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Let's assume it is possible for a spacecraft to travel at the speed of light (I've read the interstellar book by Kip Thorne, apparently this is theoretically possible if you swing around two black holes)

I have watched the video where the traveling of a light particle is simulated and while planets are certainly big enough so you can adjust your route, what would happen if a rocket (or spaceship in general) would collide with an earth-like planet (i.e. a planet having a massive surface). Would we burst through the whole planet, make it only to a core, or just a few km? I know what happens when a meteor lands, but obviously they aren't traveling at the speed of light.

And one similar another question - when a spaceship is traveling at the speed of light, is there a problem with collision with smaller objects? I think you can't avoid millions of rockets in outer space, it would surely damage the spaceship, wouldn't it?

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    $\begingroup$ It is not possible to travel at the speed of light. It would require an infinite amount of energy. Please rephrase your question to say "99%" of the speed of light, or 99.9% or some other real value. $\endgroup$
    – James K
    Commented Sep 30, 2015 at 17:06
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    $\begingroup$ I'm voting to close this question as off-topic because it is purely hypothetical and not directly related to Astronomy. $\endgroup$
    – Mitch Goshorn
    Commented Oct 4, 2015 at 13:52

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I don't know about a spaceship, but the XKCD guy wrote an interesting article about what would happen if Earth was hit by a solid asteroid, travelling at various different speeds: what-if question: Diamond

The ship would be a lot smaller than an asteroid, so I think the damage would be a lesser version of these descriptions. (The most extreme case described is the whole planet being vapourised and even neighbouring planets being affected by the radiation.)

As for the second part of the question - protecting the craft from minor collisions - I admit I have no idea how to work out the kinetic energy from collisions at such high speeds. But even a grain of sand would at least damage the front of the craft, and I guess some sort of thick shield would be needed to protect against erosion from interstellar dust...

Even at normal orbital speeds, Space Shuttle windows have had minor damage as this paper describes...

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  • $\begingroup$ Awesome, thanks, could you add some comments on the second question aswell? $\endgroup$
    – mohnstrudel
    Commented Sep 30, 2015 at 15:41
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    $\begingroup$ At near the speed of light there would be huge problems with collisions to overcome. Not just the high heat of impact and likely fusion of what you crash into at high speed, but at close enough to the speed of light, particles will actually pass through each other (the what-if article touches on that). A google search will provide a number articles on the difficulties with near the speed of light travel. Here's one I like: space.com/8011-warp-speed-kill.html $\endgroup$
    – userLTK
    Commented Oct 1, 2015 at 11:44
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    $\begingroup$ Here's another one (short and sweet) that touches on tiny sand grains. csicop.org/si/show/on_problems_with_near-light-speed_travel The good news is, there aren't many sand grains in space (er, I think), at least until you approached other star's Oort Clouds. $\endgroup$
    – userLTK
    Commented Oct 1, 2015 at 11:56
  • $\begingroup$ Thank you for the update on your answer, Andy and the interesting comments, @userLTK $\endgroup$
    – mohnstrudel
    Commented Oct 1, 2015 at 16:04
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Given Earth's atmosphere, the added drag on the ship would make it nearly impossible to collide with the planet without losing momentum (if we're traveling at 99% the speed of light here). Assuming somehow the ship were to maintain speed, the heat and drag cause by the atmosphere at this speed would tear any known design to pieces, causing it to burn up and be destroyed before colliding with the surface (any pieces that fall to earth would be traveling slower than the speed of light).

All of this aside, estimating gamma at ~70.2 for the speed of light, per kilogram, a collision should release ~5.47 x 10^17 joules (or around 132 megatonnes). To give some perspective, Meteor Crater in Arizona hit with an estimated 10 megatonnes. This sounds like a huge amount of energy (it is) but wouldn't transfer into a spaceship having the mass to vaporize or even melt the earth. The blast that led to the extinction of the dinosaurs was estimated to be ~100 million megatonnes. So if the rocket were around 1 x 10^6 kg then a collision could hypothetically (in this unrealistic scenario) have the same climactic impacts.

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    $\begingroup$ Let's say, we have 120 km for our supposed to be wrecked-into planet atmosphere (according to this site - bencraven.org.uk/atmosphere.html). Let's calculate with some rounded speed of light of 300 000 km/second. 120km/300000(km/second) would result in 0.0004 seconds required for our ship to reach the hard surface. You think the ship would've been destroyed within 0.0004 seconds? Is it even possible? $\endgroup$
    – mohnstrudel
    Commented Oct 1, 2015 at 16:13
  • $\begingroup$ Traveling at the speed of light isn't even possible. But, assuming it was, and somehow the atmosphere did not slow the ship down, the friction encountered with the atmosphere would rip any conceivable ship apart instantly, possibly even vaporize it. By your logic, the ship should be able to pass through Earth unharmed if it is moving fast enough. $\endgroup$
    – Brumder
    Commented Oct 2, 2015 at 19:29
  • $\begingroup$ So what is the answer to the original question ? Does the Spacecraft go through the Earth or is it stopped by the mass of the Earth ? $\endgroup$
    – Peter U
    Commented Jul 2, 2018 at 14:30
  • $\begingroup$ It is stopped by the atmosphere. Writing-off Earth's atmospheric impact on a spacecraft is the same as assuming you would be able to jump off of the top of a skyscraper into a large pool and be completely unharmed. Even without atmospheric influence, the ship does not "go through" Earth. $\endgroup$
    – Brumder
    Commented Aug 14, 2018 at 16:16

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