Is there a limitation of speed of a spacecraft in space because of suns gravity? Is the speed purely dependent on the engineering? Or other factors comes into play?
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Propellant: This is the main practical limitation on Δv, of the rocket's ability to change speed (go "faster" or "slower"). Assuming conventional-matter engines, no exterior propulsion, and that you want to slow down again at a destination, the maximum speed you can approach is half the speed of light.
In-practice, spaceships tend to be unable to accelerate by more than a few tens of kilometers per second. Although we do have the technology to get up to a few percent of the speed of light fairly easily, these are mostly nuclear technologies which the main spacefaring nations are too timid to ever dare launching.
Relativity: You cannot approach or depart a destination at a relative speed of more than the speed of light.
Interplanetary/Interstellar Medium: If you move relative to the tenuous gas/plasma in space at a high speed, it can damage your spacecraft. Things like "hydrogen atoms" start looking more like "proton and electron radiation".
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3$\begingroup$ "Half the speed of light" sounds like a nice round number. Do you have any references to support your assertions? $\endgroup$ Jun 9, 2018 at 0:41
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$\begingroup$ "...by more than a few tens of kilometers per second..." I estimate here the top speed of the Parker Solar Probe to be 190 km/s. Of course it is a bit of a special case, and uses orbital mechanics rather than propellant to do that. $\endgroup$– uhohJun 9, 2018 at 3:38
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1$\begingroup$ @OrganicMarble This comes from substituting best-case ISP ($30570000$) into the relativistic generalization of the classic Tsiolkovsky rocket equation to get a (rest-frame-relative) Δv of $c$. You then divide this by two to get the Δv you can use to speed up. You can read more about relativistic rockets here. $\endgroup$ Jun 9, 2018 at 5:43
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1$\begingroup$ @uhoh Yes. An additional example would be ion engines which, due to their significantly higher ISP than chemical thrusters, can have higher Δv. The Dawn spacecraft, for example, had 11km/s Δv from its ion thrusters, yet carries significant payload. A chemical rocket with this kind of Δv in a single stage would have a mass ratio of ≈19.7. $\endgroup$ Jun 9, 2018 at 5:48