Writing a book about an object in space

[nightsd01]

I'm writing a novel and a crucial element of this novel would be the following scenario. There are so many intelligent, thoughtful, and knowledgeable people on this forum that I'd like to hear what YOU would think about the following situation. Can you think of any naturalistic reasons the following scenario might occur?

It is discovered (through some unclear means) that a football-stadium sized object is hurdling towards the solar system at about 10% C (the speed of light/causality). This object is completely radio-silent, and is generating no obvious EM emissions. It is 'tumbling' a bit, making about 9 rotations a minute. It's not headed directly for earth, and will only get as close as near the orbit of Neptune before exiting the solar system. We have about 10 weeks notice before it makes its closest approach.

If you heard of this scenario, can you think of any naturalistic reasons that could cause it to occur? I personally can't think of anything, except maybe something to do with a black hole somehow accelerating a large body. I know that at some trajectories you can get a 'gravity-assist', though I have doubts that it would ever accelerate an object to such a large velocity, but I don't know.

Also, can you think of any technologies that would allow us to spot such a (relatively) small object at such a distance? Perhaps some radar experiment returns a 'ping' long after the initial experiment had concluded (maybe it was some futuristic experiment to bounce directional radar waves off Oort cloud objects, maybe that's too fanciful?).

I'd love to hear your thoughts.

[NovaSilisko]

I guess the only thing I could think of would be a coincidental approach by a piece of something that underwent a similar process to whatever creates hypervelocity stars (current hypothesis is close encounters of binary systems and supermassive black holes, as you mentioned). But those don't get nearly as quick as 0.1c. Still, it might be a start. If a hypervelocity star had an asteroid belt around it when it was accelerated, who knows where those asteroids might end up?

Hope this at least gets you a general direction to look in.

Curious to hear more about the premise of this, also. If it's a case where it's not actually a natural object, but you need a theory for someone to throw around to explain it to the public/what have you in the story, then I think the explanation of what's left of an asteroid belt around a hypervelocity star would suffice.

[nightsd01]

The fastest observed hypervelocity stars seem to be going around 0.3% C. That's pretty dang fast. I suppose that would work as a naturalistic explanation, as it's not that hard to imagine a situation where one of that star's original asteroids could have 30x the speed if it somehow got a bit closer to the black hole before being ejected. It's probably unimaginably rare but I bet it happens.

Thanks so much for your help If anyone else has any other ideas I'd love to hear it.

Basically it's not a natural object (don't tell anyone! lol). Initially, the observers on earth don't really have any idea what it is. They just have a rough estimate of how large it is and how fast it's going. A little later on, they notice its rotation.

EDIT: Now that I've done a bit more research it seems some of the fastest large objects are the neutron stars, which resulted from supernova explosions, the fastest observed ones are going 0.5% C. Perhaps they could theorize an especially fast piece of stellar debris got a 20X boost but wasn't completely blown to bits, somehow. It takes an enormous amount of energy to get a star moving so fast compared to its original velocity. It would take a lot less energy to get a football-stadium sized object to 10% C.

[nightsd01]

I have a few more questions to anyone out there who is more knowledgeable about physics than I am (i.e. the vast, overwhelming majority of you).

0. An object with a velocity of 10% C, with a mass approximately equal to a football stadium, if this object slammed into the earth I understand that the impact would be truly tremendous. I would like to know exactly how tremendous, though. I know the equation F = m*a. Does this equation still apply to objects traveling at such velocity, or did Einstein come up with something better? Could I simply compare the impact this object would produce with the comet that killed the dinosaurs using this equation, using estimations of that comet's velocity and mass?

1. An object traveling at ~10% C through the Galaxy (an area similar to the 'average' approximation of the Galaxy)...would its trajectory be pretty much a straight line? Assuming it has never come 'close' to a star during its journey (i.e.  Never more than 20 AU) and has also never been near a black hole since the initial kick made it go so fast.

2.  Can you think of any good ways that humans in the near future, with a lot of warning time (10 years perhaps), could 'catch' this object, match to velocity, and dock with it during its trip through the solar system? Right now my best idea is to invent a thousands-of-km-long magical self-assembling magnetic rail gun to shoot pellets of propellant at a space ship as it accelerates using computers to calculate exactly how fast to shoot them to intercept the space ship at the correct velocity.

