On Gravity, Charge And Geese

A beautiful April day, far too nice to be inside working.  I’m on a brisk walk toward the lake when I hear puffing behind me.  “Hey, Moire, I got questions!”

“Of course you do, Mr Feder.  Ask away while we hike over to watch the geese.”

“Sure, but slow down , will ya?  I been reading this guy’s blog and he says some things I wanna check on.”

I know better but I ask anyhow.  “Like what?”

“Like maybe the planets have different electrical charges  so if we sent an astronaut they’d get killed by a ginormous lightning flash.”

“That’s unlikely for so many reasons, Mr Feder.  First, it’d be almost impossible for the Solar System to get built that way.  Next, it couldn’t stay that way if it had been.  Third, we know it’s not that way now.”

“One at a time.”

“OK.  We’re pretty sure that the Solar System started as a kink in a whirling cloud of galactic dust.  Gravity spanning the kink pulled that cloud into a swirling disk, then the swirls condensed to form planets.  Suppose dust particles in one of those swirls, for whatever reason, all had the same unbalanced electrical charge.”

“Right, and they came together because of gravity like you say.”

I pull Old Reliable from its holster.  “Think about just two particles, attracted to each other by gravity but repelled by their static charge.  Let’s see which force would win.  Typical interstellar dust particles run about 100 nanometers across.  We’re thinking planets so our particles are silicate.  Old Reliable says they’d weigh about 2×1018 kg each, so the force of gravity pulling them together would be …  oh, wait, that’d depend on how far apart they are.  But so would the electrostatic force, so let’s keep going.  How much charge do you want to put on each particle?”

“The minimum, one electron’s worth.”

“Loading the dice for gravity, aren’t you?  Only one extra electron per, umm, 22 million silicon atoms.    OK, one electron it is …  Take a look at Old Reliable’s calculation.gravity vs electrostatic calculation Those two electrons push their dust grains apart almost a quintillion times more strongly than gravity pulls them together.  And the distance makes no difference — close together or far apart, push wins.  You can’t use gravity to build a planet from charged particles.”

“Wait, Moire, couldn’t something else push those guys together — magnetic fields, say, or a shock wave?”

“Sure, which is why I said almost impossible.  Now for the second reason the astronaut won’t get lightning-shocked — the solar wind.  It’s been with us since the Sun lit up and it’s loaded with both positive- and negative-charged particles.  Suppose Venus, for instance, had been dealt more than its share of electrons back in the day.  Its net-negative charge would attract the wind’s protons and alpha particles to neutralize the charge imbalance.  By the same physics, a net-positive planet would attract electrons.  After a billion years of that, no problem.”

“All right, what’s the third reason?”

“Simple.  We’ve already sent out orbiters to all the planets.  Descent vehicles have made physical contact with many of them.  No lightning flashes, no fried electronics.  Blows my mind that our Cassini mission to Saturn did seven years of science there after a six-year flight, and everything worked perfectly with no side-trips to the shop.  Our astronauts can skip worrying about high-voltage landings.”

“Hey, I just noticed something.  Those F formulas look the same.”  He picks up a stick and starts scribbling on the dirt in front of us.  “You could add them up like F=(Gm1m2+k0q1q2)/r2.  See how the two pieces can trade off if you take away some mass but add back some charge?  How do we know we’ve got the mass-mass pull right and not mixed in with some charge-charge push?”

Geese and ducks“Good question.  If protons were more positive than electrons, electrostatic repulsion would always be proportional to mass.  We couldn’t separate that force from gravity.  Physicists have separately measured electron and proton charge.  They’re equal (except for sign) to 10 decimal places.  Unfortunately, we’d need another 25 digits of accuracy before we could test your hypothesis.”

“Aw, look, the geese got babies.”

“The small ones are ducks, Mr Feder.”

~~ Rich Olcott

Advertisements

Water, Water Everywhere — How Come?

Lunch time, so I elbow my way past Feder and head for the elevator.  He keeps peppering me with questions.

“Was Einstein ever wrong?”

