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what benefits will a rocket get if it is made to go at a speed close to light... like 3 X 10^6?

if the rocket is supplied with more efficient fuel and designed to obtain lesser drag there are possibilities of attaining such a speed.

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    $\begingroup$ Besides "gets there faster", what benefits could you possibly be expecting? (Also, your second sentence is phrased as a statement, but is quite wrong, unless "efficient fuel" refers to radically different nuclear-powered designs that don't really use conventional thermal-expansion exhaust for thrust.) $\endgroup$ – Nathan Tuggy Mar 23 '18 at 8:25
  • $\begingroup$ My "efficient fuel" meant those things which you just mentioned... to be more precise i would like to know if there would be a problem with the spacecraft ( with the existing technology of designing) while moving at such a great speed $\endgroup$ – Shreya Sunil Mar 23 '18 at 8:30
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Well the benefits (as Nathan eloquently put it in the comments) is that you'll get where you're going faster, and that's about it really. Not that I'm saying that's a bad thing, who doesn't like getting where they are going faster?

You don't specify any units on your velocity in the question but you do mention being "close to the speed of light" and while we don't have to worry just yet (since we can't get even remotely close to the speed of light with current propulsion technologies) travelling close to the speed of light in the Earth's atmosphere isn't just a matter of "reduced drag", heck at those sorts of speeds conventional aerodynamics just doesn't apply. Also it's worth mentioning that it really wouldn't end well either for the spacecraft or for anyone in the vicinity for that matter.

Out in space itself travelling close to the speed of light would be great - it would obviously make trips to nearby star systems feasible, however we are long way off from having a propulsion system that can achieve those sorts of speeds. As for how the spacecraft would fare there would be two areas of concern:

  • how fast we could accelerate/deccelerate the ship to/from those sorts of speed as it's the acceleration that will place stresses upon the ship (and any squishy meatbags inside)

  • how we navigate at those sorts of speeds - you aren't going to have a lot of time to "dodge" anything and you really don't want to hit anything!

TL;DR: This is pretty much all moot since we don't have anywhere close to the propulsion know-how to accelerate to near-light speeds and by the time we do our "existing technology of designing" will probably be irrelevant.

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