Category: Uncategorized

Three ways to look at things

On By rolcottIn Gravitational astronomy, Physics: Black Holes and Relativity, Physics: Fundamentals, Physics: Light and Relativity, Physics: Newton and Gravity, UncategorizedLeave a comment

A familiar shadow loomed in from the hallway.

“C’mon in, Vinnie, the door’s open.”

“I brought some sandwiches, Sy.”

“Oh, thanks, Vinnie.”

“Don’t mention it.    An’ I got another LIGO issue.”

“Yeah?”

“Ohh, yeah.  Now we got that frame thing settled, how does it apply to what you wrote back when?  I got a copy here…”

The local speed of light (miles per second) in a vacuum is constant.  Where space is compressed, the miles per second don’t change but the miles get smaller.  The light wave slows down relative to the uncompressed laboratory reference frame.

“Ah, I admit I was a bit sloppy there.  Tell you what, let’s pretend we’re piloting a pair of space shuttles following separate navigation beams that are straight because that’s what light rays do.  So long as we each fly a straight line at constant speed we’re both using the same inertial frame, right?”

“Sure.”

“And if a gravity field suddenly bent your beam to one side, you’d think you’re still flying straight but I’d think you’re headed on a new course, right?”

“Yeah, because now we’d have different inertial frames.  I’d think your heading has changed, too.”two-shuttles

“So what does the guy running the beams see?”

“Oh, ground-pounders got their own inertial frame, don’t they?  Uhh… He sees me veer off and you stay steady ’cause the gravity field bent only my beam.”

“Right — my shuttle and the earth-bound observer share the same inertial frame, for a while.”

“A while?”

“Forever if the Earth were flat because I’d be flying straight and level, no threat to the shared frame.  But the Earth’s not flat.  If I want to stay at constant altitude then I’ve got to follow the curve of the surface rather than follow the light beam straight out into space.  As soon as I vector downwards I have a different frame than the guy on the ground because he sees I’m not in straight-line motion.”

“It’s starting to get complicated.”

“No worries, this is as bad as it gets.  Now, let’s get back to square one and we’re flying along and this time the gravity field compresses your space instead of bending it.  What happens?  What do you experience?”

“Uhh… I don’t think I’d feel any difference.  I’m compressed, the air molecules I breath are compressed, everything gets smaller to scale.”

“Yup.  Now what do I see?  Do we still have the same inertial frame?”

“Wow.  Lessee… I’m still on the beam so no change in direction.  Ah!  But if my space is compressed, from your frame my miles look shorter.  If I keep going the same miles per second by my measure, then you’ll see my speed drop off.”

“Good thinking but there’s even more to it.  Einstein showed that space compression and time dilation are two sides of the same phenomenon.  When I look at you from my inertial frame, your miles appear to get shorter AND your seconds appear to get longer.”

“My miles per second slow way down from the double whammy, then?”

“Yup, but only in my frame and that other guy’s down on the ground, not in yours.”

“Wait!  If my space is compressed, what happens to the space around what got compressed?  Doesn’t the compression immediately suck in the rest of the Universe?”

“Einstein’s got that covered, too.  He showed that gravity doesn’t act instantaneously.  Whenever your space gets compressed, the nearby space stretches to compensate (as seen from an independent frame, of course).  The edge of the stretching spreads out at the speed of light.  But the stretch deformation gets less intense as it spreads out because it’s only offsetting a limited local compression.”

“OK, let’s get back to LIGO.  We got a laser beam going back and forth along each of two perpendicular arms, and that famous gravitational wave hits one arm broadside and the other arm cross-wise.  You gonna tell me that’s the same set-up as me and you in the two shuttles?”

“That’s what I’m going to tell you.”

“And the guy on the ground is…”

“The laboratory inertial reference.”

“Eat your sandwich, I gotta think about this.”

(sounds of departing footsteps and closing door)

“Don’t mention it.”

~~ Rich Olcott

A Shift in The Flight

On By rolcottIn Gravitational astronomy, Physics: Fundamentals, Physics: Newton and Gravity, UncategorizedLeave a comment

I heard a familiar squeak from the floorboard outside my office.

“C’mon in, Vinnie, the door’s open.  What can I do for you?”

“I still got problems with LIGO.  I get that dark energy and cosmic expansion got nothin’ to do with it.  But you mentioned inertial frame and what’s that about?”

earth-moon“Does the Moon go around the Earth or does the Earth go around the Moon?”

“Huh?  Depends on where you are, I guess.”

“Well, there you are.”

“Waitaminnit!  That can’t be all there is to it!”

“You’re right, there’s more.  It all goes back to Newton’s First Law.”  (showing him my laptop screen)  “Here’s how Wikipedia puts it in modern terms…”

In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a net force.

