Assume a 200 ft diameter by 500 ft long spaceship traveling just under the speed of light, like .99999c.

To an outside observer, does the ship really appear to be only a little over 2 feet long? Like, instead of a beer can shape, it would be basically a flat disc 200 ft in diameter? Assuming a vantage point far enough away to be able to see it pass, and assuming a telescope with some sort of compensation for the blue and red shift as it approached and passed, would you actually see relativistic compression?

Second, what would happen if the ship hit a star at that speed (or faster)? Would the ship’s momentum and “relativistic mass” protect it and let it pass through unscathed, like a knife through butter? From the ship’s POV it would take about 4 seconds to pass through (if it survived). Or would it be the biggest firework anyone has ever seen? Either way, would the star survive? Would it make a difference if the ship didn’t go through the star’s core?

Length contraction happens and would be observable and there are a number of famous thought experiments.

As this message board is relatively limited in the ways information can be presented here is a video that will illustrate some of the more fun implications with trains, tunnels and guillotines.

https://youtu.be/kGsbBw1I0Rg

On the second question, neither. The average star is actually very dense in the interior – the sun’s core is estimated to have a density of about 150 g/cm[sup]3[/sup] and a temperature of about 15.7 million K. The object would vaporize instantly long before it got there, when it hit the outer layers of the stellar atmosphere.

Oh, I think not.
The outer layers of a star are very hot, but they have little energy. That is why comets have skimmed the sun and survived to continue on their journey: https://scitechdaily.com/unusual-comet-skimmed-past-sun/

Absolutely not. Here is a nice video. There are some interesting optical effects, though.

I think you would simply die and the star would escape unscathed, unless you posit some ludicrous initial conditions.

Of course, I made a math error in the OP. It would take about 4 seconds from an outside observer’s POV for the ship to travel through the star. it would be about .02 seconds from the ship’s POV. If they got vaporized, they’d never know.

But could the star just take it? A slight bit of localized heating and return to normal?

I assume the ship hitting a planet at that speed would pretty much destroy the entire ecosystem. But, would the planet itself have serious damage? Deep cracks? Split?

I’m not sure a distant vantage point would help you: I think either you’re so far away that you just see a small point quickly moving across our field of view, or you’re so close (yourself, or due to a telescope) that all you see is a flash when it appears and disappears in your vision.

However, that’s a boring answer. So assuming you could actually watch it move by - yes, you would see the ship shortend. In addition, you would see it strangely rotated, almost distorted.

For an illustration, watch this: https://www.youtube.com/watch?v=_ecEd9GKzog, especially the part with the street car. That is a section from a longer animation, which I remember having seen in better quality before, but cannot find at the moment.

If you want to google it yourself, try terms like “relativistic ray tracing”. In addition, spacetimetravel.org has a good collection of relevant stuff. And finally, if you want something more interactive, the MIT has released a free game called “A slower speed of light”.

It depends what you mean by ‘appear’. I suspect you mean" what visual image of the ship does an observer see?". The answerhe visual image will be distorted from the ‘rest image’, but exactly how depends on the angle of viewing. For an observer perpendicular to the spaceship’s axis of motion the image does NOT appear contracted as you may expect, instead it appears rotated and this is called Terell rotation (see link for visualization). The reason for this light from different parts of the ship takes different amounts of time to reach the observer.

Obviously working out the exact details of a collision is very complicated, but clearly the forces involved in the collision will be immensely larger than the forces holding the spaceship together.

Interesting. But all the simulations show the view from the ship’s POV. What does the ship look like to the “fixed” observer?

Fascinating! I had never heard of this. And it’s all right there in Wiki, if you know what to ask.

I’m assuming your star is our Sun, with it’s diameter of 864,000 miles. In that case it would take 4.6 seconds for a near-light speed ship to travel that distance from the ship’s PoV. Time never contracts or expands inside a reference frame. It only appears to when that time is compared to the elapsed time in another reference frame. Time always passes at 1 second per second for everyone everywhere.

Yeah. A star is freaking enormous.

It would look a bit distorted and rotated, like in rat avatar’s video with the train car.

As related to hitting a star at a relative velocity that is close to speed of light just consider what happens to Large Hadron Collider.

