Engineering A Black Hole

<bomPAH-dadadadaDEEdah> That weird ringtone on Old Reliable again. Sure enough, the phone function’s caller-ID display says 710‑555‑1701.  “Ms Baird, I presume?”

A computerish voice, aggressive but feminine, with a hint of desperation. “Commander Baird will be with you shortly, Mr Moire. Please hold.”

A moment later, “Hello, Mr Moire.”

“Ms Baird. Congratulations on the promotion.”

“Thank you, Mr Moire. I owe you for that.”

“How so?”

“Your posts about phase-based weaponry got me thinking. I assembled a team, we demonstrated a proof of concept and now Federation ships are being equipped with the Baird‑Prymaat ShieldSaw. Works a treat on Klingon and Romulan shielding. So thank you.”

“My pleasure. Where are you now?”

“I’m on a research ship called the Invigilator. We’re orbiting black hole number 77203 in our catalog. We call it ‘Lonesome‘.”

“Why that name?”

“Because there’s so little other matter in the space nearby. The poor thing barely has an accretion disk.”

“Sounds boring.”

“No, it’s exciting, because it’s so close to a theoretical ideal. It’s like the perfectly flat plane and the frictionless pulley — in real life there are always irregularities that the simple equations can’t account for. For black holes, our only complete solutions assume that the collapsed star is floating in an empty Universe with no impinging gravitational or electromagnetic fields. That doesn’t happen, of course, but Lonesome comes close.”

“But if we understand the theoretical cases and it nearly matches one, why bother with it at all?”

“Engineering reasons.”

“You’re engineering a black hole?”

“In a way, yes. Or at least that’s what we’re working on. We think we have a way to extract power from a black hole. It’ll supply inexhaustible cheap energy for a new Star Fleet anti‑matter factory. “

“I thought the only thing that could escape a black hole’s Event Horizon was Hawking radiation, and it cheats.”

“Gravity escapes honestly. Its intense field generates some unexpected effects. Your physicist Roger Penrose used gravity to explain the polar jets that decorate so many compact objects including black holes. He calculated that if a comet or an atom or something else breakable shatters when it falls into a spinning compact object’s gravitational field, some pieces would be trapped there but under the right conditions other pieces would slingshot outward with more energy than they had going in. In effect, the extra energy would come from the compact object’s angular momentum.”

“And that’s what you’re planning to do? How are you going to trap the expelled pieces?”

“No, that’s not what we’re planning. Too random to be controlled with our current containment field technology. We’re going pure electromagnetic, turning Lonesome into a giant motor‑generator. We know it has a stable magnetic field and it’s spinning rapidly. We’ll start by giving Lonesome some close company. There’s enough junk in its accretion disk for several Neptune‑sized planets. The plan is to use space tugs to haul in the big stuff and Bussard technology for the dust, all to assemble a pair of Ceres-sized planetoids. W’re calling them Pine and Road. We’ll park them in a convenient equatorial orbit in a Lagrange‑stable configuration so Pine, Road and Lonesome stay in a straight line.”

“Someone’s been doing research on old cinema.”

“The Interstellar Movie Database. Anyhow, when the planetoids are out there we string conducting tractor beams between them. If we locate Pine and Road properly, Lonesome’s rotating magnetic field lines will cross the fields at right angles and induce a steady electric current. Power for the anti‑matter synthesizers.”

“Ah, so like Penrose’s process you’re going to drain off some of Lonesome‘s rotational kinetic energy. Won’t it run out?”

Lonesome‘s mass is half again heavier than your Sun’s, Mr Moire. It’ll spin for a long, long time.”

“Umm … that ‘convenient orbit.’ Lonesome‘s diameter is so small that orbits will be pretty speedy. <calculating quickly with Old Reliable> Even 200 million kilometers away you’d circle Lonesome in less than 15 minutes. Will the magnetic field that far out be strong enough for your purposes?”

