When the first spaceship is launched, the game is basically over. We should do something to give other players opportunity to react and hope not to loose a game anyway. That could be done in two ways:
1. By extending the Alpha Centauri length arriving time ("length time" value multiplier),
2. By cutting off the maximum possible value of success rate - from 100% to 90%, or 80%, or 75%, etc. (total "success rate" value substraction).
1. "Length time" value multiplier
Well, except for the actual cost of building space-parts, extending the overall time length of arriving is an option. In the game, the spaceship arrives in a dozen or so turns. Oh really? Alpha Centauri is ~4.4 LY (which is 4.4*10^13 km) far away from the sun. That's about ~40 trillions kilometers away. And all that journey in... just 10-15 turns? Assuming, that (in late game) 1 turn = 1 year, it would be rather hard to be done... The flight of the fastest possible ship should last about 100 years (in reality, it would last not 100, but at least one hundred thousands or million years - what we're talking about is four light years length!).
There should be a multiplier to extend the expected length of flight (example: in normal game flight lasts about 15 years; you can multiply the value by a number from 1 to 10. This way, the player just choose how many times more needs a spaceship to arrive the Alpha Centauri.
Let's say the spaceship needs 100 years to arrive. If we should be able to build a spaceship in ancient age (rather impossible), it would take 5 turns (1 turn = 20 years). But if when 1 turn = 1 year, it takes 100 turns - long enough for the others to launch their own spaceship (and destroy the one who launched it in the meantime).
Here we have to carefully point it out: when the civilization launches the spaceship AND this civilization will be destroyed until it arrives the destination, it looses the game anyway! We can justify it by the pseudo-scientific blahblahblah, that the spaceships "needs to receive a signal from the Earth during the journey", and when the signal stops, the spaceship is loose - I know it's b***it, but that would give other civs some time to react and try to perish the civ that was capable to launch it; also, it would justify the loose of the game by the civilization, that was (in the meantime) destroyed, but would (eventually) reach the destination after all.
2. Total "success rate" value substraction
When the hostile civ starts building a spaceship, it is theoretically possible to stop him. But if he already launched the spaceship, there is nothing we can do! However, when the possibility of reaching Alpha Centauri is 90%, we still got the chance that the spaceship may crash and we're still in play. As for now, with all-parts-spaceship, he already won (100% of success). But there is a solution.
Here comes another trick. In my opinion, the flight should last at least 50 turns (possibly 100) to give the other civs a time to destroy the enemy, but only with the assumption, that probability of success can never reach 100% (let's say that the probability of success for the best possible spaceship is set to 90%; that means the highest possible rate of success should never exceed 90%). This way we could give theoretical chance for other civilizations to launch their own spaceships, even if not completely finished (faster but more uncertain). In real life nothing is 100% sure - especially when we talk about the space missions.
The example scenario A: Aztecs launches their 100% done spaceship (all possible parts), which reaches maximum (90%) probability of success. The spaceship is big (thus certain), but slow, and the flight will last 100 turns. This gives scared Russians few dozens of turns to hurry their own project and launch (unfinished, thus fast, but uncertain) spaceship before the Aztec's spaceship arrives Alpha Centauri (the Russian spaceship is unfinished - only 50% needed parts - so they gain 45% only of probability, but it's better than nothing; on the other hand, it's two times faster). Because, theoretically, Aztec mission can fail, which gives some chances to the Russians. Besides, the Russian spaceship is half-finished, so it takes half time for them to arrive (thus, they might even overtake Aztecs if launched quick; instead, Russians are playing Russian roulette, because it might crash much easier than Aztecs' one).
The example scenario B: Aztecs launches their 100% done spaceship (all possible parts), which reaches 90% probability of success. The flight will last 100 turns. The Russians may launch their own project (even if unfinished well, thus with probability of 40%) and pray that the Aztec's project fails, but they decide not to count on their luck. Instead, they choose to perish the Aztecs before the spaceship reaches the destination ("the Aztecs is gone; the leading signal has ceased and their spaceship didn't arrive the destination"). They have 100 turns to do so, which is enough time to perish other civilization.
Let's look at the dependencies: the more advanced spaceship you build, the greater probability of reaching the destination you get. But, on the other hand, the journey takes more time, so opponents will have more turns to kill you (and stop the signal). Greater probability of success means longer journey: the complete spaceship reaches 90% of probability, but it takes 100 years to arrive (greater mass); the spaceship with 50% parts reaches 45% of probability, but it takes 50% less time to arrive (50 years instead of 100, because it's 50% lighter). Instead, you might want to periodically flood the space with 25% done scrap, but very fast (1/4 mass = 25 turns), and hope some will arrive (90% / 4 = 22.5% chance for each of arriving the destination). The shrinked probability value means that the civilization, that launched the spaceship, might not content themselves with one ship, even very well made - they might start building another (to take precautions in case if the first mission failed); or to hope for the success and focus on the defense of civilization in case if it's attacked.
Anyway, from all of it, lowering the maximum success value by x% seems to be good idea. If somebody likes to play risky, unpredictable game, here it is!