Built on Facts

I’m out of town, visiting family and friends in the period between the end of the summer and the time things get cranking back up later this summer. One thing I did do on Friday was catch the new Star Trek. I’ll save the review and “physics of” posts for later this week. I’ll be honest and admit that when I first saw the posters I thought it would be a train wreck. Long story short: it was shockingly good.

And I think I’ll cut it some slack on the physics. Sure it was bad, but given the genre it was only normally bad rather than egregiously bad (the supernova bit excepted). But again, we’ll save the review for later. On the road it’s difficult to write a solid Sunday Function so I think odds are we’ll end up saving it for Wednesday Function once I’m actually back in a place where I’ve got the time to craft quality posts. No promises with regard to content on Monday and Tuesday, but I shall do my best.

Still it would be a shame to waste a perfectly good Sunday for doing a little bit of math, so I’ll post a Trek-movie-related Fermi problem. I’m intentionally vague, but you could construe this as a spoiler so be warned. At one point our heroes are menaced by the gravitational attraction of a black hole. The black hole was generated entirely bay the mass of an admittedly large spacecraft which had just prior fallen victim to exposure to an unobtanium-style material which causes a catalyzed collapse of whatever it contacts into a black hole. So what used to be a spacecraft of (say) a few tens or hundreds of millions of tons is now presumably a point mass with the corresponding gravitational interaction. The problem:

Estimate a minimum safe distance between the Space Shuttle in its current incarnation and such a black hole.

Presumably the Federation’s brand-new Enterprise would be even more safe, but as I don’t know much about warp engines we’ll use the shuttle as a more accessible example.

Comments

#1 CCPhysicist
May 17, 2009

I forgot this observation when I blogged about the movie last weekend.

I was very disturbed when there was actual silence in space when people got blasted out through a hole in the hull. That was very un-Trek. Fortunately, the ships still made noise as they rumbled through the universe.

Finally, since I appear to be first here, a quick poll for the commenters: Which is worse, the use of “red matter” in Star Trek or the use of anti-matter in Angels and Demons?
#2 Justin S
May 17, 2009

Ok, I’ll bite. Using a mass of (I wanted to be really generous here) a billion tons, I get a minimum safe distance of… barely above 10e-15 meters. Yeah. I thought the depiction of black holes was hideous. I swear, those things are becoming the Hollywood plot device from hell.

Still, I’m going to side with the red matter usage because (1) at least Star Trek is in the future, so we can always claim ignorance now to get out of worrying about it and (2) I like Star Trek better than A&D.
#3 a lurker
May 17, 2009

“Estimate a minimum safe distance between the Space Shuttle in its current incarnation and such a black hole.”

The radius of a Schwarzschild black hole is equal to 2Gm/c^2 where the letters have their usual meanings.
That means that radius is m times 1.48×10^-27 m/kg.
Wikipedia gives Endeavour‘s maximum mass at landing at 104,000 kg. Obviously it might had more in orbit but it could also had a much less mass as well — it depends on how much cargo it is carrying.

The Schwarzschild radius is 1.54×10^-22 m.

Lets say that we want to keep at least ten radii away (some will rant and say we can get closer):

Keep Endeavour at least 1.54×10^-21 meters away from a Schwarzschild black hole of the same mass.

Maybe the other types of black holes (with charge or rotation) can be bigger, I don’t know. But is safe to say that Endeavour can be damn close to a black hole of its mass. The uncertainty of navigating the shuttle is FAR greater than the danger zone of the black hole.

(And this assumes the hole and the shuttle are in a similar orbit. If they are on different paths then hole could go through the shuttle in a tiny fraction of a second and gobble up an nuclei or two before exiting. Exactly how much it would gobble up can be the next commentator’s problem.)
#4 Johan
May 17, 2009

Without going through any math I dare say the minimum distance is pretty small. After all, just turning into a black hole does not increase your gravitational pull. And I know that the effect of a few million tons is pretty small even when you are close by.
#5 Matt Springer
May 17, 2009

CC: Antimatter in A&D, by far. I actually thought “red matter” was a nice stylistic choice. Better to just make something up out of whole cloth than to take something real and promptly change everything about it.

Johan: “After all, just turning into a black hole does not increase your gravitational pull.” Exactly. This seems to be the single biggest thing that science fiction films seem to get wrong about black holes.
#6 tewhy
May 17, 2009

There’s another assumption possible – given the strong gravity shown by the various black holes, it might be that normal matter catalyzes some effect of the red matter instead, and the final mass is more than just the one ship’s worth.

And, trying to be vague, if that’s the case then there’s even more reason for this particular black hole to be a nasty one.
#7 Uncle Al
May 17, 2009

More to the point, why did Uhura wear brilliantly white bra and panties? Puhleeze, somebody have some fashion sense. With Scotty now in Engineering, shouldn’t he be shouldering Howard Hughes’ legacy by designing better OTSBHs?

