Widdekind

In 2004 AD, earth-world steel production exceeded 1 million metric tons, derived from over 1 billion metric tons of iron ore (98% of which is devoted to steel production). Thus, the mass-ratio, of desired output (steel), to raw input (iron ore), is roughly 1:1000. And thus, excepting other (extreme) compensating factors; and due to the extreme energy costs, of 'moving mountains of mass', in-and-out, hundreds of millions of kilometers, through inter-planetary space; so, seemingly, steel 'should' be refined in situ, and the finished products only shipped back to earth (rather than the raw space ore). Note, that on earth, the cost cargo transportation, by train, is roughly 0.2 MJ per ton-km = 30e6 MJ per ton-AU = 30 TJ per ton-AU = 8 kiloton-TNT per payload-ton-AU. Thus, order-of-magnitude, terrestrial train transport costs, applied to MAB transportation distances (~2 AU), would be of-order 0.01 megatons per ton. Wheres, nuclear decelerations, required for 'space dropping' MAB asteroids onto our moon, amount to roughly 1 megaton per ton, or, two orders of magnitude more. Thus, if steel could be refined in situ, out in space, in the MAB, reducing needed transportation masses, by three orders of magnitude, then refined steel could be 'space dropped' onto our moon, at one-tenth the transportation cost, per 'product-ton'. And, the use of nuclear power (nuclear deceleration charges, for space mining), over chemical power (diesel trains, on earth), might amount to additional monetary savings. According to the Wikipedia article that you cited, And, scientists seemingly suggest, that our moon has, over the aeons, absorbed many of the meteoroids that might have impacted our planet. And if so, then the crust of our moon, may be economically minable, as ore-bearing source-rock, for shipment back to earth. use of latent GPE, stored within 'moon-dropped' meteoroids, and released upon moon impact, could create a 'lunar lava lake', which would melt & 'self-smelt' the moon-delivered raw ore (?!) The (relative) KE, of a 'moon-dropped' meteoroid, impacting upon the moon, with [math]\Delta Vs \approx 5-7 km/s[/math], would be 10-20 GJ per ton. And, melting one ton of raw ore, currently consumes only 2 GJ per ton, roughly one order-of-magnitude less. Thus, 'moon-dropped' meteoroids store sufficient (relative) GPE, to completely melt themselves, on moon impact. So, with sufficient delivery rate, a lunar 'lava lake' could be created and maintained, into which meteoroids could be deposited, as a 'world-scale smelter system'. The lunar lava lake could be allowed, to gravitationally chemically differentiate, so that the slag rose to the surface. Then, that surfaced slag could be 'super-sleuced', through artificial canals, into the lunar maria. Then, after the deposited molten iron cooled sufficiently, it could be lunar-surface strip mined: Earth-impinging meteor-showers, thrown off by the deposit impacts, could cause collateral damages, on earth, which would have to be covered by insurance: Cost-of-Doing-Business -- "Sorry about the wind-shield, keep the rock"

Space Mining amounts to 'hurling whole hills into orbit', and so requires 'nuclear-arsenal Planet-Killer power' On earth, mining requires moving mountains worth of material. And, space mining, to economically compete, with terrestrial mining, must move similar amounts of materials. Thus, space mining requires 'land-scaping our solar system' -- to wit, 'space scaping' -- moving mountain-sized meteoroids, from MAB orbits (out at 3 AU), onto terrestrial-intercepting trajectories (1 AU), and then 'soft-landing' them on world (with, maybe, the moon in some step in between). Now, to do so, requires accelerating the 'space mountains' ('space-bergs ?') with [math]\Delta_Vs[/math] of 2 x 5 = 10 km/s. And, that's earth escape velocity (~11 km/s) ! And again, that's ~10x faster, than a speeding tank-cannon artillery shell ! So, please ponder, that space mining, which requires 'space-scaping' our solar system, energetically amounts to 'hurling whole hills', off-world, from earth's surface, into orbit, and out into deep space beyond. And so, now, please ponder, that when the reverse occurs -- to wit, when 'whole hills' and 'massive mountainous meteoroids' impinge & impact upon this world, they can cause major Mass Extinction events (e.g., 'Dinosaur-killer' 65 Mya). Thus, the power required, to mine space resources -- which requires energies equivalent to 'super-cannon-shotting' whole 'hills', or even more massive 'mountains', off-world -- is equally equivalent, to dropping 'Planet Killer' asteroids, onto earth, from the MAB. To wit, it requires Planet-Killer power, which is energetically equivalent to 'Dinosaur-killer-class' impacts, per payload: visual equivalents, of energy requirements, of actual Space Mining