“Almost certainly so, but the gravimagnetodynamic equations don’t have exact solutions. We’re not going to know until we get there.”

“That’s how research works, all right. Good luck.”

~~ Rich Olcott

The Solar System is in gear

Pythagoras was onto far more than he knew.  He discovered that a stretched string made a musical tone, but only when it was plucked at certain points.  The special points are those where the string lengths above and below the point are in the ratio of small whole numbers — 1:1, 1:2, 2:3, ….  Away from those points you just get a brief buzz.  All of Western musical theory grew out of that discovery.

sinesThe underlying physics is straightforward.  The string produces a stable tone only if its motion has nodes at both ends, which means the vibration has to have a whole number of nodes, which means you have to pluck halfway between two of the nodes you want.  If you pluck it someplace like 39¼:264.77 then you excite a whole lot of frequencies that fight each other and die out quickly.

That notion underlies auditorium acoustics and aircraft design and quantum mechanics.  In a way, it also determines where objects reside in the Solar System.

If you’ve got a Sun with only one planet, that planet can pick any orbit it wants — circular or grossly elliptical, close approach or far, constrained only by the planet’s kinetic energy.

If you toss in a second planet it probably won’t last long — the two will smash together or one will fall into the Sun or leave the system.  There are half-a-dozen Lagrange points, special configurations like “all in a straight line” where things are stable.  Other than those, a three-body system lives in chaos — not even a really good computer program can predict where things will be after a few orbits.

geared-saturnAdd a few more planets in a random configuration and stability goes out the window — but then something interesting happens.  It’s the Chladni effect all over again.  Planets and dust and everything go rampaging around the system.  After a while (OK, a billion years or so) sweet-spot orbits start to appear, special niches where a planet can collect small stuff but where nothing big comes close enough to break it apart.  It’s not like each planet seeks shelter, but if it finds one it survives.

It’s a matter of simple arithmetic and synchrony.  Suppose you’re in a 600-day orbit.  Neighbor Fred looking for a good spot to occupy could choose your same 600-day orbit but on the other side of the Sun from you.  But that’s a hard synchrony to maintain — be off by a few percent and in just a few years, SMASH!

The next safest place would be in a different orbit but still somehow in synchrony with yours.  Inside your orbit Fred has to go faster and therefore has a shorter orbital period than yours.  Suppose Fred’s year is exactly 300 days (a 2:1 period ratio, like a 2:1 gear ratio).  Every six months he’s sort-of close to you but the rest of the time he’s far away.

Our Solar System does seem to have developed using gear-year logic.  Adjacent orbital years are very close to being in whole-number ratios.  Mercury, for instance, circles the Sun in about 88 days.  That’s just 2% away from 2/5 of Venus’s 225¾ days.

This table shows year-lengths for the Sun’s most prominent hangers-on, along with ratios for adjacent objects.  For the “ideal” ratios I arbitrarily picked nearby whole-number multiples of 2.  I calculated how long each object’s year “should” be compared to its lower neighbor — the average inaccuracy across all ten objects is only 0.18%.

Period, years
2 × shorter / longer period
“Ideal” ratio
“Ideal” period, years
5 : 2
3 : 2
4 : 2
5 : 2
5 : 2
5 : 2
6 : 2
4 : 2
3 : 2

gears-2The usual rings-around-the-Sun diagram doesn’t show the specialness of the orbits we’ve got.  This chart shows the four innermost planets in their “ideal” orbits, properly scaled and with approximately the right phases.  I used artistic license to emphasize the gear-like action by reversing Earth’s and Mercury’s direction.   Earth and Mars are never near each other, nor are Earth and Venus.

It doesn’t show up in this video’s time resolution, but Venus and Mercury demonstrate another way the gears can work.  Mercury nears Venus twice in each full 5-year cycle, once leading and once trailing.  The leading pass slows Mercury down (raising it towards Venus), but the trailing pass speeds it up again.  Net result — safe!

~~ Rich Olcott