“That’s really a definition rather than a Law.  If you’re looking at an object and it doesn’t move relative to you or else it’s moving at constant speed in a straight line, then you and the object share the same inertial frame.  If it changes speed or direction relative to you, then it’s in a different inertial frame from yours and Newton’s Laws say that there must be some force that accounts for the difference.”

“So another guy’s plane flying straight and level with me has a piece of my inertial frame?”

“Yep, even if you’re on different vectors.  You only lose that linkage if either airplane accelerates or curves off.”

“So how’s that apply to LIGO’s laser beams?  I thought light always traveled in straight lines.”

“It does, but what’s a straight line?”

“Shortest distance between two points — I been to flight school, Sy.”

“Fine.  So if you fly from London to Mexico City on this globe here you’d drill through the Earth?”mex-atl-jfk-lgw

“Of course not, I’d take the Great Circle route that goes through those two cities.  It’s the shortest flight path.  Hey, how ’bout that, the circle goes through NYC and Atlanta, too.”

“Cool observation, but that line looks like a curve from where I sit.”

“Yeah, but you’re not sittin’ close to the globe’s surface.  I gotta fly in the flight space I got.”

“So does light.  Photons always take the shortest available path, though sometimes that path looks like a curve unless you’re on it, too.  Einstein predicted that starlight passing through the Sun’s gravitational field would be bent into a curve.  Three years later, Eddington confirmed that prediction.”

“Light doesn’t travel in a straight line?”

“It certainly does — light’s path defines what is a straight line in the space the light is traveling through.  Same as your plane’s flight path defines that Great Circle route.  A gravitational field distorts the space surrounding it and light obeys the distortion.”

“You’re getting to that ‘inertial frames’ stuff, aren’t you?”

“Yeah, I think we’re ready for it.  You and that other pilot are flying steady-speed paths along two navigation beams, OK?”

“Navigation beams are radio-frequency.”

“Sure they are, but radio’s just low-frequency light.  Stay with me.  So the two of you are zinging along in the same inertial frame but suddenly a strong gravitational field cuts across just your beam and bends it.  You keep on your beam, right?”

“I suppose so.”

“And now you’re on a different course than the other plane.  What happened to your inertial frame?”

“It also broke away from the other guy’s.”

“Because you suddenly got selfish?”

“No, ’cause my beam curved ’cause the gravity field bent it.”

“Do the radio photons think they’re traveling a bent path?”

“Uh, no, they’re traveling in a straight line in a bent space.”

“Does that space look bent to you?”

“Well, I certainly changed course away from the other pilot’s.”

“Ah, but that’s referring to his inertial frame or the Earth’s, not yours.  Your inertial frame is determined by how those photons fly, right?  In terms of your frame, did you peel away or stay on-beam?”

“OK, so I’m on-beam, following a straight path in a space that looks bent to someone using a different inertial frame.  Is that it?”

“You got it.”

(sounds of departing footsteps and closing door)

“Don’t mention it.”

~~ Rich Olcott

A Defective Story

On By rolcottIn General: Fun Stuff, Physics: Black Holes and Relativity, UncategorizedLeave a comment

It was an interesting knock at my office door — aggressive but feminine, with a hint of desperation.

“C’mon in, the door’s open.”

She wore a business suit that must have cost a month’s rent.  It fit her like it had been sewn on, and she had all the right sizes.  There was a button missing from the left sleeve.  On the other hand her left lapel bore a Star Trek badge, Security Section.

“What can I do for you, Miss…?”

“My name’s Victoria Baird, Mr Moire.  I’m CEO of ADastra, ‘media relations for the stars.’  I’ve been reading your posts, put two and two together, and thought I’d better drop in.”

“Well, it’s nice to know I’ve got readers.  Which posts caught your attention?”

“Several of them, but mostly this one,” pointing to a Web page on her smartphone.  It was my Breathing Space video.  “You show how gravitational waves fluctuate as they polarize local space.  They induce varying curvatures in different directions.  Curved space is mass, Mr Moire, but this curvature moves at lightspeed.  Hadn’t you noticed that?”

“It crossed my mind, yes, but when I thought about surfing a gravitational wave like ocean surfers do, I realized you’d have to get up to the wave’s speed to ride it.”

jellyfish-starcraft
Spock’s Jellyfish starcraft,
as seen in the 2009 Star Trek film
(image from the video by Rob Morey)

“There’s more.  Are you familiar with that one-man starcraft that Ambassador Spock used in the 2009 Star Trek film?  The ship with the rotating after-section?”

“I did see ‘Baby Star Trek,’ yes.”