“Sure. His equations pointed the way to black holes but he thought the Universe couldn’t pack that much mass into that small a space.  It could.  There are other cases.”

We’re on the elevator and I punch 2.  “Where you going?  I ain’t done yet.”

“Down to Eddie’s Pizza.  You’re buying.”

“Awright, long as I get my answers.  Next one — if the force pulling an electron toward a nucleus goes as 1/r², when it gets to where r=0 won’t it get stuck there by the infinite force?”

“No, because at very short distances you can’t use that simple force law.  The electron’s quantum wave properties dominate and the charge is a spread-out blur.”

The elevator stops at 7.  Cathleen and a couple of her Astronomy students get on, but Feder just peppers on.  “So I read that everywhere we look in the Solar System there’s water.  How come?”

I look over at Cathleen.  “This is Mr Richard Feder of Fort Lee, NJ.  He’s got questions.  Care to take this one?  He’s buying the pizza.”

“Well, in that case.  It all starts with alpha particles, Mr Feder.”

The elevator door opens on 2, we march into Eddie’s, order and find a table.  “What’s an alpha particle and what’s that got to do with water?”

Alpha particle

Two protons and two neutrons, assembled as an alpha particle

“An alpha particle’s a fragment of nuclear material that contains two protons and two neutrons.  99.999% of all helium atoms have an alpha particle for a nucleus, but alphas are so stable relative to other possible combinations that when heavy atoms get indigestion they usually burp alpha particles.”

“And the water part?”

“That goes back to where our atoms come from — all our atoms, but in particular our hydrogen and oxygen.  Hydrogen’s the simplest atom, just a proton in its nucleus.  That was virtually the only kind of nucleus right after the Big Bang, and it’s still the most common kind.  The first generation of stars got their energy by fusing hydrogen nuclei to make helium.  Even now, that’s true for stars about the size of the Sun or smaller.  More massive stars support hotter processes that can make heavier elements.  Umm, Maria, do you have your class notes from last Tuesday?”

“Yes, Professor.”

“Please show Mr Feder that chart of the most abundant elements in the Universe.  Do you see any patterns in the second and fourth columns, Mr Feder?”

Element Atomic number Mass % *103 Atomic weight Atom % *103
Hydrogen 1 73,900 1 92,351
Helium 2 24,000 4 7,500
Oxygen 8 1,040 16 81
Carbon 6 460 12 48
Neon 10 134 20 8
Iron 26 109 56 2
Nitrogen 7 96 14 <1
Silicon 14 65 32 <1

“Hmm…  I’m gonna skip hydrogen, OK?  All the rest except nitrogen have an even atomic number, and all of ’em except nitrogen the atomic weight is a multiple of four.”

“Bravo, Mr Feder.  You’ve distinguished between two of the primary reaction paths that larger stars use to generate energy.  The alpha ladder starts with carbon-12 and adds one alpha particle after another to go from oxygen-16 on up to iron-56.  The CNO cycle starts with carbon-12 and builds alphas from hydrogens but a slow step in the cycle creates nitrogen-14.”

“Where’s the carbon-12 come from?”

“That’s the third process, triple alpha.  If three alphas with enough kinetic energy meet up within a ridiculously short time interval, you get a carbon-12.  That mostly happens only while a star’s going nova, simultaneously collapsing its interior and spraying most of its hydrogen, helium, carbon and whatever out into space where it can be picked up by neighboring stars.”

“Where’s the water?”

“Part of the whatever is oxygen-16 atoms.  What would a lonely oxygen atom do, floating around out there?  Look at Maria’s table.  Odds are the first couple of atoms it runs across will be hydrogens to link up with.  Presto!  H2O, water in astronomical quantities.  The carbon atoms can make methane, CH4; the nitrogens can make ammonia, NH3; and then photons from Momma star or somewhere can help drive chemical reactions  between those molecules.”

“You’re saying that the water astronomers find on the planets and moons and comets comes from alpha particles inside stars?”

“We’re star dust, Mr Feder.”

~~ Rich Olcott

Is there a lurker in the Solar System?

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

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