SNs create more than enough pressure, presumably, to squash carbon into diamonds ("electron chemistry") -- they create so much pressure, that they squash carbon atoms together ("nuclear fusion"), into other, heavier, elements (like N, O, S, Fe). SNs spew out heavy-element enriched, chemically polluted, 'star soot'. The word "droplets" paints a picture, of a molten liquid -- that's a state of matter, which only exists, at high densities & pressures, characteristic of planetary conditions, not the diffuse "polluted soot dust" spewed into space's vacuous void, by SNs. And, asteroids only re-accumulate, from microscopic mineral dust grains, millions of years later -- there's no "fast-and-direct" solidification, of SN debris, straight into full-fledged asteroids (they have to gradually build up, from nanoscopic bits & pieces). (anybody disagree??)

'Creationists' often cite the complexity, of biological systems (e.g., human eye), as 'proof' of Divine Design. Yet, gradual evolution, through variation & selection, applied 'patiently & persistently', for long periods of time, can also account, for those complexities. Now, 'Fine Tuning' sounds strikingly similar, of a like line of logic. For, some cite such a set of 'perfected parameters', as 'proof' of 'something special' having happened -- essentially, Divine Design. Yet, again, evolution, through variation & selection, could, equally again, account for Cosmic parameter 'perfectification'. According to the DC documentary How the Universe Works, cosmo-genesis may be cyclical -- every Big Crunch begets an ensuing Big Bang. Such suggests, or sketches, the contours of a 'Cosmos-selection system': Big Bang Big Crunch ('unfit' universe 'dies') 'the stuff of space-time' is modified, to some degree, by the fiery inferno ('clay re-thrown'; parameter values varied) next Big Bang Such a scheme seems entirely 'natural' -- 'selection' by, 'variation' from, Big Crunch -- since most FT arguments allege, that 'typical' parameter value 'settings' would generate universes which were wildly unstable, suffering from infinitesimal lifetimes. Our Cosmos, then, would be one of the first 'long lived' universes, after an 'endless infinity of ephemeral fizzling failures'. However, what would happen, if some universe 'failed' in a 'Big Stretch' scenario, expanding forever -- unlike 'natural' selection, such a scenario attributes infinite lifetime, to a 'failure'*... * Er go, no Cosmological Constants ??? Wow, the author seems to suggest, that the space-time fabric, of our Cosmos, is a "dermal skin", composed of Planck-scale "skin cells", whose "replication & division" accounts for the observed expansion -- to wit, "growth" (!) -- of our Cosmic space-time. Spatially, such a structure is "cellular"; temporally, such a structure is "fibrous", the world-lines of the "skin cells" stranding together, like extruded spaghetti. Such seemingly says, that space-time itself is "living", a "living tissue membrane", in some informational-processing-sense -- an "H R Geiger" space-time:

Using our moon's ~1 km s-1 orbital velocity, to 'cushion the landing', of lunar-delivered MAB asteroids, would reduce their relative overtake velocities, to ~5 km s-1. Thus, 'space dropping' ore bodies, from the MAB, to our moon, would require deceleration [math]\Delta Vs[/math], of roughly - 5 km s-1 'at both ends', both 'up' in the MAB, and again immediately prior to moon impact. So, even with optimal nuclear-energy-to-momentum-transfer efficiencies, it would require 2 x 0.5 = 1 megaton per payload ton, to 'space drop' MAB bodies, to our moon. 'Space drops' would occur every New Moon, when our moon was on the 'outside' of earth's orbit, moving 'forward', +1 km s-1 faster around than the earth (to cushion the delivery landings). And if so, then such a scheme, would amount to 'nuclear mining', for each ton delivered... to the moon, not even as far as the earth. Could that possibly be economical ?? Economics: Since the 1940s AD, the U.S.A. has spent roughly 400 billion dollars, building nearly 70 thousand nuclear warheads. For sake of sci-fi, then, one could conceive of costs near $5 million per device, or $10 million dollars per pair of devices (both the 'drop' and 'deliver' [math]\Delta Vs[/math], at the 'top' and 'bottom' of the MAB-to-moon transfer trajectory). What, then, is worth >$10 million per payload ton ? At current earth market prices, most metals sell for $3 - $30 thousand per ton -- of order 1% minimum space-mining costs. Only precious metals (palladium, gold, platinum) sell for $20-60 million per ton. Thus, this space-mining proposal could, conceivably, work well, for precious metal extraction, from space deposits.

