Under no circumstances or conditions is it permissible to discard obligatory prayers, and they must be made in any possible situation. If possible, a person who is in space or on a spaceship should try to settle in a fixed location using the available means in order to complete his prayer; and if he can not do that then he should make his prayer in any way possible, even if he can only use motions.
If an Astronauts stand facing towards the earth, then they are facing the qibla and they should pray in that direction, but if they could not distinguish the earth's position, then they must pray in all four directions (if possible), and if all directions are not possible, then they must pray in as many directions as possible.
As far as wudhu goes, if he can or if it is possible then he should make wudhu, and if it is not possible then he should make tayamum, and if that is also not possible, then he should take precaution and make prayer without wudhu or tayamum, but later he should make up the Qaza prayers for the prayers which were made without wudhu or tayamum.
And on the subject of complete prayer vs. traveler's prayer; if an astronaut were to know that he was going to stay in one area of space for at least ten days then he should make his prayers complete, and in any other instance then he should shorten his prayers. However, if being an astronaut is his occupation, then as long as after the first trip, he does not stay in his hometown or outside of his hometown for more than ten days, then on his second trip his prayers will be complete. However if he were to stay in his hometown or other than his hometown for ten days or more, then if he traveled to space again then he would have to shorten his prayers.