Apparently yer man is a well-known crackpot. He spent a years worth of salary taking out an ad in the NY Times to promote his ideas. Nobody else who wasn’t paid to take him seriously has done so. His quip at the beginning about scientific advancement coming from lone individuals is self-aggrandising nonsense. It might have been true of Newton or Cavendish, but in the modern era even Einstein – the quintessential lone genius – had to wait decades for mainstream acceptance after his ideas had been carefully validated.
His main factual claim is that the Sun is not a gas but rather condensed matter, perhaps metallic hydrogen. He also claims a gas cannot be a blackbody radiator. Firstly, nobody ever claimed the Sun was a gas. It’s a plasma which is a different state of matter. In a plasma the atomic nuclei and electrons are moving independently, somewhat like a metal where the valence electrons can be considered an electron gas. A metal also has lots of other more regular electron orbitals, so the nuclei can still be locked in a lattice structure, unlike a plasma. But in both cases there are unbound electrons free to interact thermally and generate continuum radiation. The radiative transfer within a star is quite successfully modelled as a combination of free-free and bound-free scattering of photons.
This is by no means to imply that the Sun is a perfect blackbody emitter. At the surface where recombination of nuclei and electrons start to occur due to the falling temperature, we do indeed see a line spectrum superimposed on the continuum. Notable is the red hydrogen alpha line that can be seen vividly in the chromosphere during a solar eclipse, but there are thousands of other absorption lines in the Sun’s spectrum characteristic of its constituent chemical elements.
The absorption line spectrum of very hot stars departs even more radically from the blackbody ideal. Line driven winds occur where the line absorption acts as such a brake on escaping radiation that large amounts of material can be torn from the surface and lead to significant mass loss for heavy stars. Our own Sun only loses an Earth-sized mass every ten million years, but big stars could lose a hundred Earth masses every year!
Contrast this with the metallic hydrogen claim of Robitaille. Metallic hydrogen is thought to occur at low temperatures but extremely high pressures of hundred of gigaPascals. The pressure at the surface of the Sun is many billions of times too low for this condition. On the other hand, the solar pressure is enough to produce continuum radiation in the region of the photosphere (just as we can produce approximations to the continuum here on Earth with mercury and xenon arc lamps). The photosphere is not a surface, as such, but a layer about five hundred miles deep in which the Sun gradually becomes transparent to light as recombination occurs. We are looking at the underlying plasma through a clearing fog (in very much the same way as I described how the CMB formed in the last post). This explains limb darkening in the Sun and other stars in a way that Robitaille’s condensed matter surface can’t. Limb darkening is where our line of sight grazes the edge of the Sun, passing through a greater depth of the cooler layers, resulting in less intense light.
His remark about blackbody radiation being impossible in the presence of convection doesn’t ring true. I would imagine that the argument is that convection requires a temperature gradient, and a temperature gradient implies a lack of thermal equilibrium, a prerequisite for blackbody radiation. But by the same token no body that is heated from the inside and cools from the outside could be a blackbody emitter as there must always be a temperature gradient. The term that astrophysicists use is local thermodynamic equilibrium, a condition that allows a star to be considered as concentric shells that approximate blackbodies. Within this there may be convection cells, but bear in mind that the granulations at the surface of the Sun (which are the tops of convection cells) are typically about the size of the Earth. I see no reason why these can’t be in LTE and approximate black body emitters.
And finally, the one about transverse waves being impossible in a gas … I don’t know a lot about it but I know they are possible in stratified layers of a gas. Here are gravity waves in Earth’s atmosphere caused by orographic lift over an island in the Indian Ocean, and seismic waves on the surface of Jupiter’s clouds after the impact of Comet Shoemaker Levy 9.
