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It's not hard to do, just keep burning till it tells you you are good, then turn around and burn retro before you actually get shot out into space.
So you had the right idea you just need to go abit further.
Just go really fast and you'll trigger the condition.
Some test contracts want you to right click the part and hit the "test part" button, others want you to activate the part through staging (The space bar.) The contract should say which.
Just by the way; most people skip part test contracts unless they are on the pad for easy funds. Part contracts are rarely worth the reward for the work involved.
I'll strap on an extra 0.1 tons of junk for some extra munny.
i use probe to do it with a good antenna.
once done, i delete it. And keep the cash. :)
There are two different conditions that look identical in the game UI:
(1) - Your orbit is *really* an escape trajectory, meaning it has a hyperbolic shape and the apoapsis is a negative number (*) (which is the formula's way of telling you it's not an actual valid real distance measurement - i.e. you don't really *have* an apoapsis).
(2) - Your orbit is elliptical and has an actual apoapsis, so it's not *really* an escape trajectory, but the apoapsis is still high enough that it's outside the sphere of influence of the current body.
The game draws both of these with almost identical looking UI elements in the map view - you see your arc of predicted orbit leaving the body. They have alomst the same effect in the game (because with how it works. (2) is kind of a "soft escape" where it wouldn't really escape in the real world, but it does in KSP.)
The contract won't be satisfied until you have condition (1), even though condition (2) *looks* like it would be enough when you look in the map view, and in practical terms of gameplay it's the same given that KSP will make your ship escape when you leave the SOI. The contract is merely running the math formula and looking for a negative number for apoapsis, so it will only be satisfied by condition (1).
(*) - Technically because in the game the apoapsis is measured from the sea level surface of the body, instead of the true radius to the center of the body, your orbit is hyperbolic once (Apoapsis + body_radius) < 0, rather than just Apoapsis < 0 (i.e. an object that glitched through the ground that is now orbiting underneath the surface of the world in its hollow interior could have an apoapsis < 0 but still not be hyperbolic if that Apoapsis is between the body's center and its surface.)
I'm pretty sure 50k contract won't require 6000+ delta v and there is rather Kerbin escape trajectory somewhere. You just need your Ap leave Kerbin SOI (twice as high as Minmus) which is roughly 1000m/s from LKO. You just have to be on that trajectory! No need to fly far.
As for test there may be 3 cases.
Running engine may be fine.
You may need it started with a staging sequence.
You may need to rightclick and hit Test in the context menu.
Place screenshot of the actual contract and we may point you out your mistake.
If it looks like you have an escape of Kerbin, but the contract doesn't count it, there's a chance all you need to do is just add a little bit more velocity, just a tad, to cross the threshold into a true hyperbolic orbit.
And you need to be on an escape trajectory out of kerbin, anywhere along the trajectory. then run test or whatever.
An escape trajectory from Kerbin is entering the Sun's SOI.
Did you actually read what I said?
I told him to turn around and burn retro before he actually left.