The LHC accelerates protons to 0.999999990 c before causing a collision.

A space ship traveling near the speed of light hitting a star would suffer a similar amount of destruction. Although on a practical level remember that all EM emitted by a star will also be shifted into high energy gamma-radiation and as the ship approaches the star it will suffer the effects of that too.

Hmmm. Thinking about it, this isn’t right. Strike the whole thing except for the last sentence, which is true but not relevent here.

While all analogizes and 3D depictions will have problems here is another video that will help build some type of intuition of the effects.

https://youtu.be/i6AouFHLb2g

Note it is a 3D video so pause the video and use your mouse to look around. None of these are going to be perfect but this video will help show just how crazy things get.

I’ll guess your 500 foot spaceship has a mass of about 40,000 tons, like a medium sized aircraft carrier. Then traveling at .99999c, it has a relativistic kinetic energy of about 2 x 10[sup]26[/sup] J (according to this calculator).

The gravitational binding energy of our sun is about 2.5 x 10[sup]41[/sup]. The ship’s K.E. is less than a millionth of a billionth of what would be required to disrupt the sun.

The Earth’s gravitational binding energy is 2.2 x 10[sup]32[/sup] J. The ship’s kinetic energy is still a factor of a million lower than that.

Getting to your second question, its all about energy. There is no way you are surviving, but one might ask how big a boom you leave when you hit.

Going at 0.99999c will give you a Kenetic energy of mc^2*(1/sqrt(1-0.99999)-1) or m2.8310^19 (meters/second)^2

For arguments sake, lets say that your spaceship is a souped up Delorean that with you as a single passenger tips the scales at around 1350kg. In which case the total energy 3.83*10^22 J. Or the equivalent of a 9.2 Teraton bomb. Observable solar flares vary from between 10^20 J to 10^25 J. So solar scientists on earth would probably record your passing but alas the rest of the earth probably won’t notice.

ETA: didn’t notice the mass of the ship in the OP, so take markn+'s answer.

For comparison a 747 is 230 feet long, and it’s wingspan is under 200 feet. It weighs 7.35 x 10[sup]5[/sup] pounds. Suppose we scale one up to your dimensions, maybe multiplying the weight by 8. If we convert this to metric we get 5.88 x 10[sup]6[/sup] kg.

But the weight isn’t that important compared to the speed. We have an object going hella fast, about 3.00 x 10[sup]5[/sup] km/sec.

The kinetic energy of such an object would be

0.5 x mv[sup]2[/sup]

or

0.5 x (2.65 x 10[sup]6[/sup]) x (3.00 x 10[sup]5[/sup])[sup]2[/sup]

I get 5.83 10[sup]17[/sup] joules of energy. Modern nuclear bombs max out at around 210,000 terajoules, or 2.1 x 10[sup]17[/sup] joules. So if our ship’s collision resulted in a net momentum of zero of the system consisting of the ship and star, then it would be like half a nuclear explosion happening in the star. Considering that a star is a big fusion reactor, I am guessing the star won’t notice.

My calculation does not take into account the relativistic increase in mass. At that speed it would be significant.

To add some context to just how dense the core of the sun is. It can easily take 100,000 years for a single photon to travel from the core of the Sun to get to the surface but it only takes 8 minutes to reach the earth once it does. (liberal use of the term single photon but note my avatar)

Note that fusion in stars does not happen due to pressure as much as being due to the fact that matter is so densely packed that due to quantum effects the changes of a particle will end up inside another particle is high enough that it happens enough to sustain the reaction. On earth we have to use a lot more energy to accomplish fusion because we don’t have this “closeness” which allows it to happen with much less energy.

The comet example isn’t really relevant. Comet nuclei are composed of ice and other volatiles that outgas as they get close to the sun and if they come close enough can get completely vaporized by the heat. The article cites an unusual comet that came within 2.2 million miles of the sun and survived intact.

That’s not what we’re talking about here. To an object traveling at 0.999…-whatever of the speed of light, a collision with any matter at all – no matter how tenuous – would release colossal amounts of energy (ETA: in fact, the energy given in post #17). Just how far into a star do you imagine such a spaceship would penetrate intact?