Diamonds are formed, only under high pressures -- pressures characteristic, only of the interiors, of large, planetary-scale, bodies. Diamonds, per se, may not be common occurrences, in meteoroids, or asteroids (except through shock formation, from impacts, with other bodies).

If you 'moon crashed' a meteoroid, all the way from the MAB, onto our moon; and if it was composed of volatiles; then wouldn't it 'explode', and all the volatiles boil off, into space, on moon impact ? What would be the relative 'over-take velocity', of the infalling ore body, relative to the earth-moon system? Please ponder, that infalling asteroid's 'space drop' transfer-to-intercept orbit. By conservation of (specific) angular momentum, w.h.t. (perihelion vs. aphelion): [math]L_p = L_a[/math] [math]\therefore r_p v_p = r_a v_a[/math] [math]\therefore \frac{v_p}{v_a} = \frac{r_a}{r_p} \approx 3[/math] Thus, the inbound body will be speeding through space ~3x faster, at intercept, then immediately after the -5 km s-1 deceleration burn, back in the MAB. But, how fast was it then moving? Now, for the assumedly circular orbits, of the MAB body, and the earth, [math]v^2 = G M_{\odot} / a[/math]. This gives velocity values, of roughly 30 km s-1 (earth), and 17 km s-1 (MAB). After a -5 km s-1 de-orbit burn, then, the now-infalling ore-load was moving at roughly 17 - 5 = 12 km s-1; and, it accelerates, in-bound, upto ~3x that, or roughly 36 km s-1. Thus, the over-take velocity, is ~6 km s-1. The moon orbits around the earth, at roughly 1 km s-1. Thus, by timing the space-drops, on an appropriate monthly basis, the infalling payloads would overtake the moon, as it was 'moving away' from them. Then, their relative velocities would be 6 - 1 = 5 km s-1. The point being, that's more-than-cannon-shot-fast ! Anything that slammed into the moon, at ~5 km s-1, would take a profound pounding. What other than metal, could survive such speeds?

Please ponder, a presumed metal-rich asteroid, in our sun's Main Asteroid Belt (MAB), circling our central star, in an assumedly circular orbit ([math]e \approx 0[/math]). And now, please ponder detonating (appropriate, shaped) nuclear charges, on its spin-ward side, to de-orbit the body, and 'drop' it down, onto an earth-crossing trajectory. Now, the largest such earth-crossing orbit, requiring the minimum [math]\Delta v[/math] de-orbit burn, out in the MAB, is the 'earth-touching', tangential, Hohmann transfer orbit: minimal transfer orbit 'drops' body from [math]3 \rightarrow 2[/math] Now, ignoring reduced mass effects, for a rough calculation, w.h.t.: [math]\frac{L}{m} = \sqrt{G M_{\odot} a (1 - e^2)}[/math] Before the de-orbit burn, the body begins, on an assumedly circular MAB orbit ([math]a_{ast} \approx 3 AU[/math]). After the burn, the body ends, on an elliptical earth-touching orbit ([math]2 a = a_{ast} + a_{\oplus}[/math]). Thus, [math]a \approx 2 AU[/math]. And, since our sun (essentially) resides at the perihelion focus, of that ellipse, w.h.t.: [math]a_{\oplus} = a (1 - e)[/math] [math]\therefore e = 1 - \frac{a_{\oplus}}{a} = 1 - \frac{2 a_{\oplus}}{a_{ast} + a_{\oplus}}[/math] [math]\therefore e = \frac{a_{ast} - a_{\oplus}}{a_{ast} + a_{\oplus}}[/math] Thus, [math]e \approx 1/2[/math]. And, so, the specific angular momentum, of the metallic meteoroid, must be muted, by the amount: [math]\frac{L}{m} = \sqrt{G M_{\odot} \times 3 AU} \rightarrow \sqrt{G M_{\odot} \times 2 AU \times \frac{3}{4}}[/math] Thus, [math]\Delta \left( \frac{L}{m} \right) = \sqrt{G M_{\odot} \times 3 AU} \times \left( 1 - \sqrt{\frac{1}{2}}\right)[/math] And, that specific angular momentum reduction is realized, by a burn, out at [math]3 AU[/math]: [math]\Delta \left( \frac{L}{m} \right) \approx \Delta v \times 3 AU[/math] Thus, [math]\Delta v \approx \sqrt{G M_{\odot} / 3 AU} \times \left( 1 - \sqrt{\frac{1}{2}}\right) \approx 5 \, km \, s^{-1}[/math] Now, 1 kiloton TNT equivalent yields roughly 4 TJ of energy. So, if, for the nuclear charges, [math]E \approx c \Delta p = c m_{ast} \Delta v[/math]; then, the specific de-orbital energy required, is approximately 400 kilotons per payload ton. Allowing for inefficiencies, then, to de-orbit asteroids, from the MAB, onto earth-crossing, moon-crashing orbits, would require 0.5 - 1 megaton per ton. Proposal -- de-orbit asteroids, from MAB, to moon surface; and, transfer ore to earth, via Lunar space elevator