“Did you know that the starcraft’s official design designation is Jellyfish?”

“No, I hadn’t heard that.”

“Well, it is.  And you’ve written about Earth jellyfish, haven’t you, Mr Moire, and how their propulsion system is so efficient?”

I was getting a little tired of her aggressive questions, so I challenged her with one of my own.  “And you see a connection?”

“I do, and that’s why you have to help me, Mr Moire.  Can I trust you?”

“Secrets are my business, Miss Baird.  Uncovering them or covering them up, it’s all the same to me.”

“Maybe I need to let my hair down.”  She removed her cloche cap and her pointed ears sprang free.  “I need you to get me back to my crew.”

“Can’t you just call them on that communicator badge?”

“This is costume jewelry.  The spectrum here on Earth is so crowded that my real badge is useless at long range.  I’ve been looking for subtle signals in the media.  I thought your posts were just such a signal … but I can see you’re a local.”

“Guilty as charged.  I take it the connection you saw resembled the signal you sought?”

“Yes.  You’ve published two of the essential principles of the LaForge Drive.  The first was your displays of spatial curvature in motion.  The second was your description of how jellyfish move by stepping along a ladder of seawater vortices.

jellyfish-2“That’s what the LaForge Drive does, Mr Moire.  The counter-rotating blades are an osmium-hassium alloy, the densest substance known, and under tremendous compression.  Together their mass creates a complex pilot wave in the gravity field.  The spacecraft surfs on that waveform the way a jellyfish surfs on the eddies it creates.

“The wave’s phase velocity exceeds lightspeed by some enormous factor we’ve never been able to measure.  In fact, I’m here on Earth because I was on a research cruise to find if there’s a limit.  We … ran into a problem and I’m part of an away team sent to procure … something we need.”

“That trope’s been done to death, Miss Baird.  And besides, that design wouldn’t be practical.  What’s your real story?”

“What do you mean it’s not practical?”

“You can’t steer.  Pilot waves follow the most intense local spatial curvature, which means the craft will always home like a torpedo on the nearest large mass.”

Suddenly that badge chirped.  “We’ve recovered the detonator, Lieutenant.  Have you kept him from looking out the window?”

“Yes, his eyes have been on me the whole time.  Ready for beam-up.  Goodbye, Mr Moire, that was fun.”

Her form began to shimmer, twinkle … and disappeared.

“Don’t mention it.”

~~ Rich Olcott

Breathing Space

On By rolcottIn Gravitational astronomy, Physics: Black Holes and Relativity, Physics: Fundamentals, Physics: Newton and Gravity, UncategorizedLeave a comment

It was December, it was cold, no surprise.  I unlocked my office door, stepped in and there was Vinnie, standing at the window.  He turned to me, shrugged a little and said, “Morning, Sy.”  That’s Vinnie for you.

“Morning, Vinnie.  What got you onto the streets this early?”

“I ain’t on the streets, I’m up here where it’s warm and you can answer my LIGO question.”

“And what’s that?”

“I read your post about gravitational waves, how they stretch and compress space.  What the heck does that even mean?”

gravwave
An array of coordinate systems
floating in a zero-gravity environment,
each depicting a local x, y, and z axis

“Funny thing, I just saw a paper by Professor Saulson at Syracuse that does a nice job on that.  Imagine a boxful of something real light but sparkly, like shiny dust grains.  If there’s no gravitational field nearby you can arrange rows of those grains in a nice, neat cubical array out there in empty space.  Put ’em, oh, exactly a mile apart in the x, y, and z directions.  They’re going to serve as markers for the coordinate system, OK?”

“I suppose.”

“Now it’s important that these grains are in free-fall, not connected to each other and too light to attract each other but all in the same inertial frame.  The whole array may be standing still in the Universe, whatever that means, or it could be heading somewhere at a steady speed, but it’s not accelerating in whole or in part.  If you shine a ray of light along any row, you’ll see every grain in that row and they’ll all look like they’re standing still, right?”

“I suppose.”

“OK, now a gravitational wave passes by.  You remember how they operate?”

“Yeah, but remind me.”

(sigh)  “Gravity can act in two ways.  The gravitational attraction that Newton identified acts along the line connecting the two objects acting on each other.  That longitudinal force doesn’t vary with time unless the object masses change or their distance changes.  We good so far?”
long-and-transverse-grav
“Sure.”

“Gravity can also act transverse to that line under certain circumstances.  Suppose we here on Earth observe two black holes orbiting each other.  The line I’m talking about is the one that runs from us to the center of their orbit.  As each black hole circles that center, its gravitational field moves along with it.  The net effect is that the combined gravitational field varies perpendicular to our line of sight.  Make sense?”

