thinking about spacecraft design

[Anthony]

Originally Posted by whswhs

I've done some looking at orbital mechanics, using Paris, the innermost planet of Omicron Polypi B, as an example. It has 80% of Earth's radius, 80% of Earth's density, and thus 41% of Earth's mass, and has no atmosphere. It's tidelocked to its primary, so a synchronous orbit is impractical.

Well, there are some synchronous orbits -- anything located at a lagrange point is synchronous for a tide locked planet -- but probably too far away to be useful unless it's very close to the primary.

[whswhs]

Originally Posted by Ulzgoroth

You're leaving out the extremely important consideration of high fuel fraction. (SS p17, basically the Tsiolkovsky rocket equation in tabular form)

A quasi-maximal single stage chemical rocket with a control room, a rocket, and 18 fuel tanks gets 18*2.5*0.15 mps = 6.75 mps.

Granted, that's still not enough if you can't refuel on the surface, and that's got zero payload so it isn't really useful. But it's also relevant to HEDM. 9 tanks gives 9*1.4*0.5 = 6.3 mps, so you 'only' need 7 or 8 tanks (4.2 or 4.8 mps). If you need 8.7 mps for the down-and-up, 13 tanks HEDM gives you 10.4 mps without staging and leaves you a little actual payload capacity too.

EDIT: But yes, if you can deal with the antimatter-catalyzed fuel, antimatter thermal is probably your best option out at the end of a long supply line. Especially if you have TL11 versions. At list price, their delta-V per dollar is actually not bad for a boost engine, and if you're carrying it over interplanetary distances using fewer tons is a pretty big advantage.

Interesting suggestions. I'll have to work on this some more.

[Anthony]

Honestly, unless there's a really compelling reason to visit the planet, people will probably just not do so, as it's an absolutely atrocious planet to try and get on or off of, but given the limits on rocket options, might be worth considering non-rocket options such as a momentum exchange tether (it's a formidable materials science problem with the sheer amount of delta-V required, but might still be less effort than rockets).

[whswhs]

Originally Posted by Anthony

Honestly, unless there's a really compelling reason to visit the planet, people will probably just not do so, as it's an absolutely atrocious planet to try and get on or off of, but given the limits on rocket options, might be worth considering non-rocket options such as a momentum exchange tether (it's a formidable materials science problem with the sheer amount of delta-V required, but might still be less effort than rockets).

No, the really atrocious planet is the one with 1.54G, escape velocity 9.8 mps, and all its atmosphere boiled off. I expect that one remains unvisited even if the others are colonized.

[whswhs]

To carry things forward, I wanted to work out orbital mission plans for various planets. Doing the calculations in mixed units was just insane, and doing everything in metric proved tediously time consuming, so I worked out a set of canonical units, in which the radius, mass, and density of Earth are all 1.00. Here are the calculations I came up with:

Start with the planet's radius and density.
The planet's mass is equal to density times the cube of radius.
The surface gravity is the product of radius and density, in G.
The escape velocity is the square root of (mass divided by radius), times 7 mps.
For a standard circular orbit at an altitude of 0.3 (or 1911 km), and thus an orbital radius of planetary radius plus 0.3, the orbital period is the square root of (orbital radius cubed, divided by mass), times 5050 seconds. The orbital speed is the square root of (planetary mass divided by orbital radius), times 4.73 mps.
For a grazing elliptical orbit, with apoapsis at the circular orbit, and periapsis at the planetary surface, the semi-major axis is the planetary radius plus 0.15. Each of the two orbital velocities is the square root of (2 divided by orbital radius, minus 1 divided by semi-major axis, quantity times planetary mass), multiplied by 4.95 mps. Then you can subtract the apoapsis speed from the circular speed, and add the periapsis speed, to find how much delta-V is needed for landing.
For takeoff, you need downward thrust to compensate for planetary surface gravity. This calls for a thrust angle of arcsin(planetary surface gravity/spacecraft acceleration). You then divide the periapsis speed by the cosine of this angle to find how much delta-V you have to expend to get into an elliptical orbit, and add the delta-V you need to speed up to circular orbit speed.

Assuming an acceleration of 2.00G, I came up with delta-V of 0.67 mps for both landing and takeoff on a tiny world (0.09G); 5.51 mps for landing and 5.82 mps for takeoff on a small world (0.64G); and 7.30 mps for landing and 10.12 mps for takeoff on a large world (1.40G). So that gives me estimates of what performance is needed to make each of these worlds a viable site for missions (assuming that the colonists aren't going to be shipping masses of fuel/reaction mass down to the respective planetary surfaces!).