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Old 11-24-2017, 11:05 AM   #8
ericthered
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Default Re: [Blog] n-Body Politics

They start at rest with regards to the object? Ok, that took guts to go for. It also means that if your STL light drives fails, you face certain death after a FTL jump.

5 kps is a huge delta-V cost, particularly if you make it apply both ways. with 10 kps I can get into orbit from earth's surface. And I can't just use an efficient Ion drive, because I'll slam into the earth first. So it looks like I'm going to have to spend large parts of my ship either storing fuel or massing three rocket engines to get the acceleration I need. Its not as bad as planetary take-off, fortunately, because falling is an option, and because you don't need to accelerate quite as fast, but it still places restricting demands on the drives.

So I wanted to know how different sizes of planet act with these rules, and what minimal spacecraft engines look like. And you made me spend an hour doing math. Hopefully some of it will be useful to you:

if you don't use engines after appearing around earth, you have a little less than 8 hours before you impact. using 1.11 * (R^3/(GM))^.5 gives the time to the center of the body. I figured the actual numbers, but those equations are nasty, and this gives pretty good results.

Resting time to impact simplifies down to about 35 * (GM)^.25 if you use .1 newtons instead of .01G

Engines need to be .015 G's or greater in order to make orbital velocity before the powered crash time is up. This is constant regardless of the body you are orbiting. the actual minimum is something else, but it lower, depends on the mass and radius of the orbiting body, and this is probably a good rule of thumb. It's also interesting, because a lot of rocket engines play just above or just below this values.

The KPS for the resting orbit of a body is (GM)^.25

the resting orbit for a body is (GM)^.5

* I am sorry for liberally mixing earth gravity with the gravitational constant, both represented by G. If the G has an M next to it, its the gravitational constant.

On minimally viable objects, all the planets have a recharge zone, the Galileans and Titan have recharge zones, but Pluto and Ceres do not, reinforcing the categorization of them as dwarf planets. Earth's moon does have a recharge zone, and in fact bodes like it take less fuel to use as stopping places. The cheapest place to stop in the solar system is Europa, but the next is earth's moon, both being about of third of what you'd spend to land on earth. There are probably some kuiper belt objects that can be used as rechargers, but we haven't found any in the solar system, which means they may very well be secrets well guarded by militaries, guilds, and smugglers. Or valuable waypoints through gaps in a network.

You CAN use a star directly, but you'll want really big fuel tanks to pull that off. A minimal red dwarf requires 50 kps to stabilize, and twice that if you ever want to leave. The sun requires 107 kps to stabilize. I think the minimum vessel I'd try jumping to a star would have 3 Advanced pulsed fusion drives, 2 fusion engines, and 11 tanks of fuel at TL9. The remaining fifth of the ship is probably shielding, control, life support, and living quarters for the nuts trying this out. And two weeks worth of food.
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Last edited by ericthered; 11-24-2017 at 11:43 AM.
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