eventually you wind up with something like this:

orbit 4

If that long side reaches out close enough to, say, the moon, then eventually the moon will dominate in the gravity equation and you will be able to transfer from Earth orbit to lunar orbit. If you burn long enough the ellipse will expand until suddenly (when you reach escape velocity) it’s a circle centered on the sun instead of the Earth! Then you have escaped the gravity well of the Earth and are on an interplanetary journey.

The same principle exactly applies to your solar orbit. If you continue to burn then your nice circular orbit will elongate until you cross the orbit of, say, Mars. Then you can slow down a bit while close to Mars and orbit there.

To shrink your elongated orbit, you decelerate while on the short side of the orbit. To circularize you accelerate while on the long side (which runs this process in reverse).

Point is, all you need to do to get to Mars is, barring some fine tuning, accelerate and decelerate along the tangent to your orbit at the right time.

So how does a solar sail do that?

Well it turns out light has momentum. Photons from the sun reflecting off your space craft provide a very tiny amount of thrust. It’s not much, but it’s enough that it will deflect your ship by hundreds or thousands of kilometers from your careful orbital course. Our space probes must deal with this to arrive safely. It’s a real thing.

But if you build a giant, very light, reflective sail then you can reflect enough photons that their momentum is significant. And continuous. And free. You don’t need any reaction mass because this isn’t a rocket. It’s slow to build, but build it does.

solar 1So if you orient your sail at 45° to the sun, the photons will bounce off as shown in the dotted line. In doing so, thanks to Newton, you will get a vector full of momentum following the solid line. You are now accelerating and your orbit will elongate as desired! To slow down, just flip around 180° and bounce the light the other way. With these two moves and some minor adjustments you can fly anywhere there are enough photons from the sun. Practically that’s probably out to Jupiter or so.

But wait a second: photons have no mass. Momentum is mass × velocity. So where does the momentum come from? Well it turns out that mass is very intimately related to energy. It’s a pretty famous equation: E=mc². And the energy of a photon is its frequency time Planck’s constant. So though it seems like magic, photons have momentum. It’s not a lot since a little algebra gives us m=E/c² and c is huge. But again, it’s constantly on and it’s free.

This seems useful to me for a number of things:

Space probes. Since no one’s on board it doesn’t matter that it can take a while to increase that orbit usefully.

Cargo trains. If you wanted to move a continuous stream of cargo, it doesn’t really matter how long any given deliver takes since one is leaving/arriving every six days (or whatever your launch period is). And your six million tons of ice doesn’t care how long the trip takes.

Emergencies. It’s pretty scary that you might lose all your reaction mass and drift forever. Packing along a solar sail is like carrying a parachute. And it will be really bright!

In the context of Diaspora in particular, this is a pretty much perfect way to station-keep a space station at the slipknot.

questions about the ∆v diagram and aerobraking

I also had some excellent questions about this diagram:

Delta-Vs_for_inner_Solar_System

Specifically, the places where aerobraking can occur to assist (decrease the ∆v cost). The first thing we need to understand is what these places even are.

Well, they aren’t all places, per se, and that’s where it gets confusing. They are orbits. GEO, for example, is a “geostationary orbit” meaning it’s an orbit at an altitude such that you are moving around the Earth at the same rate the Earth spins, meaning you hold your position apparently stationary over one place on the planet. Sri Lanka is fine; that’s where Arthur C. Clarke put his space elevator in Fountains of Paradise. Since there’s no air there and there’s no air on any direct path to its links (GTO, L4/5, and LEO) there’s no opportunity for aerobraking.

You would guess from this diagram that GTO is further away than GEO. But that’s an artifact of the diagram which is not showing distances at all. GTO is a “geostationary transfer orbit” which means it’s an elliptical orbit with one end in a potentially geostationary position. The other end will be much closer to the Earth:

aero1
Approaching the GTO orbit from C3=0 and using aerobraking to reduce the cost of that burn.

So we can see that if you were entering GTO from somewhere else (say, C3=0 which we’ll explain later), you could enter at the shallow end of the orbit and use the atmosphere to slow down enough to complete the burn for the orbit and wind up in GTO.