**Nature: OBSERVATIONS of the collisions of the fragments of comet Shoemaker–Levy 9 with Jupiter provided an unprecedented opportunity to probe the depths of the planet’s atmosphere. Images taken by the Hubble Space Telescope revealed circular rings surrounding five of the impact sites. The rings were observed for up to 2.5 hours after the impacts and spread at a constant velocity of 450 m/s. There are three types of disturbance that might explain these observations: acoustic waves trapped at the tropopause temperature minimum, gravity waves propagating vertically and horizontally in the stratosphere, and gravity waves trapped in a stable layer which acts as a horizontal waveguide and is located within the hypothesized tropospheric water cloud. (See also: Lessons from Shoemaker-Levy 9 [pdf])
Thanks for the informed response PS (as always) . Most of this is beyond of my own understanding and knowledge. When he was discussing the limitations of gas it should have dawned on me - what about Plasma.
Is he even onto anything about Planks inference in relation to reflectivities being equal for arbitrary materials?
I tried to chase that reference, but it’s so out of context it’s hard to know what he’s talking about. I’ll see if I can dig further.
Ok, Project Gutenberg has a copy of Planck’s book, The Theory of Heat Radiation. Chapter 2 deals with radiation at thermodynamic equilibrium. This is the same basic stuff that you would cover in astrophysics about radiative diffusion in stars. There are lots of formulas, but I would summarise it as follows:
Take a heterogeneous isotropic medium in thermodynamic equilibrium. In layman’s language that means you have a lump of “stuff” – all made of the same thing and the same in all directions – in which the heat energy has been allowed to even out so there is no net flow of heat in any direction. By definition if you take a volume element (i.e. a small chunk somewhere within the material) there is no net flow of energy into or out of the element. So if we consider its surface, there must be exactly the same number of photons going in through the surface as coming out through it. We’re able to deal with a single wavelength at a time here because if the behaviour wasn’t the same for all wavelengths then some wavelength would preferentially flow in or out, contradicting the condition of thermodynamic equilibrium.
Planck summarises this situation as follows (p.34): “It is thus found that, when thermodynamic equilibrium of radiation exists inside of the medium, the process of scattering produces, on the whole, no effect. The radiation falling on a volume-element from all sides and scattered from it in all directions behaves exactly as if it had passed directly through the volume-element without the least modification. Every ray loses by scattering just as much energy as it regains by the scattering of other rays.”
Ok, now we come to consider a volume element that is made of a different material to the rest. When light passes through the surface of this element it is moving from one medium into another. There are various laws of optics at play here (Snell’s Law, Fresnel’s Laws). Some light will be reflected and some transmitted through the boundary. But we can pretty much ignore all that because of the condition of thermal equlibrium. We know from the previous discussion that the same amount of energy must be going in through the surface as coming out through it. That means the amount of inbound light that is reflected from the outer surface must be the same as the amount of outbound light that is reflected from the inner surface, as the amount of light transmitted in both directions must be the same.
This is where Robitaille comes completely unstuck. He claims that this p = p’ relation (Equation 40 in the book) implies that all materials have the same reflectivity. That’s a total misunderstanding. If you take two different types of glass and shine a light on them (from air into the glass) they may indeed have different reflectivities. But that is a completely different situation compared to sticking the two pieces of glass together and shining a light across the boundary between them. Indeed, many lenses are compounds made of different types of glass (e.g. flint and crown) to correct for optical aberrations. If Robitaille was right, the amount of light transmitted through the lens would be different depending on which direction the light went through it. That clearly wouldn’t make any sense. The laws of optics governing such a boundary are symmetrical.
In fact, Planck is merely quoting a well known principle called Helmholtz reciprocity. See the footnote at bottom of page 42 citing Helmholtz’s Handbook of Physiological Optics. As the Wikipedia article says: “The most extremely simple statement of the principle is ‘if I can see you, then you can see me’”. Contrary to popular belief, there’s no such thing as a one-way mirror, only partial mirrors lit differently on both sides. In the case of thermodynamic equilibrium our “mirror” (i.e. boundary between two media) is by definition lit the same on both sides.
In short Robitaille is full of sh1t.
I do feel obliged to mention one other interesting passage from Planck which hadn’t occurred to me before. Referring to the next formula after the one Robitaille takes exception to, he explains:
“The second formula (41) establishes a relation between the intensities of radiation in the two media, for it states that, when thermodynamic equilibrium exists, the specific intensities of radiation of a certain frequency in the two media are in the inverse ratio of the squares of the velocities of propagation or in the direct ratio of the squares of the indices of refraction.”