Dinosaur 'death pose' resembles ancestral, proto-Dinosaur, "maximum effort" posture ??? In the immediate aftermath, of the Permian Mass Extinction c.250 Mya, early 'proto-Dinosaurs', like Euparkeria (south Africa), survived the cauldron of competition, by rearing up, on their hind legs, and, thereby, "reaching high for the sky", to consume flying insects, otherwise unreachable from ground-level (BBC Walking with Monsters DVD): Over many millions of years, Dinosaurs therefore evolved more advanced lungs, hearts, and hips, until the first true Dinosaurs evolved true bipedal postures, c.230 Mya (south America). Now, that feeding posture, of 'proto-Dinosaur' Euparkeria, resembles the classic 'Dinosaur death posture', seen in scores of specimens, from the fossil record: These opisthotonic (Gk. opistho- ['back'] tonos ['tension']) Dinosaur 'death throes' are "seen only in dinosaurs, pterosaurs and mammals, which are known or suspected to have had high metabolic rates" and which were warm-blooded. And, those 'death-throes' are what commonly "accompanies a long, slow death". Now, please ponder, the evolutionary, and psychological, centrality, of (1) feeding; (2) survival instinct. Indeed, the Will to Live necessarily involves a 'Will to Feed'. Perhaps, then, even into death, Dinosaurs drew upon the ancient "terror tenacity", of their archaic 'proto-Dinosaur' progenitors, who fought ferociously for life, in the aftermath of the Permian Mass Extinction, and lived... when 95% of all land life on earth fizzled, in failure, into oblivion (???). Dinosaur 'death pose' resembles human "throw back your head & laugh" in exultation, rage -- suggesting its psychological basis ??? Since the mind drives bodily behavior, a behavior common to mammals, theropod dinosaurs, & pterosaurs might imply a shared psychological inheritance, from Permian Period progenitors c.300 Mya (???): "You think this is the real Quaid" (Total Recall)

Globular Clusters obey galaxy scaling laws: source: Mordechai Milgrom. Ninety-five percent of the universe has gone missing, Or has it? in: Does Dark Matter Really Exist (Scientific American Special Report), p.2-ff. Also available online. Addendum: galaxy scaling laws reflect origin of observed brightness in column density along LOS According to Geach (2011), over half of all baryonic conventional matter, across our Cosmos, is so diffuse (optically thin) that it is, as yet, non-visible. central BH masses, in GCs, range from One Hundred - Ten Thousand solar masses According to Rejkuba (2007 AD): Such implies central BH masses ranging from [math]100 < M_{BH} < 10,000 M_{\odot}[/math], and velocity dispersions ranging from [math]7 km/s < \sigma < 20 km/s[/math].