“Gimme a sec…  OK, I can see that.  So now what?”

“So now that variation also gets transmitted to us in the gravitational wave.  We can ignore longitudinal compression and stretching along our sight line.  The black holes are so far away from us that if we plug the distance variation into Newton’s F=m1m2/r² equation the force variation is way too small to measure with current technology.

“The good news is that we can measure the off-axis variation because of the shape of the wave’s off-axis component.  It doesn’t move space up-and-down.  Instead, it compresses in one direction while it stretches perpendicular to that, and then the actions reverse.  For instance, if the wave is traveling along the z-axis, we’d see stretching follow compression along the x-axis at the same time as we’d see compression following stretching along the y-axis.”

gravwave-2“Squeeze in two sides, pop out the other two, eh?”

“Exactly.  You can see how that affects our grain array in this video I just happen to have cued up.  See how the up-down and left-right coordinates close in and spread out separately as the wave passes by?”

“Does this have anything to do with that ‘expansion of the Universe’ thing?”

“Well, the gravitational waves don’t, so far as we know, but the notion of expanding the distance between coordinate markers is exactly what we think is going on with that phenomenon.  It’s not like putting more frosting on the outside of a cake, it’s squirting more filling between the layers.  That cosmological pressure we discussed puts more distance between the markers we call galaxies.”

“Um-hmm.  Stay warm.”

(sound of departing footsteps and door closing)

“Don’t mention it.”

~~ Rich Olcott

Gentle pressure in the dark

On By rolcottIn Cosmology, Gravitational astronomy, Physics: Black Holes and Relativity, Physics: Newton and Gravity, UncategorizedLeave a comment

“C’mon in, the door’s open.”

Vinnie clomps in and he opens the conversation with, “I don’t believe that stuff you wrote about LIGO.  It can’t possibly work the way they say.”

“Well, sir, would you mind telling me why you have a problem with those posts?”  I’m being real polite, because Vinnie’s a smart guy and reads books.  Besides, he’s Vinnie.

“I’m good with your story about how Michelson’s interferometer worked and why there’s no æther.  Makes sense, how the waves mess up when they’re outta step.  Like my platoon had to walk funny when we crossed a bridge.  But the gravity wave thing makes no sense.  When a wave goes by maybe it fiddles space but it can’t change where the LIGO mirrors are.”

“Gravitational wave,” I murmur, but speak up with, “What makes you think that space can move but not the mirrors?”

“I seen how dark energy spreads galaxies apart but they don’t get any bigger.  Same thing must happen in the LIGO machine.”

“Not the same, Vinnie.  I’ll show you the numbers.”

“Ah, geez, don’t do calculus at me.”de-vs-gravity

“No, just arithmetic we can do on a spreadsheet.” I fire up the laptop and start poking in  astronomical (both senses) numbers.  “Suppose we compare what happens when two galaxies face each other in intergalactic space, with what happens when two stars face each other inside a galaxy.  The Milky Way’s my favorite galaxy and the Sun’s my favorite star.  Can we work with those?”

“Yeah, why not?”

“OK, we’ll need a couple of mass numbers.  The Sun’s mass is… (sound of keys clicking as I query Wikipedia) … 2×1030 kilograms, and the Milky Way has (more key clicks) about 1012 stars.  Let’s pretend they’re all the Sun’s size so the galaxy’s mass is (2×1030)×1012 = 2×1042 kg. Cute how that works, multiplying numbers by adding exponents, eh?”

“Cute, yeah, cute.”  He’s getting a little impatient.

“Next step is the sizes.  The Milky Way’s radius is 10×104 lightyears, give or take..  At 1016 meters per lightyear, we can say it’s got a radius of 5×1020 meters.  You remember the formula for the area of a circle?”

“Sure, it’s πr2.” I told you Vinnie’s smart.

“Right, so the Milky Way’s area is 25π×1040 m2.  Meanwhile, the Sun’s radius is 1.4×109 m and its cross-sectional area must be 2π×1018 m2.  Are you with me?”

“Yeah, but what’re we doing playing with areas?  Newton’s gravity equations just talk about distances between centers.”  I told you Vinnie’s smart.

“OK, we’ll do gravity first.  Suppose we’ve got our Milky Way facing another Milky Way an average inter-galactic distance away.  That’s about 60 galaxy radii,  about 300×1020 meters.  The average distance between stars in the Milky Way is about 4 lightyears or 4×1016 meters.  (I can see he’s hooked so I take a risk)  You’re so smart, what’s that Newton equation?”

“Force or potential energy?”

“Alright, I’m impressed.  Let’s go for force.”

“Force equals Newton’s G times the product of the masses divided by the square of the distance.”

