Into orbit

On NY Eve 2019 I started an investigation on how to get off of Venus, using Dan Allen's summary in Koboldt's book. First I had to calculate escape-velocity (v_e) from my 70 km flying port, which I did, but hadn't got as far as framing it in terms of energy-requirements. In the meantime I digressed into potential Fry-By interference, which I decided was, also, a prerequisite. Since I've done all that: I'll resume where I left off.

My Venus-70km escape-velocity is 10300 ms^-1, and classical is 10360 ms^-1. Neither is much better than Earth's. It should be rare that the rocketry push payload straight from Venus out of that gravity well, off to Earth or to L5 or wherever (at which point we move on, into the Sun's imperium). Even with nuclear fuel this is expensive.

We do have a compromise. Most flights will aim at an orbital waypoint: which stockpiles fuel, and takes its own, midway velocity. (It has its own economy, as well.) The book would have us divide that 10360 v_e by root-2 (the book says 1.4): yielding orbital speed of 7325 ms^-1 (which the book calls "minimum").

But I distrusted Dan Allen. I think "minimum" is used here in the sense of eccentric orbits. And anyway the summary assumes too much - namely, an Earth-dense planetoid allowing a near-surface orbit (i.e. negligible atmosphere, and no traffic). That works for most asteroids and Mercury - maybe Phobos over Mars. But we're doing Venus here.

For starters, Venus extends an atmosphere at a non-negligible height. 150 km is the number generally given. Even over our Earth, LEO satellites don't dip under 300 km. And then there are those swift Fry-By visitors, running as close to the planet as they can, thus making that part of orbit quite over-stimulating.

Venus traffic-controllers want outgoing craft to dock on a planetary orbiting hotel, far above all this. I'll enforce a minimum 1948 km up, which nets an even semimajor of 8000.

Back to the characteristics of an orbital station, I need x between 8000 and 1000000 km: between the higher levels of Low Venus Orbit, and the L1-2.

?Math.Sqrt(324774910000 / x)

A satellite whizzes by at 7236 ms^-1 (not too far off what the book got me) if skimming atmo at 150 km. It does a more-sedate 570 ms^-1 at the outer edge of Venus' gravity well; L1 and L2 themselves, on that edge, are zero, with reference to Venus. At 1950 km: 6370 ms^-1.

To push a rocket from 70 km over Venus to an orbital at 1950 km requires 12453595 x Mass for a change in potential energy (mercifully, not mgh=16293333m). Add the kinetic-energy for a Delta-V of 6370 ms^-1 which is 20288450 x Mass (although we might knock out a fifth of this, planetside). Total: 32742045 x Mass. I was considering last Tuesday to harness the 100 ms^-1 wind-speed but, as you see, it's not worth the effort. (Although we should see some energy savings toward the end, after mass was expelled for lift.)

To overcome delta-V 10300 ms^-1, straight up, takes 53045000 x Mass. A low-orbit satellite is, then, well over halfway to anywhere! - or halfway to L1/2 and beyond, anyway. Robert Heinlein was right, as usual.

We are still dealing in kilotons, so will still be needing nuclear rockets.