Cosmological computer simulations show, that large 'mother-ship' galaxies are accompanied by fleets of 'support craft' galaxies: And, indeed, local spiral galaxies have 100-500 GCs, and elliptical super-galaxies have over 10 thousand. Interpreting GCs, as 'mini-dwarf galaxies', goes far toward rectifying simulations w/ observations. If GCs typically mass [math]10^{4-5} M_{\odot}[/math], then, by the 0.1% rule, GCs should swarm around central BHs with masses of [math]10-100 M_{\odot}[/math]. According to the M-sigma relation: [math]log \left( \frac{M_{BH}}{M_{\odot}} \right) \approx 8 + 4 log \left( \frac{\sigma}{200 km s^{-1}} \right) [/math] such systems should show velocity dispersions of order 4-6 km/sec. Is that accurate? Do GCs obey galactic laws?? According to Scarpa (2007 AD), "all [Globular] Clusters studied so far do behave like galaxies".

Central BH's mass ~0.1% of the galactic central bulge mass (M-sigma). There is only, seemingly, a weaker correlation, and certainly secondary, between bulge & disk/galaxy:

Is not the Stress-Energy tensor, of GR, essentially 'blind', to the 'means' by which 'mass-energy' is present, caring only about the 'end' amount of 'mass-energy' ? To my current comprehension, the only real difference, between 'matter' and 'energy', is that the former can be localized, into a stable & static configuration, of 'substantive stuff' -- a little like 'light, pinned permanently in place'. "Mass", meaning "rest mass", is the ability of 'matter' to localize, into some particular, and potentially permanent, 'place' -- a 'frozen in' curvature, of the space-time fabric, instead of a 'sonic vibration' of the same, perpetually propagating thru the same. Biological 'anabolism' amounts to injecting energy, into the electrical bonds with molecules, to stick molecules together, and build ever bigger macro-molecules, thereby. Although it is a tiny, electro-chemical caliber amount, Living (bio-)chemical systems convert energy, via such endothermic chemical reactions, into stable matter molecules.

Europa 'ice rafts', near moon equator, jut 300 meters above frozen 'water line', implying 4 km submerged below According to NASA, the resolution, of the Europa Ice Rafts image, is 54 meters per pixel. And, the 'ice cliffs', of the presumed 'ice rafts', which just up above the presumed '(frozen) water line', are roughly 3 pixels wide. Accounting for the viewing angle, therefore, those 'ice cliff edges' are probably about 300 meters high. Now, water ice, at roughly 90 K, has a density of 0.934 g/cm3. And, the ratio of (1-0.934) : 0.934 is roughly 1:14. Doesn't that mean, that there would be about 14x as much ice 'below the water line', than above it, on Europa? And therefore, those ice rafts, when they were rafts, were probably about 300 meters x 14 = 4 km thick. Since then, the surface has obviously frozen over, enclosing the rafts in more ice. Ipso facto, that surface is colder, now, than whenever those rafts were rafts. Er go, that 4 km thickness is a 'minimum thickness when warm' figure. This writer concludes, therefore, that that ice formation, near Europa's equator -- "9.4 degrees north latitude, 274 degrees west longitude" -- is, currently, >4 km thick.

If Europa is colder at the poles (55K) than the equator (110K), the ice would be thicker at the poles -- so best to do the drilling/melting, at the equator (at moon noon-day) ?

Whenever two particles interact, even when one is an "energy-borrowed" virtual particle, the pair are entangled. And, according to the more detailed account, in the link, provided by Swansont (thanks again!), virtual photon emission occurs in pairs of opposite-but-equal momentum ([math]\pm k[/math]); and, charged particles interact, with the 'appropriate' virtual photon, of that pair, in order to effect the appropriate EM interaction (e.g., electrostatic repulsion (same charge), or attraction (opposite charge)). Thus, what such seemingly suggests, is the following: a charged particle "borrows [math]\Delta E[/math]", and emits a virtual photon, with which the emitting particle is entangled that virtual photon has "outward" (positive) & "inward" (negative) momentum components if that virtual photon "fizzles away", without interacting with any other charges, then, due to the entanglement, the emitting particle "pops back" to the way it was otherwise, if that virtual photon interacts with another charge, then that charge "pays the [math]\Delta E[/math] bill", promotes the 'appropriate' aspect of the virtual photon into reality, and absorbs the 'appropriate' amount of momentum (moving towards, or away, from the emitting particle, per opposite, or same, charge) and, that fact is 'communicated', to the emitting particle, through the entanglement; therefore, and thereby, the emitting particle "pops" into the appropriate position (towards, or away, from the absorbing particle, per opposite, or same, charge) This writer is still unclear, on how photons can have "backwards" momentums. For, according to Zukav, virtual photons are exactly the same as real photons, except that "they're in energy debt mode" (my words), having been "borrowed" into existence, "on [math]\Delta E[/math] loan". And, if so, then their 'ought' to be such a thing, as a "backwards" real photon, too (shine your flashlight, in the direction, that you want to go -- a 'puller', not a 'pusher', thruster). Note, too, that, according to this picture, the actual 'detailed' motion, of charges, 'accelerated' by interactions, via virtual photons, with other charges, is not smooth and continuous. Instead, it occurs, via successive quantum jumps, as the charges simultaneously emit paired [math]\pm k[/math] virtual photons, with which they are, having interacted, entangled; and, then, 'ghost out' into corresponding 'pushed' & 'pulled' states. Those then wave-function collapse, if/when the emitted virtual photons actually interact, with other charges (which promote the virtual photons, into reality, and then absorb the 'appropriate' energy/momentum). Thus, the Classical differential equations, represent only the 'macroscopic Classical continuous limit', of the actual discrete, 'Quantum-hop-skip-and-jumping', which is rather more of a series of staccato 'snaps'.