“Full credit, Vinnie.  G is about 7×10-11 newton-meter²/kilogram², so we’ve got a gravity force of (typing rapidly) (7×10-11)×(2×1042)×(2×1042)/(300×1020)² = 3.1×1029 N for the galaxies, and (7×10-11)×(2×1030)×(2×1030)/(4×1016)² = 1.75×1017 N for the stars.  Capeesh?”

“Yeah, yeah.  Get on with it.”

“Now for dark energy.  We don’t know what it is, but theory says it somehow exerts a steady pressure that pushes everything away from everything.  That outward pressure’s exerted here in the office, out in space, everywhere.  Pressure is force per unit area, which is why we calculated areas.

“But the pressure’s really, really weak.  Last I saw, the estimate’s on the order of 10-9 N/m².  So our Milky Way is pushed away from that other one by a force of (10-9)×(25π×1040) ≈ 1031 N, and our Sun is pushed away from that other star by a force of (10-9)×(2π×1018) ≈ 1010 N with rounding.  Here, look at the spreadsheet summary…”

 Force, newtons Between Galaxies Between stars
Gravity 3.1×1029 1.75×1017
Dark energy 1031 1010
Ratio 3.1×10-2 17.5×106

“So gravity’s force pulling stars together is 18 million times stronger than dark energy’s pressure pushing them apart.  That’s why the galaxies aren’t expanding.”

“Gotta go.”

(sound of door-slam )

“Don’t mention it.”

~~ Rich Olcott

Here we LIGO again…

On By rolcottIn Gravitational astronomy, Physics: Black Holes and Relativity, UncategorizedLeave a comment

I suddenly smelled mink musk, vintage port, and warm honey on fresh-baked strawberry scones.

“C’mon in, Ramona, the door’s open.”

She oscillated in with a multi-dimensional sinusoidal motion that took my breath away and a smile that brought it back.

“Hi, Sy.  I came right over as soon as I got the news.”

“What news is that, Sugar Lumps?”

“LEGO, Sy, they’ve switched LEGO to science mode!”

“That’s LIGO, sweetheart, Laser Interferometer Gravitational-wave Observatory.”  She means well, but she’s Ramona.  “LEGOs are designed to hurt your feet, LIGO’s designed to look at the Universe.”

“Whatever.  I knew you wrote a . whole . series . of . posts . about . it so I thought you’d want to know.”

“It’s worth chasin’ down, doll-face.  Thanks.”symoire

So I headed over to the campus coffee shop.  It just happens to be located between the Astronomy building and the Physics building so I figured it as a good source.  Al was in his usual place at the cash register.

“Hi, Sy.  Haven’t seen you in a while.”

“Been busy, Al.  Lotsa science going on these days.”

“Good, good.   Say, have you heard about LEGO goin’ live?”

“That’s LIGO, Al.  Yeah, Ramona told me.  So what’s the word?”

“OK, you know all about how when they first turned it on for engineering tests back in September, it blew everyone’s mind that they caught a signal almost immediately?”

“Yeah, that’s when I started writing about it.  Two 30-solar-mass black holes collided and jolted the gravitational field of the Universe.  When the twin LIGOs detected that jolt, it confirmed three predictions that came out of Einstein’s General Relativity theory.”

“Had you heard about the second signal they caught the day after Christmas, from a couple of smaller black holes?”

“I bet you sold a lot of coffee that week.”

“You couldn’t believe.  Those guys had so much caffeine in ’em they didn’t even notice New Years.”

“So what came out of that?”

“Like I said, these were smaller black holes, about 10 solar masses each instead of 30, and that’s really got the star-modelers scratching their heads.”

“How so?”

“Well, we pretty much know how to make a black hole that’s just a bit heavier than the Sun.  Say a star’s between 1.3 and 3 solar masses.  When it burns enough of its fuel that its heat energy can’t keep it puffed up against gravity the whole thing collapses down to a black hole.”

“What happens if it’s bigger than that?  Wouldn’t you just get a bigger black hole?”

“That’s the thing.  If it’s above that threshold, the outermost infalling matter meets the outgoing explosion and makes an even bigger explosion, a supernova.  So much matter gets blown away that what’s left is too small to be a black hole.  You just get a white dwarf star or a neutron star, depending.”

“But these signals came from black holes 3-10 times that upper limit.  Where did they come from?”

“That’s why the head-scratching, Sy.  I mean, no-one knows how to make even one and yet they seem to be so common that two pairs of ’em found each other and collided less than four months apart.  The whole theory is up for grabs now.”

“So we got all that just from the engineering test phase, eh?  What’ve they done since that?”