3. This magical enormous magnetic rail gun would require astronomical amounts of power. I was thinking it would use radiation from the sun as the energy source. It would have large solar panels throughout its entire length. From what I understand, this would be a problem, because it would effectively create a solar sail that would push the rail gun out of orbit. From what I understand of orbital mechanics, we could account for this when putting it into orbit correct? It's orbital velocity would have to be lower than it would otherwise have to be, since the sun's radiation is imparting an outwards acceleration on the object and it would have to orbit slower to compensate. Is that correct or am I completely and utterly wrong?

4. From my understanding relativistic time dilation would not be a significant problem for astronauts at 10% C for a short period of time. If I remember right, the effects of time dilation are basically exponential as velocity asymptotically approaches 100% C but aren't that significant until you get going close to C. Is this correct?

5. What would you guess NASA and other space agencies would do if an unknown object with such an incredible velocity was going to make such dip into the solar system? I understand that my idea of NASA trying to launch a mission to 'dock' with the object is rather fanciful but I'm not entirely sure what their real response would probably be.

[Jarnis]

Real response? Get as much scientific hardware (telescopes etc) to watch it as much as possible during the closest pass. How many depends on how much lead time they have. Write a lot of papers.

Tho with the "size of a football stadium", I dunno how plausible it would be to actually detect that from those distances in the first place, unless it was somehow very unusual (extremely bright, visible or EM)

10% C is so ridiculously fast that there is no current or foreseeable-future way of catching that and matching velocities, even unmanned, plus even if you somehow did that, you would be then on an interstellar voyage with the object as getting back to Earth would be... "complicated".

Getting astronauts there is just... sorry, implausible without some really cool tech (ie. sufficiently advanced to be indistinguishable from magic). Even getting Astronauts to the orbit of Neptune without the "10% of C" problem would be very very complicated with travel time of many years, with all the problems of ferrying all the supplies needed for that long time, plus everything needed to get back as well. Accelerating all that to 10% of C... nope...as a bare minimum you'd need to visit the EM drive thread first and ask them for some exotic propulsion tech

With very long lead time it might be possible to somehow devise a flyby of the object with a tiny probe but the velocities are so massive that it would probably be a "close but not *that* close" and that closest pass would be very very very short. Basically New Horizons except both the target and the probe would be moving faster - the target a LOT faster.

[MP99]

I have a few more questions to anyone out there who is more knowledgeable about physics than I am (i.e. the vast, overwhelming majority of you).

0. An object with a velocity of 10% C, with a mass approximately equal to a football stadium, if this object slammed into the earth I understand that the impact would be truly tremendous. I would like to know exactly how tremendous, though. I know the equation F = m*a. Does this equation still apply to objects traveling at such velocity, or did Einstein come up with something better? Could I simply compare the impact this object would produce with the comet that killed the dinosaurs using this equation, using estimations of that comet's velocity and mass?

More important is kinetic energy = 1/2 * m * v^2.

AT 10% of C, that means it has energy equivalent to 1% of its rest mass. That's about the fraction that is released in atomic fusion. But an atomic bomb is a few Kg of reaction mass, not thousands (millions?) of tons.

1. An object traveling at ~10% C through the Galaxy (an area similar to the 'average' approximation of the Galaxy)...would its trajectory be pretty much a straight line? Assuming it has never come 'close' to a star during its journey (i.e.  Never more than 20 AU) and has also never been near a black hole since the initial kick made it go so fast.

Well, a relatively straight line.

An orbit at our distance from Galactic centre takes about 200 million years, so 100m years to go from one edge to the other.

Your object would make that transit in about 0.5m years. At a first approximation it would deflect towards Galactic centre by about 0.5% as much as the Sun does in a half orbit. So, it's a gentle curve (a hyperbola actually), but I suspect it would look like a straight line if it was drawn on a page.

But, if you were thinking of tracing it back to a source object, I think you'd need to take that curve into account.

Also, I wonder how fast the source object would be travelling, and in which direction?

2.  Can you think of any good ways that humans in the near future, with a lot of warning time (10 years perhaps), could 'catch' this object, match to velocity, and dock with it during its trip through the solar system? Right now my best idea is to invent a thousands-of-km-long magical self-assembling magnetic rail gun to shoot pellets of propellant at a space ship as it accelerates using computers to calculate exactly how fast to shoot them to intercept the space ship at the correct velocity.

No.

3. This magical enormous magnetic rail gun would require astronomical amounts of power. I was thinking it would use radiation from the sun as the energy source. It would have large solar panels throughout its entire length. From what I understand, this would be a problem, because it would effectively create a solar sail that would push the rail gun out of orbit. From what I understand of orbital mechanics, we could account for this when putting it into orbit correct? It's orbital velocity would have to be lower than it would otherwise have to be, since the sun's radiation is imparting an outwards acceleration on the object and it would have to orbit slower to compensate. Is that correct or am I completely and utterly wrong?