Please ponder the SWE, for the Hydrogen atom: [math]E \Psi \; = \; \hat{K} \Psi \; + \; V \Psi[/math] where [math]\hat{K} \propto - \nabla^2[/math] is the 'QM KE', or 'Q-KE', operator. Now, the energy [math]E[/math] is a constant. But, the potential energy [math]V[/math] varies through space, being "very negative" near the nucleus, and "nearly zero" far from it. Thus, this leads to two regions, of the Schrodinger solutions, for the Hydrogen wave-functions: Classically-allowed region (r < rBohr,n) -- Q-KE is positive; wave-function is 'concave down'; "body" Classically-forbidden region (r > rBohr,n) -- Q-KE is negative; wave-function is 'concave up'; effervescent exponentially-decaying "tail" Now, what does negative KE mean ? If KE is "stored Work energy", does that mean, that the "tails" of wave-functions can do no Work, on other objects ?? To wit, only the "bodies" of wave-functions resist compression forces, generating the 'structural strength' of some molecular quantum system ??

Quick Analogy: When a comet comes near some central star, it heats up, off-gases, producing jets, which "rocket" the body around. And, when a charge, comes near some other charge, and accelerates rapidly, it emits various radiation-reaction forces (e.g. Synchrotron, Bremsstrahlung). These scenarios are a little alike.

