to Collect the Spaceship Parts, you need the Sidemission
from Omega called "Far Out" This Mission is available after the Mainstory Mission "Fame or Shame" (circa 15-20% in the Game)
You see a new green "?" on your Map. This Mission is for Franklin only! Trevor and Michael cant start or End this Mission but with this 2, you can collect Spaceship Parts too.
Drive to the "?" and after a little Cutscene you can now collect the 50 Spaceships Parts
in the whole World of GTA 5.
IF you finish with the 50th Part, Omega send you a SMS to meet him. Drive to the new green "?" and after a Sequence you can go inside in your brand new "Spaceship" :)
Two Words to the Collectible Parts.. First, you have in the Game NO Overview which Scrap you have and which Scrap not! but i create a Map for all of us :) And the other Option is the Social Club from Rockstar. Go to http://socialclub.rockstargames.com - create an account, link your Gamertag and then you see which Part you have or not.
And second, for 3 Parts ( 5 / 35 / 36 ) you really need a Helicopter, there is no other Option to reach this 3.
The Bridge from Number 5, is a part from the Close Shave
Achievement Fly under 50 Bridges / 15 Knife Flights)
Here my selfcreated Map with all (Video) Numbers:
Video: The Links in spoiler open in a new window, in the YT Description you have the same Timeline. There can you click a Timestamp without open a new Window.
I create a Video and Map for all Letter Scraps, Spaceship Parts and Stunt Jumps. Click the Spoiler below to see a Preview. The Timelinks, Maplinks etc can you found in the Youtube Description.