If a droplet of red matter can collapse a planet, why take along a five gallon jug? Dark Star?
#8 Andy Craig
May 17, 2009

@tewhy

I was thinking something similar- how do we know that the mass of the ship = the mass of the black hole? When I saw it, I assumed that the red matter itself was super-massive and then just sucked all around it- ship, planet, whatever- into a black hole that is, at least initially, entirely of the red matter’s making. In that case the mass of the destroyed ship would be a minute percentage of the mass of the black hole.
#9 ppnl
May 17, 2009

Better question. What is the minimum safe distance from the explosion caused when massive parts of a planet fall into a black hole.

There is no threat of being dragged into the black hole. But there is a threat of being vaporized by the flashback of the black hole forming.

And could someone explain why they needed to drill down to the center to inject the red matter?
#10 Andrew
May 17, 2009

I don’t see anyone addressing the question of tidal forces yet.

My calculations suggest that a close (a few metres) approach between the hole (taking a fairly large estimate for the hole mass of 500 or so megatons) and a shuttle orbiter could produce tidal forces of up to about 10^4 N along the long axis of the orbiter, so the safe distance would depend on the shuttle’s tolerance for such forces. A human with their feet 1 metre from the hole would experience tidal forces comparable to their own bodyweight under normal gravity; this would probably not be very comfortable and might cause injury if it happened suddenly without warning. So I would recommend a safety margin on the order of tens to hundreds of metres to avoid the risk of damage to sensitive components, heat-resistant tiles, etc., from sudden changes in tidal forces caused by a near approach (tidal force drops off as R^3, so a close pass at high speed could represent a significant shock).

(This force is larger than I’d originally guessed at, but the mass of the hole at ~10^11 kg is enough to balance out the small size of G (6.7×10^-11), so it’s not surprising.)
#11 Chris Hertlein
May 18, 2009

Star Trek The Next Generation was known for the fact that although things like Warp Drives and Matter transportation were bogus, was mostly feasible. They even had a few physicist writers.

I was holding my breath for the movie (even though I like the series) but it was awesome. Very very awesome.
#12 Charles
May 18, 2009

Umm, I had some problems with this.

First off, warp drive IS FASTER THAN LIGHT. They were not anywhere near the event horizon. They could easily have gotten away.

Second, assuming they were actually stuck, jettisoning the core does what? Yep, cuts power to shields and warp drive. Meaning they’d be instantly both crushed and sucked into the black hole.

Third, without shields detonating the core at that distance would vaporize the ship. (Several previous trek examples here)

They could have at least tried for just a little hint of physics. Just a hint. I mean, I didn’t expect the new trek to be Battlestar Galactica by any stretch, but it’d be nice to not re-write both real physics and already-screwed-with Star Trek-canon physics.

Charles.
#13 Teramut
May 18, 2009

Charles, first off you can’t travel faster than light. Second, the scene would sort of make sense that they actually were inside the event horizon. In that case, again sort of making sense, by jettisoning the cores you might be able to warp the geometry of spacetime enough to escape.
#14 not home
May 20, 2009

@Teramut

Are you being tricky with that remark?

The Warp Drive in the fictional universe of Star Trek is a superluminal or FTL (Faster Than Light) drive.

If we assume that it is based off the Alcubierre metric then it’s correct that the ship and passengers are not going faster then light but end up in their destination faster than light could have by conventional means.

But if you needed to warp the geometry of spacetime to escape something like a black hole then an Alcubierre drive would seem to be perfect for this, or?
#15 Scott
May 20, 2009

To travel faster than light, it is the space around you that moves from point A to point B, so it kind of makes sense that they were stuck if the black hole was pulling in the space around the enterprise. The exploding warp cores simply pushed the ship farther ahead of the portion of space that was “leaking” into the black hole.

I am not a physicist, just a reader of all things sciency…
#16 anon
May 25, 2009

About Alcubierre drive, I don’t quite understand how you get the space ahead of you contracting FLT in unwarped space ahead of you. I mean, the space warp itself must be travelling FTL, how do you get space far away from you to contract (FTL)??

If you start warping the space ahead of you, don’t you slow down the propagation of the warping effect while doing that?

Perhaps the basic question I have, is something able to move through contracted space like it wasn’t contracted. If everything in contracted space would feel it as “normal” space, then you could contract space to your heart content, but nothing would go through it any faster than light in the same uncontracted space.

Am I missing something??
#17 previous anon
May 25, 2009

In addition to previous post, I’d like to bring up another aspect in relation to FTL travel.

You see, we haven’t been contacted by any other spacefaring sivilizations. If FTL travel was really possible, it would be conceivable that another race would already contacted us, or at least is watching us. A “North-Korea of Universe” might also have wiped us out as unwanted future nuisance.

Or, perhaps we are really the first self-conscious sivilization in the universe.