C3=0 is the escape orbit of the planet (Mars or Earth in this diagram). This is the velocity at which you are no longer orbiting the planet but rather are now orbiting the sun while in the rough vicinity of the planet (or not, but that’s where the transfers take place).

aero2
The blue dot is Earth. The little spaceship is your little space ship. It is no longer orbiting the Earth–its orbital velocity is past Earth’s escape velocity but less than the Sun’s. This is C3=0.

So if you wanted to burn into a GTO around Earth you need to slow down. Nothing’s stopping you from doing that so your vector passes through the atmosphere, using that friction to make the burn cheaper. However, going from GTO to C3=0 needs more velocity not less, so aerobraking is no help and that’s why the arrow only goes in one direction on the chart. It’s only useful to go through atmosphere when you’re slowing down.

Similarly, in “deep space” at your Mars transfer orbit you want to enter the C3=0 of Mars. While there’s no air there, you can plot your path such that you pass through some air on the way. Why would you want to though? If you have an elliptical transfer orbit you probably want to speed up to reach C3=0. I am guessing that they mean that you could be on a longer elliptical orbit for transfer such as:

aeri3
Earth is blue, Mars is red, and you are clearly in way too much of a hurry to match up with Mars’ orbit so you are going to plan a path way past it and brake in the atmosphere as you pass.

 

In this case you want to slow down or possibly change direction and it seems like there’s an opportunity to use Mars to do it. I’m not sure I see exactly how that would help, but you certainly can pass through Mars atmosphere from a transfer orbit. I’m just not sure why.

Although the atmosphere at Mars is much much thinner, at high speeds and with a high cross section, it will still slow you down a bunch. The Odyssey mission, for example, used aerobraking to slow down. They burned from capture orbit (the orbit at which they just start to move slower than the escape velocity of Mars and so are now orbiting Mars instead of just the sun) to what they called an “aerobraking orbit” which was designed so that every time the craft passed through the short side of the orbit the vessel would slow down, slowly circularizing the orbit until it was suitable for the mapping work.

Over at the moon there’s no atmosphere at any of the adjacent nodes to lunar orbit so there’s no aerobraking. At the moon you have to do all the work. It’s also pretty cheap to land and take off from though!

Thanks to Pierre Savoie for the questions that spawned this

questions about the ∆v science

20190602_010436

I got some excellent questions on the last few articles and the answers deserve some space, so here’s that space.

I’m about to reveal how clueless I am about these topics, but these are making me reflect on recent sifi fiction. Could weapon recoil provide ∆v significant enough to be strategic (assuming weapons use power that doesn’t steal from thrust capacity)?

This will become clearer in a later answer but the short version is: probably not. Ships are going to be very hard to move due to their mass. Additionally, you probably don’t want a weapon that costs you ∆v unless you point it in exactly the right direction: the odds of that being both the direction of your target and opposite your desired vector change is mighty small.

Could you use weapons as thrust in an emergency? You could probably use some weapons to rotate the vessel rather than apply ∆v. Rotating your ship is comparatively cheap! In fact any weapon with recoil probably has a compensating jet to avoid this. I believe this is the case with the Rocinante in The Expanse! From the entry on PDCs in the fandom wiki:

They also utilize thrusters on their rear to counteract the recoil of the firing cannon, that would otherwise knock the ship off course.

To be clear, though, it probably wouldn’t affect the ship’s course, but it would rotate the ship. And I suppose if you’re burning the drive while firing that would indeed knock you off course.

Or nearby detonations (does space conduct shockwaves)? It’s intriguing to weigh the ∆v cost of any sort of space confrontation or skirmish.

Since there’s no atmosphere in space (by definition) there’s nothing intrinsic to transmit a shock wave. There will be some shock from the expanding plasma of the explosion of course, but we normally call that “damage”! And maybe a little photon push as well. Nothing that you would want to use as thrust.

However! If the explosion is energetic and close enough (and ideally shaped for the task), you can indeed propel your space ship with nuclear bombs. This would be a very poor ad hoc solution to a problem, but not an infeasible design. Obviously there are significant drawbacks to the design.

How does starship mass impact ∆v strategy? I’m probably wrong but I’m assuming greater mass requires greater thrust to achieve the same vector, and more thrust requires more fuel or efficiency, which all rolls into a single measure of total ∆v capacity.

rocketChartThumb
I’ve only put the thumbnail here because it’s massively detailed and you should go to Winchell’s site to read about it and download the whole thing.

