∆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.

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