Parking Earth's supplies at Venus

They let us out early at work. So: earlier Wednesday post than usual. Let's look at Hohmann insertion into Venus.

I might not be as smart as some working this field but even I know we're not landing on Venus' surface. I'm here to park supplies in orbit - "supplies" including monkeys. So I want some place cool. Some of these supplies will go to the Landis-stan in the clouds. Some will go to SVL2. Mind, first we have to get there.

I find the easiest way to get Earth supplies to Venus is the Hohmann trajectory. This is an orbit... based on the Sun. We need to shift that to some orbit around Venus. That is: Delta-V. Hop David calculates 400 m/s. He gave us a spreadsheet, which is XLS but easily conversible to ODS for those who don't trust Bill Gates. I am looking at F51 insertion burn from periapsis. Periphrodisis, here. Also called pericytheree.

This orbit upon delta'ing the V shall be an eccentric / elliptical orbit. Venus' influence goes to 610238 km over the surface that is 616290 km radius, not far over Wiki's 616 Mm. (Nor from mine own maximal calculation 616176 km.) So this delta-V gets us an ellipse swinging from that down to - whereever you like, mate. The spreadsheet goes with 300 km up. The higher up, the more delta-V I need.

On initial entry, we're at an angle to the Sun. The "sphere" of influence is squashed. Given a unit sphere and angle θ the C# factor is Math.Pow(Math.Cos(θ)*Math.Cos(θ)*3.0 + 1.0,-.1). So: from straight-on zero radians a 0.87055 factor to, when at right angle π/2, cleanest 1. This initial θ differs from synod to synod over the metonic. Either way I expect initial effective influence to be on the high side; but angle will change in a fraction of the Venus year. I expect Venus' influence to dwindle as far down to 536412 km. No matter what happens I need more delta-V to pull in my orbit.

Such craft which we want to return to Earth on the next synod or two, will prefer resonance with said synod. That 616290 km maximum / 6352 minimum around the planet is, I reckon, 311321 km semimajor. With more delta-V I can increase the semimajor to 317078 km which yields synodic 20.13 days, 29:1 against the Earth/Venus synod. At the same time I'm aiming for worst-case 536412 km maximum... 219335 km pericytheree. Obviously I cannot use the atmosphere to brake me to that.

But that's for the return trip back to Earth. That's a different angle than the angle I arrived. My arrival angle is useless for Earth for the next four synods. The distended orbit I start in is not even good for SVL2 for another, what, 400 days. We do get SVL1 sooner - not the most useful Libration, and the riskiest for capture by our own Sun besides. So in the meantime, I want to circularise this orbit some. (I'll have to twist inclination too but only by, what, 1.5 degrees.) I can lower my e by skating atmo; here, to pull this orbit closer to Venus for an overall (much) shorter "month". Kerbalians have other ideas, doubtless better ones.

As long as I'm adjusting orbit I care less with being resonant with Earth directly; more with interfacing with whatever stations we have over Venus - or, indeed, with Venus herself and its Lagranges, as in those polar satellites. Hop David figured the atmo could knock apocytheree down to 68000 km. Maybe alongside its personal satellite, one of five to receive cargo. Five other 300-68000 km satellites are angled toward the return Hohmann.

For such craft as I'm returning to Earth I've got 467 days for well over 23 "months" to pull the apocytherion in, and then to push it out where I want it.

We depend here on the (new) satellites' mass and robustness. Maybe it takes another synod or two to convert a full habitat's orbit from Venus-facing to Earth-facing. The very angles might be closer on that later pass. That suggests sending spare Hohmann-ready habitats at least modules. The good news here is that Venus got lots of energy and propellant. If we want to push craft to alternatives, yea even unto SVL2: we can! - once we get started.

Once we really get going here: old Earth might dispense with Type II shots like Pioneer and Magellan, forever.