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"Lunar Lander" does not resemble this game at all:
- It was not an arcade-style game.
- The game was about building and launching a rocket. It had absolutely nothing to do with landing on the moon.
- The graphics were primitive by current standards, but a good deal more advanced than what's in "Lunar Lander".
What part of "It was not an arcade-style game." was so hard to understand? Stop suggesting arcade games! It was probably something much more along the lines of the original Oregon Trail.
Edited by Random888Wikipedia did come up with Rocket Ranger as a possibility in that it does include building and designing a rocket that is used in a jet pack even though some aspects do not match up but the real reason for no one trying to identify your game is that your tone is rude. It's not like everyone is suggesting arcade games when only two persons have even attempted a response and saying that they did not understand makes it worse.
Edited by Kevonni4Sorry for my earlier rudeness. I guess GIFT got the better of me. It's not any of the games suggested above, but "Project: Space Station" is at least on the right track.
I am sorry as well about overreacting. There was one other possibility mentioned on Giantbomb called Space Agency which fits all aspects of your description except for when it was released. What do you remember about the game that makes you think that it was from the 1980s?
Rocket Factory matches everything you describe. https://www.youtube.com/watch?v=itrfdpD3uv4
I really don't see how their rocket program got funding for rockets that launch, and then hang indefinitely in the air such that the pilot has to parachute out.

A really ancient computer game, probably mid-to-late 1980s. You build and design a rocket. Then you see the rocket launch, followed by, if I recall correctly, the astronaut parachuting down.