In layman’s language, Planck is noting that light travels at different speeds in different media. We know from the previous discussion that it doesn’t matter whether the light travels unhindered across a volume element or bounces its way from atom to atom. When it emerges through the surface of a medium of higher refractive index it will have spent less time in that volume element than one of lower refractive index. You can imagine light getting stretched in its passage across such an element. As a result, the light intensity will be lower inside a volume element of high refractive index, even while being in thermodynamic equilibrium with adjacent elements.
Sirius seemed to be changing colour last night from white to green to red, possibly atmospheric conditions but never noticed it like that before
Well spotted, but I’d have said that was the norm! Sirius (declination -17°) only gets to 20 degrees above the horizon in Ireland, and that’s if you catch it crossing the meridian. That’s currently just a couple of minutes after midnight. An evening sighting will be at lower altitude. Stars near the horizon are affected by higher air mass which both dims them and moves their apparent position by refraction. Twinkling (which is more technically called scintillation) occurs when undulations in the atmosphere move the star out of our line of sight.
It’s most noticeable for bright stars like Sirius in the south in winter, and Capella in the north in summer. Our clammy winter nights seem (to me) to cause more scintillation than normal. Whereas dimmer stars will seem to fade and brighten, or even flick off and on, bright stars will flash different colours. That’s because refraction in any medium is wavelength dependent. The different colours of light are bent by different amounts. On an already dim star there probably isn’t enough light for your eye to perceive colour when the light is diminished even further. Our low-light (scotopic) vision is poor at colour discrimination. But a very bright star like Sirius which is already intrinsically white, and therefore bright at a range of visible wavelengths, will be seen to cycle through red and green and back to white.
We don’t see blue in the scintillations, at least that I’ve ever noticed. That’s despite the fact that Sirius’s high temperature means its peak spectral radiance is at 290 nm, well into the ultraviolet. It should have copious amounts of blue in its spectrum. I think it can be explained exactly the same way as a red sunset. Short wavelength radiation is scattered by our atmosphere, which is why the Sun looks yellow instead of white, and the sky is blue. At high air mass the effect is more pronounced – the amount of blue in the direct light is increasingly attenuated close to the horizon. So sunsets are red and Sirius doesn’t twinkle blue. It is also the case that our photopic vision is more sensitive at the red end of the spectrum. (Open to correction if anyone has more info).
There are few phenomena in astrophysics at the moment that are as enigmatic as Fast Radio Bursts (FRBs). They are radio pulses that last just a few milliseconds but seem to be of extra-galactic origin. This implies a very powerful source, as the short length of the bursts tells us the source is compact – smaller than the distance that light can travel in those few milliseconds. Yet it is visible from cosmological distances.
Aside from these few facts, we have no idea what FRBs are. Quasars – the black holes feeding at the centre of active galaxies – can produce powerful radio waves, but FRBs appear and disappear just as quickly, never to be seen again. Pulsars, which are the remnants of collapsed stars, also produce radio waves but they repeat at regular intervals and are generally not bright enough to see in very distant galaxies.
A series of repeating FRBs discovered by the Australian Parkes telescope in 2010 famously turned out, to everyone’s great embarrassment, to be caused by opening the door of microwave oven in the facility’s canteen. But one genuine repeating FRB was discovered in 2015. Now there’s another, discovered by a dedicated fixed radio telescope in Canada.
Doctor Becky talks FRBs…
Dr. Becky’s vid (previous post) was a fortuitous find when I was looking for something on FRBs. Her youtube channel seems to be in its infancy, and is improving with age. Her latest item on supermassive black holes and active galaxies is cool, check it out. Compared to anything you’ll find on TV it’s so much less dumbed down. In fact, she lists all the academic papers she cites, so you can read it all from the horse’s mouth if you wanna go full nerd. Youtube is definitely the place for decent astronomy content these days.