“Oh, the usual tinkering and tweaking.  The unit down in Livingston LA is about 25% more sensitive now, especially in the lower-frequency range.  That’s mostly because they found and plugged some light-leaks and light-scattering hot-spots here and there along its five miles of steel pipe.  LIGO doesn’t look at incoming light, but it does use laser light to detect the gravitational variation.  The Hanford WA unit boosted the power going to its laser and they’ve improved stability in its detectors, made ’em more robust against wind and low-frequency seismic activity.  You know, engineer stuff.  So now they say they’re ready to do science.”

“I can’t write that the tweaks’ll let us look deeper into the Universe, ’cause LIGO doesn’t pick up light waves.  How about I say we get a better feel for things?”

“Sounds ’bout right, Sy.”

“Oh, and give me one of those strawberry scones.  For some reason they look really good today.”

~~ Rich Olcott

The Solar System is in gear

On By rolcottIn Astronomy: Planetary Science, Astronomy: Stellar Science, Physics: Waves, UncategorizedLeave a comment

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%.

Object
Period, years
2 × shorter / longer period
“Ideal” ratio
“Ideal” period, years
Real/”Ideal”
Mercury
0.24
0.24
Venus
0.62
5.11
5 : 2
0.60
102%
Earth
1.00
3.25
3 : 2
0.92
108%
Mars
1.88
3.76
4 : 2
2.00
94%
Ceres
4.60
4.89
5 : 2
4.70
98%
Jupiter
11.86
5.16
5 : 2
11.50
103%
Saturn
29.46
4.97
5 : 2
29.65
99%
Uranus
84.02
5.70
6 : 2
88.37
95%
Neptune
164.80
3.92
4 : 2
168.04
98%
Pluto
248.00
3.01
3 : 2
247.20
100%

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

Is there a lurker in the Solar System?

On By rolcottIn Astronomy: Planetary Science, UncategorizedLeave a comment

The Solar System is much bigger than we learned in school, with a more complicated history.

pillars-with-vortex
NASA’s 2014 edition of “The Pillars of Creation,”
plus a speculative addition

This famous photograph shows a portion of the Eagle Nebula, about 7,000 lightyears away from us but still within the Milky Way Galaxy.  The nebula is a diffuse mass of dust, gas  (mostly hydrogen atoms, of course) and hundreds of stars aborning.  Spectroscopic red- and blue-shift data could prove me wrong, but to my eye those “pillars” are exactly what you’d expect to see if each had formed around a vortex such as I described in my previous post.  Those two bright rings look very much like solar nebulae, don’t they?

If that’s what the rings are, then the region between them should be even emptier than normal interstellar space (estimated at one hydrogen atom per cm³ or about 30 atoms per fluid ounce if you swing that way).  If you’re floating in vacuum and a whole solar system’s gravity is pulling you towards it, then that’s where you’ll go.  Interstellar space will be emptier without you.

By the way, space between galaxies is a million times emptier than space between stars.

The solar nebula hypothesis does a decent job of explaining the familiar structure — an inward succession of gas giants, then an asteroid belt, then rocky planets, all orbiting within a degree or so of their common Plane of The Ecliptic.  When the Sun lit up 4.6 billion years ago, its fierce light stripped hydrogen and other light elements from the region where the inner planets were coalescing.  Those atoms fled outward to the asteroids, the gas giants and beyond.  An eon later, the rocky planets collected water and other volatiles from impacting comets and such.

But some incoming objects, especially the long-period comets, seem to have no respect for the Ecliptic.  They come at us from all angles, an oddity that led Ernst Öpik and Jan Oort to suggest that the familiar planar Solar System is in fact enclosed by a spherical shell of loosely-held objects, ready to pelt us at any time from wherever they happened to be.

No-one’s yet seen that shell, but statistical models suggest it’s huge.  Earth is one Astronomical Unit (AU) from the Sun.  Neptune, our farthest-out known planet, orbits at about 30 AU.  Researchers think the Oort Cloud starts somewhere near 2,000 AU and runs out to 20,000 or more.  Some suggest it may contain material from other solar systems.

Astronomers also think the Cloud contains something like a trillion objects, pebble-size up to planetoids or bigger.  In a volume that large, the average distance between objects is about 30 AU.  When NASA’s New Horizon spacecraft finally flies through the Oort Cloud 900 years from now, accidentally colliding with something shouldn’t be a problem.

outer-orbits
I drew the Oort Cloud much too small
compared to the purple Kuiper Belt Object orbits
(adapted from the Batygin-Brown paper)

In between the familiar Solar System and the Oort Cloud there’s a whole zoo of objects we’ve only started to glimpse in the past 25 years.  The Kuiper Belt is a doughnut of about 100,000 bodies that stay close to the Ecliptic Plane but orbit from just beyond Neptune’s orbit out to about twice as far.  (By my calculation the average distance between the rocks is, you guessed it, about 30 AU.)  These guys are heavily influenced by Neptune’s gravity and thought to be leftovers from our solar nebula.  Most short-period comets seem to come from the Kuiper Belt.

