Crazy Hermann

Let's work with vinf. I found a paper on that (pdf) last week.

My highest stable orbit over Venus is 536412 km. For Earth-serving sats I'll actually be orbiting a bit lower, say 530567 km (and 782.5 m/s). Per Hop David, v_∞ to Hohmann Earthbound is 2706.7 m/s. To 2L4 it's 3864 m/s and, unlike Hohmann, it's not ballistic. With 2L4, I'm needing to blow off some steam no matter what. Can I blow off... LESS steam?

Hermann Oberth has a delta-V for this. If I do a big reverse thrust against my orbit, I fall down to say 950 km altitude. That is semimajor 7000000 m. I then use that kinetic energy and another thrust to shoot off whitherever.

Probably best, for Microsoft, if we separate its concerns. Let X = (v_∞/v₀)²; let Y = 2 * r₀/r_in.

For Hohmann: X = 11.965; for that 530567 km semimajor / 950 km altitude ratio, Y = 151.59. So, 782.5 * (1 + Math.Sqrt(11.965 + 151.59) - Math.Sqrt(2 + 151.59)) ends up 1092 m/s.

If I wasn't doing pulsed thrust, Y is just 2. I'd have this much delta-V to make up: 782.5 * ( Math.Sqrt(2 + 11.965) - 1) = 2141.7 m/s. I'm Crazy Hermann and our savings are iiinsaaaane!

Off to 2L4 (again, 3864 m/s), my delta-V on an ion drive would be 3236.8 m/s. Crazy Hermann does even better: 1465 m/s. Theodore Edelbaum in 1959 made tell of a three-pulser, first jumping out to like 795850 km before that big turn planetward - which smacks of the biëlliptic. But let's not get too crazy just yet.

Note that although I've used less total energy, I've told my ship engineers never to mind about a high-impulse rocket, but to use a high-thrust one. And 1092 m/s is a lot of delta-V for thrust. You should see what it's like to use the solar well for Oberth, starting from Earth v₀ = 30000 and, of course, constraining r_in so's you don't get a bad tan (Y ≤ 10). Nobody's ever tried that UPDATE 10/8/22 ...yet.

But anyway - back to planetary orbits. I've also careened my runaway sat down every damn orbit that planet's other sats are using. That might not matter for the wide-period sats, each likely angled away and on some other angle on its orbit. The inner sats, for Venus, I want for scooping oxygen and firing it off to my higher sats, or for catching tourists off Landisopolis - they're important and there will be a crowd of them. Even if I convince their operators I'm not going to hit one, they're still going to ban me from using the Orion down there. Just like... over Earth! I don't recall many satops using Oberth locally, either.

THRUST 5/17/21: Chemical detonations in lieu of Boom Boom.