The following fails to consider that Europa is tide-locked, into synchronous revolution-rotation, in its orbit around Jupiter. Thus, the gravity field experienced by Europa is spatially non-uniform, which would distort the equilibrium shape of the moon (making it oblate, squashed down at the poles, and pulled apart in the middle). However, a spatially varying field does not, thereafter, induce tides -- only a time-varying field does, by preventing any single moon shape from 'fitting' all the induced tidal forces. So, what actually matters more, is the time-varying 'differential tidal forces', caused by the orbits eccentricity (which, from the moon's perspective, moves Jupiter inward & outward); or, caused by the moon's http://axial tilt of 1 degree (which, from the moon's perspective, moves Jupiter up above, and down below, the moon's mid-plane). The former effect makes all tidal forces felt by the moon, vary by the cube of the ratio of the orbital periapsis to apoapsis (= (1+e)^3). And thus, the differential tidal force (= (1+e)^3 - 1 ~= 3e), for Europa (e = 0.009), is only a few percent, of the value calculated below -- which would imply experienced surface tides, of only a few meters, a little like the ocean tides experienced on earth. Jupiter induces ~100 meter tides on Europa ? Planetary bodies approximately obey a simple scaling relation, between bulk average density, and surface gravity. (Essentially, gravity squeezes, and compresses, the material.) There-from, the change in surface gravity, caused by tidal forces from Jupiter, creates compressions & decompressions, in Europa, which contractions & expansions are experienced as surface tides. From said simple scaling relation, said tides are predicted to be order-of-magnitude 100 meters: [math]\bar{\rho} \equiv \frac{<\rho>}{<\rho>_{\oplus}}[/math] [math]\bar{g} \equiv \frac{g}{g_{\oplus}}[/math] [math]\bar{\rho} \approx 0.29 + 0.44 \times \bar{g}[/math] [math]\therefore \; <\rho> \; \approx \; 0.29 <\rho>_{\oplus} \; + \; \; 0.44 \frac{<\rho>_{\oplus}}{g_{\oplus}} g[/math] [math]\delta <\rho> \; \approx \; 0.44 \frac{3}{4 \pi G R_{\oplus}} \delta g [/math] [math]\delta <\rho> \; \equiv \; \delta \left( \frac{M}{V} \right) \; = \; - \frac{M}{V^2} \delta V \; = \; - <\rho> \frac{\delta V}{V} \; = \; -<\rho> \frac{3 \delta R}{R}[/math] [math]\therefore \; - < \rho > \frac{3 \delta R}{R} \; \approx \; 0.44 \frac{3}{4 \pi G R_{\oplus}} \delta g [/math] [math]\delta R \; \approx \; - \frac{0.44}{3} \left( \frac{R}{R_{\oplus}} \right) \left( \frac{\delta g}{g} \right) \times R [/math] [math]\delta g \equiv \frac{2 G M_J}{D^3} \times (2 R)[/math] [math]\therefore \; \frac{\delta g}{g} \; = \; 4 \left( \frac{M_J}{m} \right) \left( \frac{R}{D} \right)^3[/math] [math]\therefore \; \delta R \; \approx \; - 0.59 \left( \frac{M_J}{m} \right) \left( \frac{R}{D} \right)^3 \left( \frac{R}{R_{\oplus}} \right) \times R[/math] [math]\therefore \delta R \; \approx \; \pm 110 \, m[/math] Europa's pack-ice produces Pressure Ridges 300 meters high; such 'sails' suggest underlying 'keels' ~10x as thick (~3 km) On Europa, pressure-induced ridges, up to 300 meters high, form at the boundaries, between ice-crust plates. And, on earth, at earth arctic temperatures, these pressure-ridge 'sails' overly downward projecting 'keels', 7-8x as deep, below the water, as the sail is high, above the water. Assuming Europan ice, being colder, is denser, such 'sails' of 300 meters, probably imply corresponding keels 10x as deep, ~3 km (not including the intervening ice-crust thickness itself). Moreover, the largest Europan ice-crust plates are ~30 km across. And, aspect ratios (width : thickness) of ~5 could be common. Such would suggest, that Europa's ice crust could be 30 km / 5 = 6 km thick. If so, Europa's ice-crust is 'glacially thick' (~3-6 km, or several miles). estimate ice-crust thickness from heat flows ?? Europa's expected equilibrium surface temperature is ~90 K: [math](1 - a) \; \pi R^2 \; \frac{L_{\odot}}{4 \pi D_J^2} \; \equiv \; \left( 4 \pi R^2 \right) \; \sigma T^4[/math] [math]\therefore \; \frac{(1 - a)}{\sigma} \; \frac{L_{\odot}}{16 \pi D_J^2} \; \equiv \; T^4[/math] [math]\therefore \; T \approx 93 K[/math] Europa's actual surface temperatures vary, pole-to-equator, from 50-110 K.

According to the Scientific American special issue Majestic Universe: only metal-rich stars are associated with surrounding planetary systems. (Somehow, condensed dust is needed to 'seed' planet formation?) And, metals are steadily accumulating, at the rate of +8% per Gyr, in our neighborhood. And more, more metals were manufactured, more quickly, closer to the core of our galaxy, where disk densities, and star formation rates, are higher. Thus, moving inwards, from our sun's galactic orbit, disk metallicity increases at the rate of +17% per 'coreward' Kpc. Er go, comparing the figures, the galactic core is 'more mature', than our sun's vicinity, by the rate of ~2 Gyr per coreward Kpc. Now, citing the same source, our star formed with an anomalously large amount of metals, ~40% more than nearby stars, of similar age. Thus, our star formed ~5 Gya, with as much metal, then, as nearby stars do, today. However, merely moving coreward 2 Kpc (7 Kly), one would commonly see star systems as old, and as 'metal mature', as our solar system. And, moving even closer to the core, one would witness star systems billions of years more metal mature still. Fig. 1 -- Milky Way galaxy disk metallicity profile. Our sun is anomalously metal rich, for its remote neighborhood (+5 Gyr). Now, reflecting the relatively recent metallization, of our region of the galactic disk, most exo-planetary systems, which humans have observed to date, are relatively young (<3 Gyr). Yet, they are also nearby (<100s ly). To observe the expected cornucopia of exo-planets, then, human sensing systems will need to peer hundreds of times further afield (10,000s ly) -- something along the lines, of a Pharaonic-scale 'Eye of Horus' super-telescope.

