Sunday, November 29, 2020

Who meets whom?

Looking at Hop David's ten cyclers I drew up a diagram for the angles when inbound Hohmann starts. Running in the direction of the ecliptic, and given the almost 0.8 year of the Venus-Earth Hohmann ellipse: that's a pentagram. Morning Star indeed! (That ellipse is 1.3 of a Venus year. Odd number.)

Anyway the inbound from the A synod will find itself 1/5 a circle ahead of Terra on its triumphant return to nothing, at the start of B. 72 degrees. (Actually a tiny bit less but I'm allowing for a solar-sail to keep the most valuable junk together so Earth and Lagrange tradesfolk can get it all back some day.) That's ahead of Achaean STL4 at 60 degrees - still in halo, but we're additionally discussing whatever doesn't stay there. Which a Hohmann won't because it is going forward in the ecliptic, and faster than STL4 is going at that. (Unless it's delta'ed.)

The fun starts because Venus and Earth are pretty close together when a Hohmann starts - any Hohmann. They actually get to the zero degree Conjunction when the inbound and outbound Hohmanns are in orbit / transit. On 9 November 2005 when the Venus Express started (admittedly a few weeks late so Venus was further along), the angle looks less than 45. The two planets and that Hohmann mission between them were all easily in the same quintant if that's a word. And that's when Earth launched its inbound Venusward; Venus outbound would be five days later when this angle is tighter.

And if I hadn't clarified all this, that angle runs behind Earth. The Venusward runs ahead of it but I don't care about this one for its own sake... yet.

Venus outbound, after any inbound synod starts, is in position to boost supplies to that very synod's inbound in transit. That synod's inbound can in turn (especially if it now has spare propellant) help the previous synod's outbound which is on its way to STL4. So who helps outbound?

Outbound should come into view from the inbound synod stray from behind STL5 and four synods back - which of course had also commenced after the outbound launched. Anything still here from Earth will have been stuck in interplanetary space for maybe six-and-a-half Earth years. (And anyone still alive, who didn't disembark at a Lagrange, will appreciate this additional foretaste of home.) For A, that will be the prior Metonic's B. One synod later, the outbound after B inbound would so "intersect" with the old C synod stray. And so on until post-E outbound when those Venus expatriates catch up with earlier A's Earthers.

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