Congress will most likely cancel the low-orbit program or force its commercialization so that NASA can focus on the moon. Most likely, for the first years, instead of Soyuz, there will be Hermes, and later we will see ITTL Dragon and Starliner.
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The station that will be built from the expansion of Columbus will be a proposal similar to that of BAe.
Keep in mind that the Shuttle almost got canceled several time in OTL with the Cold War still an ongoing "threat". (See
this thread for how Carter saved the Shuttle)
Of course if Congress ends up authorizing and paying for "Freedom" it's probably going to be the "Program of Record" focusing NASA on building and using it.
If they start "Freedom" it's not likely they will stop, OTL they never actually started it which was why Clinton could turn it into the ISS.
If the Soviet's continue Lunar Missions it's probably a toss up if Congress care enough to match them. The LEO space station could be argued to cost much less than trying to go to the Moon again.
Freedom was horribly mismanaged and NASA had the issue of putting EVERYTHING into each idea, making a monster space station to build ships for Mars, Congress did give NASA money to find contractors for modules (get hardware started) but NASA spent the money on the Freedom design
Clinton was able to cancel it due to the lack of hardware made and his want to cut enough to have a surplus in the buget. The ISS was started due to Goldin proposing an international program for a FAR cheaper station (and bringing Russia on)
Given that hardware for the moon program is being built, it is likely the US will land as long as the Soviets do, if the Soviets stop the US might do a few more missions as a "f-you" to the Soviets, but if the Soviets continue even with 1 mission per 2-3 years the US will have to, less lose A LOT of prestige due to walking away from the moon TWICE and giving it up to the Communists
Actually the opposite, Congress doesn't really want to support NASA going to the Moon again and would probably prefer having NASA focus on LEO instead. Even if the Soviets are still going to the Moon they can justify not trying to match them with "We got there First".
"We got there first" is a silly excuse, the US Public of the 80s is very anti-communist and any lead the Soviets had would be magnified by the US Media
(This is why the US suddenly started actually funding Commercial Crew in 2014, after Russia invaded crimea and the US had to develop their own capability due to public outcry)
At this point the TL is in 1987 with nearly 6 years of Soviet lunar landings, the US does have to respond to this by landing or it will take a huge prestige hit
I could see ESA being "torn" in the 90s between staying in LEO with their ongoing hardware and participating in the phase 2 american lunar program. With the more homegrown, independent capabilities and the worse precedents with cooperation with NASA compared to IRL I think the former would take precedence, but there's probably enough budget, political incentives (and ESA just traditionally never learning not to depend on other agencies, lol) that the latter won't be dismissed and will be pursued to some capacity.
And doing both to their full extent isn't possible with the european space budget of the 90s, especially with Hermes in production.
Depends if Britain has thatchers nationalism and cutting spending
and Germany reunifying would also kill their spending in ESA due to the costs associated with integrating East Germany with their financial system, government spending and debt
Likely ESA will be in LEO and partner with the US on Lunar missions, ESA even in the 80s and 90s was cheap IRL, and the countries making up ESA might not be willing to spend more (or give more of their existing budgets to ESA)
Likely just a small LEO station with a manned spacecraft, Ariane's dominance in the launch market will be significantly smaller due to American Launchers being in better shape ITTL with no Challenger gap driving people away to other countries
For the needs of its space station, ESA could develop an equivalent of NEP or even purchase the project from Russia.
I have said this MULTIPLE TIMES
Nuclear Power in Space IRL is asking for political and VERY public trouble, people protested RTGs, a full reactor will cause mass media attention and outright cause the mass public to think its very unsafe (watching CNN or FOX talk about it and fail to explain the safety, just issues and risks)
In THIS TIMELINE, A nuclear reactor KILLED a person in space, the reactor was partially protected and its disposal failed. the dead guy in orbit would be big enough news, when the media gets all the details and talks about it the issues of the Soviet reactor will be made public and cause a near Chernobyl-like reaction to nuclear space efforts (Chornobyl and TMI, then Fukushima killed Nuclear power, EU made Russia scrap RBMK's and Germany decommissioned all its reactors)
People do not CARE about technical details, that fact something happened ONCE means it CAN happen AGAIN and the public will be more antagonistic (same with the media), this happened with the Shuttle Program, Apollo 1 and 13 (NASA wanted to cancel 17 and Nixon 16 AND 17), The nuclear reactors failing (TMI, Chernobyl and Fukushima) all happened for various reasons, the public doesn't care WHY just that it DID happen
(It doesn't help that 99 percent of people have zero knowledge of these things beforehand, so their first experience with a nuclear reactor on the news is one blowing up, which would cloud later judgment)
Or in normal words, the Challenger disaster killed a generation of enthusiasm for human space travel, given that the kids who watched it believed that the risks are higher (even
ESA will likely have a small pressurized "tin can" space station, anything like the design you posted (a Russian proposal, not ESA) will not be flown, Ariane is too small and the US will not fly a nuclear reactor aboard their shuttle for obvious political reasons (aborts and stuff)