Energy is not conserved, in a detailed sense -- moment by moment, virtual particles can occur, "borrowing" energy from the background (the Zero-Point Energy ??), and existing for some small amount of time, consistent with the HUP. Most of the time, those virtual particles, apparently, "fizzle out" at the end of their HUP-allowed lifetime. However, if they encounter a real particle, which can supply the energy that they've "borrowed", then the virtual particles can be "promoted" into real particles (per Zukav).

I tried to derive the relevant equations in this thread.

Were we to please permit an over-extended analogy... Charged fundamental particles, are a little like 'submarines'... which constantly fire 'virtual photon torpedos'... in various different directions... and which 'time the torpedos', based upon how much energy ([math]\Delta E \implies \Delta t[/math]) they 'borrow from the energy bank'. And now, if those 'virtual photon torpedos', fired in some direction, actually 'hit something' -- interacting, with another charged fundamental particle -- then they 'explode' ('promoted', into 'actualized reality' -- albeit, immediately [and destructively] absorbed). For, that other particle, by adjusting its momentum-and-energy, can pay back the 'debt to the energy bank'. And, so, in some sense, those 'virtual photon torpedos', are like Cash-on-Delivery (CoD) 'debt instruments', bearing the words 'bearer owes the energy bank 1 eV'. Thus, they are 'fired' from one charged fundamental particle; propagate through space; and 'hit' another particle, who 'picks up the tab, and pays the bill' (the ultimate 'passing the buck'). Again, at that point, the photon is immediately 'actualized', 'promoted' from virtuality to reality -- and promptly absorbed, deflecting the other particle, and so accounting for the EM charge interaction. If this picture is appropriate, then charged fundamental particles are constantly 'emitting messengers', with which they are constantly 'probing their environment', constantly querying "is their a charge over there? or, how about over that-a-way" ?? And, if any of their 'CoD virtual photon torpedos' actually 'hit' other particles, those particles 'pick up the tab, & pay back the bank', thereby 'actualizing' the photon, from virtual-to-real, and then absorbing the ensuing momentum/energy, accounting for the EM interaction. (Again, such virtual photons, being destroyed upon actualization, amount to a private point-to-point communication, whose former virtuality, and ensuing instantaneous reality, are utterly unobservable, to all other particles, who are "not involved", which is why the photons, underlying the EM interactions, are never observed, except by their effects upon charged particles, whose paths are visibly deflected by those photons.) Otherwise, the 'virtual photon torpedo' presumably 'fizzles out like a dud'... and the firing particle 'goes back to the way it was', 'undoing the recoil of firing the torpedo in the first place'. (Perhaps all those 'recoils', from constantly 'borrowing from the bank', and 'firing photon torpedos every which way', accounts for the Schrodinger-equation spreading of Wave Functions ???)

oops -- upon awaking, I realized, that velocity = change in distance / change in time. Thus, an anti-particle, moving 'to the left', but 'backwards in time', has a 'minus sign in the numerator & denominator'. And so, the 'double negative' means that it has the same velocity (not minus the velocity). In turn, such suggests, that anti-matter must, still, have normal mass (??).

(sorry for the late response / realization) That's an important distinction, planetary formation is only-in-some-ways similar, to star formation. In particular, smaller planetary systems might actually create larger 'inner moon system' tides, than are present in inner star systems. For example, although our sun is ~1000x more massive than Jupiter, Mercury orbits ~450x farther from the sun, than Metis from Jupiter -- and tidal forces depend on D-3. Perhaps, then, Jupiter thusly possesses an inner ring system, of tidally disrupted debris, whereas our sun does not. And, so, that illustrates, that due to the critical presence of fusion power, present in stars but not planets, the 'temperature regime', in which planetary formation occurs, around stars, is dramatically different, than that of moons, around (gas giant) planets -- which determines the body's 'bulk composition', from available materials, and makes 'all the difference in the world / moon' (if you will).