You are absolutely correct! For any given drive capability you can calculate the ∆v of the whole system by estimating the proportion of reaction mass (the mass you store only so you can shoot it energetically out the back) to the payload mass (the mass you have to keep). This is because of the “rocket equation” which I’m not going to go into, but Winchell Chung has an awesome chart showing ∆v for any given hypothetical drive type and any given mass ratio! It’s the basis of the game design that’s emerging here.

So yes, one of the joys of using ∆v as the core resource is that it encapsulates all kinds of information about the ship.

But would reducing your mass increase ∆v capacity through fuel efficiency?

IMG_0711
The Marie Therese before ejecting the spin-grav luxury cabins and swimming pool.

Essentially yes! Let’s say you were the players in my last Diaspora campaign and were escaping in a luxury liner with a huge rotating spin-gravity living space. And you’re being chased. Ejecting that useless mass (which was huge) would change your r-mass:p-mass ration substantially, and give you a ton of spare ∆v.

Mass also impacts gravitational vectors, right?

Nope. The force you experience is dependent on your mass, but the acceleration you experience is not — it’s pretty much 9.8 m/s² for everything on Earth (but an elephant gets a lot more harm falling from a height than a mouse does — that’s the force). But not everywhere, and certainly not at different altitudes. But that’s way more detail than we need.

Does anything in space provide opportunity for aerobraking other than atmospheres?

Atmosphere is all I can thing of. Most interstellar gas clouds are way too tenuous to be interesting at this scale. Doesn’t mean you can’t invent one though!

Renewable sources of ∆v reserves look increasingly important (e.g. rechargeable solar vs consumable fuel?).

Well, basically your ∆v is going to be based on how much and how fast you can throw something out the back. So renewable is pretty tough unless you have a way to convert energy into mass. At least for rockets anyway. Remember for a rocket we’re not talking about power (although you might need some power to run the rocket, and that power supply will have its own energy needs which might include solar) but rather reaction mass.

Many thanks to Adam Minnie for the questions!

aerobraking

Okay let’s look at aerobraking. This is a way to get free ∆v for deceleration We’ll look at the principle and then talk about its utility. First recall our gravity example but I’ll add an atmosphere to the planet.

a1

Now the atmosphere is a source of friction and friction reduces your velocity. As you bang into gas molecules, you slow down. We can treat this as a third vector in the system, opposing our direction of travel (our initial velocity vector).

a2

Back when we were first talking about vectors, we said that you add vectors by arranging them head to tail and finding the hypotenuse. This was a lie, of course, as all science education advances by correcting the lies told in earlier lectures. In fact you just connect the last head with the first tail, like so:

a3

Oops. I crafted this example without figuring out ahead of time what it would do and it looks like this atmosphere is too dense for our maneuver! When science fiction stories talk about a “degrading orbit” this is what they mean if we’re being charitable: eventually atmosphere will drag you in if you’re too low.

However, that doesn’t have to be a crash! That could be a landing! In which case we saved the atmospheric vector from our ∆v resources. We totally meant to do that! Of course that’s not what that diagram represents since that enormous vector is our velocity and it does not look like a safe landing speed. Or angle. But that’s the principle and however much additional ∆v we have to spend to land safely, it’s reduced by the amount of drag provided by the atmosphere.

So let’s consider a hypothetical interception scenario — you are fleeing through space and the cops are after you. You have, let’s say, 7 units of ∆v and spend 2 planning a course to a safe planet. It’s months away and you’re committed and you now have only 5 units of ∆v. You’re saving some for slowing down at the far end — you need 3∆v to make orbit at your destination.

You: 5∆v

The cops spot you and match your course with 2 ∆v of their own. They have fast interceptors (high thrust for tactical corrections) but less reserves so let’s say they start with 5∆v. Now they have 3.

You: 5∆v

Cops: 3∆v

You spot the cops on your infrared telescope and track them for a couple of days, identifying their planned intercept point. You have a bunch of options. You have more total ∆v and if you know this you could burn more than they can afford to to change your course and correct back. If they spend any more than they have they won’t have the ∆v to slow down and stop somewhere to refuel. But if they aren’t tricked and don’t burn, then when you correct back they will still be on target.

You could also fake a course to a totally different location, spending maybe 3 more ∆v leaving you with 2. If the police correct for that they will be totally committed (they won’t be able to slow down so they are clearly going to try to kill you in a flyby and then count on other cops to save them from leaving the solar system) but you have some spare.