Recently, CalTech astrophysicists Konstantin Batygin and Michael Brown, drew attention to a half-dozen objects with orbits that were strangely similar.  Unlike the other thousand-or-so Kuiper Belt Objects characterized so far, these all

  • go further than 250 AU from the Sun despite getting as close as 50 AU
  • have a perihelion (the point of closest approach to the Sun) at about the same equatorial latitude (see the diagram)
  • (the kicker) the perihelion drops below the ecliptic by about the same amount.

The authors account for these observations, and more, by hypothesizing a Planet 9 that roams out beyond the Kuiper Belt.  They call it “a mildly inclined, highly eccentric distant perturber.”  I know what you’re thinking, but in the paper those are technical terms.

~~ Rich Olcott

Gettin’ kinky in space

On By rolcottIn Astronomy: Planetary Science, Astronomy: Stellar Science, Physics: Newton and Gravity, UncategorizedLeave a comment

Things were simpler in the pre-Enlightenment days when we only five planets to keep track of.  But Haley realized that comets could have orbits, Herschel discovered Uranus, and Galle (with Le Verrier’s guidance) found Neptune.  Then a host of other astronomers detected Ceres and a host of other asteroids, and Tombaugh observed Pluto in 1930.whirlpool-44x100-reversed

Astronomers relished the proliferation — every new-found object up there was a new test case for challenging one or another competing theory.

Here’s the currently accepted narrative…  Long ago but quite close-by, there was a cloud of dust in the Milky Way galaxy.  Random motion within it produced a swirl that grew into a vortex dozens of lightyears long.

Consider one dust particle (we’ll call it Isaac) afloat in a slice perpendicular to the vortex.  Assume for the moment that the vortex is perfectly straight, the dust is evenly spread across it, and all particles have the same mass.  Isaac is subject to two influences — gravitational and rotational.

making-a-solar-nebula
A kinked galactic cloud vortex,
out of balance and giving rise
to a solar system.

Gravity pulls Isaac towards towards every other particle in the slice.  Except for very near the slice’s center there are generally more particles (and thus more mass) toward and beyond the center than back toward the edge behind him.  Furthermore, there will generally be as many particles to Isaac’s left as to his right.  Gravity’s net effect is to pull Isaac toward the vortex center.

But the vortex spins.  Isaac and his cohorts have angular momentum, which is like straight-line momentum except you’re rotating about a center.  Both of them are conserved quantities — you can only get rid of either kind of momentum by passing it along to something else.  Angular momentum keeps Isaac rotating within the plane of his slice.

An object’s angular momentum is its linear momentum multiplied by its distance from the center.  If Isaac drifts towards the slice’s center (radial distance decreases), either he speeds up to compensate or he transfers angular momentum to other particles by colliding with them.

But vortices are rarely perfectly straight.  Moreover, the galactic-cloud kind are generally lumpy and composed of different-sized particles.  Suppose our vortex gets kinked by passing a star or a magnetic field or even another vortex.  Between-slice gravity near the kink shifts mass kinkward and unbalances the slices to form a lump (see the diagram).  The lump’s concentrated mass in turn attracts particles from adjacent slices in a viscous cycle (pun intended).

After a while the lumpward drift depletes the whole neighborhood near the kink.  The vortex becomes host to a solar nebula, a concentrated disk of dust whirling about its center because even when you come in from a different slice, you’ve still got your angular momentum.  When gravity smacks together Isaac and a few billion other particles, the whole ball of whacks inherits the angular momentum that each of its stuck-together components had.  Any particle or planetoid that tries to make a break for it up- or down-vortex gets pulled back into the disk by gravity.

That theory does a pretty good job on the conventional Solar System — four rocky Inner Planets, four gas giant Outer Planets, plus that host of asteroids and such, all tightly held in the Plane of The Ecliptic.

How then to explain out-of-plane objects like Pluto and Eris, not to mention long-period comets with orbits at all angles?outer-orbits-1

We now know that the Solar System holds more than we used to believe.  Who’s in is still “objects whose motion is dominated by the Sun’s gravitational field,” but the Sun’s net spreads far further than we’d thought.  Astronomers now hypothesize that after its creation in the vortex, the Sun accumulated an Oort cloud — a 100-billion-mile spherical shell containing a trillion objects, pebbles to planet-sized.

