We will soon have fibers leaving just five techs and 43,800 beakers left to research. My guess is we will complete research on the last required tech in about 33 turns after finishing fibers. (See discussion below.) I took a stab at laying out the timing of our spaceship build assuming we want to build Apollo at the last minute and have pre-builds ready for all ten parts set to complete the turn after we build Apollo.
Since we're mobilizing soon an additional constraint is to be able to remain mobilized as long as possible. I will assume we will not use unit pre-builds during mobilization. Under mobilization we are limited in the invisible pre-builds that are available. We have only one battlefield medicine (500s) pre-build and airports (160s). For visible pre-builds we have Manhattan and Universal Suffrage (800s each) and the United Nations (1000s). We will have to decide what level of invisibility we want to maintain, remembering that our plans are always susceptible to being uncovered by spies.
We will have to devote 11 cities to the Apollo and SS parts pre-builds. If we plan on using our top 11 production cities for these pre-builds, does it make sense to say mobilized as long as possible? I guess we could use lower production cities at least for the 160s parts.

The airport pre-builds cover these nicely. We have enough cities doing ~10spt that could be used for these.
That still leaves four parts @320s, two @640s and Apollo @500s with only 160s airports and one 500s Battlefield Medicine for (invisible) pre-builds. Airports will only work for one turn in The Treasury, and two turns in The Chamber, The Institute, The Admiralty and The Silo. The options are to demobilize several turns before launching (in order to be able to use solar plants (320s) and the palace for pre-builds) or use Manhattan, US and UN as (visible) pre-builds. The latter option also means we forego building Manhattan and nukes. Even using the three wonders as pre-builds we can only get three of the 320s SS parts not quite half-way with pre-builds. The conclusion is we'll have to demobilize some turns before launching.
Here's my time line. t = the turn we launch our SS.
- t-16: Begin 160s SS part (airport pre-build) in The Phoenix (10spt).
- t-14: Begin 160s SS part (airport pre-build) in The Marina (12spt).
- t-11: Begin 160s SS part (airport pre-build) in The Pier and The New Yard (15spt each).
- t-9: Begin 640s SS part (airport pre-build) in The Institute (72spt) and The Chamber (78spt).
- t-7: Switch The Chamber and The Institute to a wonder pre-build.
- t-6: Begin Apollo (Battlefield Medicine pre-build) in The Treasury (102spt).
- t-6: Begin 320s SS part (airport pre-build) in The Gulag, The Arboretum, The Silo and The Admiralty (53 spt).
- t-3: Demobilize.
- t-3: Switch The Gulag, The Arboretum, The Silo and The Admiralty to solar plant prebuilds and MM shields to at least 54spt.
- t-2: Switch The Treasury to Apollo.
- t-1: Finish researching last tech.
- t-1: Build Apollo in The Treasury.
- t-1: Switch all pre-builds to appropriate SS part.
- t: Complete all SS parts and launch.
This plan let's us stay mobilized the longest. Any spies in our country would not see our spaceship progress until the turn before we launch. We do have to use wonder pre-builds as early as seven turns before our launch and this may tip off our rivals. If we use Manhattan they may think we want nukes. If we use the UN we might be able to sell that as a legit build since by then SABER and FREE will know we have a BABE settler sequestered. Once we demobilize our competition may discern our plans if they investigate the cities building solar plants. The troubling aspect of that is they will also be able to easily calculate the timing of our launch. They would only have a couple turns to react though.
I'm not a micro-manager so I'm not certain this is the
best plan but I think it is doable. Some of the pre-builds are tight with little overflow meaning pollution could end up costing us a turn.

We also have to begin the 160s SS part pre-builds early meaning we need an accurate estimate of when we will finish the last tech and we'll need it 16 turns ahead of time. We could substitute The Aerie and The Meeting Room for The Phoenix and The Marina cutting our lead time down by five turns. We may want to keep those two cities on military production though.
When is t? We will have fibers on turn 226. I assume we will research in the following order: laser (8400), robotics (9600), space flight (9000), satellites (7800) and superconductor (9000). I estimate we'll have 1200g in the treasury box and this assumes we don't spend any gold. Here's my estimate for research times:
- Laser: turn 232 (5 turns @80% and 1 turn @40% costing us 150g leaving 1050g)
- Robotics: turn 238 (5 turns @80% and 1 turn @100% costing us 800g leaving 250g)
- Space flight: turn 245 (6 turns @70% and 1 @50% netting us 200g leaving 450g)
- Satellites: turn 251 (5 turns @70% and 1 turn @60% netting us 100g leaving 550g)
- Superconductor: turn 258 (6 turns @70% and 1 turn @50% netting us 200g leaving 750g)
I used the turn 224 save and CA II for these estimates/guesses. I was conservative since I am not sure how many units we'll be building while mobilized. Each unit we build will cost us 2gpt.
If this time line is correct we'll be able to launch on turn 259. We'd have to demobilize on turn 256. We'd also have to begin our 160s pre-builds before we get spaceflight. Actually we'd have to begin the 10spt pre-builds before we
start researching space flight.
Comments welcome.