You: 2∆v

Cops: 0∆v

Maybe it’s not enough to make orbit around your original destination — you’ll be going too fast. But if you’re equipped with heat shields for aerobraking, you can steal 1∆v from the atmosphere and get the 3 you need to make orbit despite going way too fast!

Or maybe you won’t slow down! Maybe you’ll steal 1 ∆v from slingshotting your destination on order to head somewhere completely else!

You: 3∆v

Cops: 0∆v

Finding spare ∆v in the system geography is how you exceed your space craft’s specifications, and it’s a skill your character might have. Yes, we’re almost talking games now.

Since this is science fiction, what other sources of ∆v might be lying around a high tech industrialized star system?

∆v

Okay so now we can talk about delta-v (∆v from now on because it looks cool) in a larger context. We can see from the last post that the thing that really matters in space travel is how much you can change your velocity before you run out of gas. And I’ve talked previously about orbital mechanics. Let’s tie these together. First a diagram I have lifted from a much more detailed article about the topic at Wikipedia:

Delta-Vs_for_inner_Solar_System

This is a map of the solar system from Earth to Mars assuming you are travelling using orbital transfers — that is, you don’t care how long it takes and your plan is to burn just enough to enter the orbit of your target eventually. Exactly which way you point and how long you travel depends on many factors that are largely out of your control — at a given time with a given rocket you have essentially one choice.

The numbers on that map are not distances but rather costs in ∆v. And this is why ∆v is the critical resource both tactically and strategically in Diaspora Anabasis: it’s the only resource that matters for planning. Everything else is roughly fixed. Everything you might do to influence travel is going to boil down to changing your ∆v resource or cost.

So to get from the surface of the earth to Low Earth Orbit (LEO) you need to go 9.3 kilometers per second faster than when you started. Soak that in. Notice that almost every other transfer is somewhere between cheaper and vastly cheaper. This is why starting your trip on a planet is so incredibly expensive and why space and low-gravity-planetoid bases are essential to industrialized (and certainly private) space travel: this is an unnecessary expense that dominates everything.

If you have a space craft with 11km/s ∆v in resources, you can reach orbit and sit there. If you built the same ship in orbit, however, you could go to Mars with resources to spare. LEO is 2km away. Mars at its closest is 56,000,000km away. It’s 20 million times more efficient to travel with orbital transfers from Earth orbit than it is to orbit the Earth. When people talk about how hard it is to go to Mars and how we so handily went to the moon remember that: those Mercury and Gemini project orbits were actually the very hardest part of the whole endeavour. Everything after that is vastly simpler.

Now what if you don’t use orbital transfers? What if you want to spend less than 18 months to go to Mars? Well, you spend more ∆v. You can speed up any orbital transfer by burning harder at the start and burning again at the end to slow down. It changes the path of the transfer substantially — you’ll get there faster because you’re going faster but also because you’ll take a physically shorter path — your lazy elliptical arc will straighten as you dump reaction mass into the fire. But it costs twice as much because you have to slow down at the end.

You can think of an orbital transfer as basically matching courses with your destination (since planets are moving too). Imagine you want to catch up with a skier further down the slope than you. You can dig in the poles a little so you’re going faster and take an arcing path down the hill so that you slowly catch up, with friction equalizing your speed at intercept. It’s a lot of calculation and might need a little correction and it’s not the fastest path but it takes very little energy. That’s the orbital intercept.

Or you can drive on your snowmobile straight at your target. You’ll have to correct continuously as they move but you will arrive much sooner. You’ll also have to figure out how to slow down or you won’t be matching courses at all. That’s a “hyperbolic” intercept.

The other interesting thing on that map is the “aerobrake”. This is a way to steal ∆v from planets with an atmosphere: you can use that friction to slow down. We know that slowing down is just ∆v spent pointing backwards. So friction is free ∆v for slowing down! In the last post we talked about slingshotting, which steals ∆v from planets for speeding up. So the natural universe provides a landscape that can lighten the load and this is where strategic play will happen: we have a determination problem in that the math tightly constrains exactly how much ∆v a maneuver costs and you ship defines how much you have — so where are the player choices? What knobs can you turn to defy (rely manipulate) the math? The natural environment provides two.

We’ll talk about how the artificial environment can help next time.