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Yes, easily with a Kraken drive, or unlimited fuel cheat enabled.  I've done both, Kraken by accident, cheating not by accident. 

KSP doesn't model relativistic effects, so theoretically it's possible.  Enough fuel and you can reach any speed you want.  Practical, no.

 

 

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There's no way to do it in stock without the debug menu or some weird Kraken drive. Taking the PB-ION engine's 4200 s-1 Isp as reference, you would need a mass ratio of 1.5*10^3162 to reach the speed of light.

Most mods aren't going to be able to do it either. To do it on a mass ratio of 1000:1, you would need a specific impulse of 4,427,058 s-1 of specific impulse. This would entail an exhaust velocity of 0.145c.

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3 hours ago, The Aziz said:

Thanks to Kraken I once got slinged out of the solar system at approximately 44 million times the speed of light. So yes. Millennium Falcon is really a piece of slow junk in comparison to my OKTO2 probe core.

I think I've had that happen to me with the mechjeb AR202 case back when it was massless.

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Just recently i *kinda* broke the speed of light many many times over, full stock, no cheats, and everything was still controllable. the key is to get an escape trajectory around the sun (super easy using a jool assist) and switch you velocity mode to surface. Warp a couple (hundred if you use mods) years and you are well above 300m m/s. I got a speed that was 17 digits long (10000000000000000) before my game softlocked and refused to let me load a save game. 

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5 minutes ago, The_Cat_In_Space said:

Is the Kraken drive the glitch where your ship or Kerbal suddenly ends up in space at an altitude of NaN and an escape trajectory out of the sun?

"Kraken drive" is a nickname for types of propulsion which rely on glitches or exploits in the code, at least some of which have been fixed.

For example, a Kerbal climbing up a ladder into something overhead would produce an upwards force in defiance of the laws of physics, permitting any speed you want so long as you are patient enough.

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18 hours ago, Starman4308 said:

For example, a Kerbal climbing up a ladder into something overhead would produce an upwards force in defiance of the laws of physics, permitting any speed you want so long as you are patient enough.

 

Ah, the old lifting by the bootstraps :D

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