At the shell’s average distance from the Sun (see how tiny Neptune’s path is in the diagram) Solar gravity is a millionth of its strength at Earth’s orbit.  The gravity of a passing star or even a conjunction of our own gas giants is enough to start an Oort-cloud object on an inward journey.

These trans-Neptunian objects are small and hard to see, but they’re revolutionizing planetary astronomy.

~~ Rich Olcott

Plutonic Goofyness

On By rolcottIn Astronomy: Planetary Science, UncategorizedLeave a comment
goofy-and-dp-pluto
Is Pluto wearing a space helmet?
No, that helmet is Pluto.
(Based on a cartoon by Andy Diehl)

Andy Diehl brings up a question worth considering over a tasty beverage.  How come Pluto’s a dog and Goofy’s a dog but Pluto gets the collar end of the leash?  Hardly seems fair.

Which brings us to that other controversial Pluto, the one that NASA’s New Horizon spacecraft visited last July.  (News flash — on 28 October, NASA announced that they’d received the very last of the data NH accumulated during that 2½-hour visit.)  Official Astronomy has reclassified Pluto from “planet” to “dwarf planet,” but NH honcho Alan Stern and much of the rest of the world say, “No way!”

The traditionalist position is, “But we’ve always called Pluto the ninth planet.”  Well, “always” only goes back to when the preternaturally persistent Clyde Tombaugh discovered the object in 1930.  At the time he found it Pluto was indeed the ninth “planet” out from the Sun.  However, it spends about 10% of each orbit* closer to the Sun than the eighth planet, Neptune.  So should we call it the “seven-and-a-fraction-th” planet?

No, because (1) that contravenes Official Astronomy’s rules, and (2) it’d be silly.

So what are the rules for what’s a planet?

  1. The object must be in orbit around its star.
  2. The object must be massive enough to be rounded by its own gravity.
  3. It must have cleared the neighborhood around its orbit.

“Rounded” is a bit tricky.  It doesn’t mean “spherical” because if you spin a  sphere, centrifugal forces move mass towards its equator.  Earth’s equator is 13.3 miles further away from its center than its poles are.  Miller’s Planet in the Interstellar movie is also a spheroid, even further deformed by elongation towards the black hole it orbits, yet it still rates as “rounded by its gravity” and qualifies as a planet.

“Clearing the neighborhood” means “my gravity dominates the motion of everything in my orbit.”  Earth and Jupiter, both acknowledged planets, each have retinues of asteroids in the Trojan positions, at the same distance from the Sun as the host planet but in regions 60º ahead of or behind it.  Even so, both planets often suffer messy encounters (remember Chicxulub and Chelyabinsk?) with asteroids and such that hadn’t gotten the memo.

Neptune meets all three criteria.  Its gravity dominates Pluto’s motion even though Pluto’s in a separate orbit.  For every three of Neptune’s trips around the Sun, Pluto makes exactly two.  The gravitational converse doesn’t hold, though.  Pluto’s mass is 0.1% of Neptune’s so the big guy doesn’t care.

pluto-orbits-1This video, from an Orbits Table display at the Denver Museum of Nature and Science, shows a different Plutonian weirdness.  We’re circling the Solar System at about 50 times Earth’s distance from the Sun (50 AU).  Reading inward, the white lines represent the orbits of Neptune, Uranus, Saturn and Jupiter.  The Asteroid Belt is the small greenish ring close to the Sun.  The four terrestrial planets are even further in.  The Kuiper Belt is the greenish ring that encloses the lot.

The  yellow-orange line is Pluto’s orbit.  Most of the Solar System lies within a thin pancake, the Plane of The Ecliptic. Pluto’s orbit is inclined 17º out of the Plane.  That’s odd.

Theory says that the System evolved from an eddy in a primordial cloud of dust and gas.  Gravity shrank that blob of stuff to form a disk at the eddy’s equator as it drew 99.9% of the system’s mass to form the Sun at the disk’s center.

Newton’s First Law is all about Conservation of Momentum.  When applied to circular motion, it says that if you’re whirling in a certain plane, you’ll continue whirling in that plane unless something knocks you out of that plane.  Hence, the Plane of The Ecliptic.

Pluto’s path is a puzzling challenge to the theory.  It was only a minor puzzle until the 1990’s when astronomers discovered a plethora of Pluto-type objects outside of Neptune’s orbit.  Most run way out of the Plane.  Worst is Eris, at inclination 44º .  Clearly, Pluto’s not special.  It belongs to a large tribe that Astrophysicists must explain if they’re to claim to  understand the Solar System.

~~ Rich Olcott

* – During its current 248-year orbit, Pluto was inside Neptune’s orbit between 1979 and 1999.