The rail gun would be pushed backwards by the objects it fires. This would overwhelm any solar sail effect. (Perhaps you make it fire objects in opposite directions to cancel out.)

4. From my understanding relativistic time dilation would not be a significant problem for astronauts at 10% C for a short period of time. If I remember right, the effects of time dilation are basically exponential as velocity asymptotically approaches 100% C but aren't that significant until you get going close to C. Is this correct?

https://en.m.wikipedia.org/wiki/Tau_Zero#Origin_of_the_title

It's only of order about 1% (a few days per year), so could be quite a long time and still OK.

5. What would you guess NASA and other space agencies would do if an unknown object with such an incredible velocity was going to make such dip into the solar system? I understand that my idea of NASA trying to launch a mission to 'dock' with the object is rather fanciful but I'm not entirely sure what their real response would probably be.

Observe with every telescope at every wavelength available. Probably RADAR, too. I'd assume a crash programme to build telescopes and RADAR for the job.

Cheers, Martin

[gargoyle99]

I have a few more questions to anyone out there who is more knowledgeable about physics than I am (i.e. the vast, overwhelming majority of you).

0. An object with a velocity of 10% C, with a mass approximately equal to a football stadium, if this object slammed into the earth I understand that the impact would be truly tremendous. I would like to know exactly how tremendous, though. I know the equation F = m*a. Does this equation still apply to objects traveling at such velocity, or did Einstein come up with something better? Could I simply compare the impact this object would produce with the comet that killed the dinosaurs using this equation, using estimations of that comet's velocity and mass?

More important is kinetic energy = 1/2 * m * v^2.

AT 10% of C, that means it has energy equivalent to 1% of its rest mass. That's about the fraction that is released in atomic fusion. But an atomic bomb is a few Kg of reaction mass, not thousands (millions?) of tons.

Does the object have the mass of a football stadium or is it the size of a football stadium? 

To provide some numbers, if it is a round ball of iron 100m across, that works out to a mass of roughly 4 x 10⁹ kg.  V = 4/3 pi r³, density is 7 g/cm³ or 7000 kg/m³.

KE = 1/2 mv², consider v of 3 x 10⁷ m/s

For this kind of back of the envelope estimate (and I actually did this on the back of an envelope), we should be able to safely ignore relativity at 0.1 c.  (The kinetic energy would only be about 1% higher due to relativistic effects.)

KE = 1.6 x 10²⁴ J or 4 x 10¹¹ kilotons of TNT

That's a huge number of hydrogen bombs whether or not I made any silly math errors.  Curiously that works out to just a bit more energy than the theorized Chicxulub impactor asteroid (1 x 10²⁴ J according to Wikipedia).

So, its impact on Earth would be a serious extinction level event and the worst asteroid strike in 65 million years, but probably wouldn't destroy ALL forms of life.  It would be a seriously bad day for Earthlings, though.

[NovaSilisko]

So, its impact on Earth would be a serious extinction level event and the worst asteroid strike in 65 million years, but probably wouldn't destroy ALL forms of life.  It would be a seriously bad day for Earthlings, though.

Just for a bit of fun...

[Comga]

Styx the smallest and last to be discovered of Pluto's five moons, is about six km across.
A stadium is more than 100 times as large, possibly 1000 times.
It took many hours of accumulated images, all centered on Pluto, with the Hubble Space Telescope to get the images that took days of careful processing to pull out the sequence of fuzzy blobs that were confirmed to be multiple images, with motion across the field, of the new moon.
An object moving at 0.1 C would be ten times as far away as Pluto 40 hours from closest approach. 
So far that would make the object five or six orders or magnitude less bright than Styx.  And it wouldn't be moving across the sky.  (Pre-collision astrometry has objects coming to rest with respect to the background stars as the intersecting trajectories become straight lines over relatively short distances.)  It would be a fixed point growing brighter, as many objects do periodically.
We would need many orders of magnitude more image collecting power and image processing power to find such an object and we would have to be looking in that particular part of the sky on that particular evening.
It would show a blue shift, if someone was looking, but imaging spectrometers reduce the signal even more, require more observing power, and searches usually look for red shifts, not blue.
But if we can imagine warp drives, these are not unimaginable advances.  And the fact that the odds are a few million to one against it lining up with some other target, like looking for moons of Sedna with super adaptive optics and super duper laser guide stars, it's not physically impossible.
But at 0.1C, it's going to be a very short story.