I’ve been finding some other interesting stuff. I’m gutted that I never heard about this one. It’s only from last October and I’d certainly have gone to the event had I known about it. At age 87 there can’t be too many more opportunities to see the legendary Roger Penrose in the flesh, let alone waxing lyrical about his recent work. What a mind! Haven’t watched the whole vid myself yet, but it’s about his recent idea of conformal cyclic cosmology (which is a bit way out there, even for other cosmologists). What I love about Penrose is that he’s never been a follower of fashion, and even at this age he is never shy of controversy. Also, that in the age of PowerPoint and computer simulations, his slides are pithy little hand drawings.
Some super blood wolf trump end-of-days lunar eclipse on Monday apparently.
And I thought this is quite a stereotypical Irish comment the eclipse is from 4:41am to 5:43am)
Thanks for the Penrose lecture, listening to it now.
Such a sharp mind.
It was mentioned that Andrew Wiles gave the previous year’s presentation.
Might flick onto that next.
Youtube really is an excellent source of information, but you have to know the right channels to visit.
I find PBS Space Time slightly beyond my limit (which is what I like).
There are many far beyond this and a lot more dumbed down, but still watchable as light entertainment.
I chucked out my TV a decade ago.
Absolutely no regrets.
Yesterday I fulfilled a sometime personal project, to locate the grave of George Johnstone Stoney, the man who named the electron. It is almost under the Luas bridge in Dundrum, in St. Nahi’s churchyard, though you’d never find either church or grave unless you knew they were there…
"Righteousness Exalteth a Nation", G. Johnstone Stoney M.A, Hon. Sc. D.T.C, Dub, F.R.S. died July 1911, aged 85 years. "Felix qui potuit rerum cognoscere causas"
Stoney lived just the other side of the Luas bridge on what is now Stoney Road, Dundrum from the 1860’s to the 1890’s. You could write a book – and I sincerely hope somebody does – about the scientifically important 19th century connections between a number of Anglo-Irish families including Stoney, Parsons, Grubb, Blood and Fitzgerald. Between them they built the biggest telescopes in the world, the longest railway viaduct (across the Boyne), invented the steam turbine, the periscope and precast concrete, designed Dublin’s most famous bridges and Grand Canal dock, and laid the foundations of Einstein’s theory of Relativity.
Below: Another hint of the family connections from the side of the Stoney grave – his mother Anne Blood, “widow of George Stoney of Oakley Park, Kings County”. George Johnstone Stoney and his brother Bindon Blood Stoney by chance grew up less than three miles from where William Parsons built the world’s largest telescope in Birr, Co. Offaly, and in their early twenties both of them worked as assistants on the telescope, making many significant discoveries. This may have been out of necessity as the family fortunes had taken a turn for the worse along with those of many of the Anglo-Irish country houses in the mid 19th century, forcing them to move to Dublin to join the professional classes. Parsons, the Earl of Rosse, befriended the young Stoney.
Below left: George Johnstone Stoney with daughters Edith (a physics and mathematics lecturer and considered the world’s first female medical physicist) and Florence (first female radiologist in the UK). Right: Stoney’s nephew George Francis FitzGerald, known for the FitzGerald-Lorentz contraction, an integral part of Einstein’s special theory of relativity.
Stoney and Fitzgerald were mainstays of the scientific proceedings of the Royal Dublin Society, with Stoney acting as its vice-president. His wide-ranging scientific work is all the more remarkable because it was done in an amateur capacity and almost entirely “on the side” of his main job in educational administration. He used to get up at five in the morning to do a bit of science before starting his day at the office. An excellent assessment of Stoney can be found in the lengthy Royal Society (UK) obituary. His work in which he names the electron (a number of years before its actual discovery) and estimates its charge at about a third of today’s known value can be read here.
Have an upvote ps200306! Thank you.
The sling is a wonderfully simple and effective weapon which has been in use for tens of thousands of years. It relies on the principle of inertia, which causes a stone that has undergone a circular acceleration to fly off in a straight line from the point of release.
If the stone wants to fly off in a straight line then there must be some force preventing it from doing so when it is being swung. It’s called a centripetal force because it is directed toward the centre of rotation, and in the case of the sling it is provided by the stretched cords.
The gravitational orbit of a moon or planet is similar, but also different in an important way. No matter how fast you twirl a sling the stretched cords will increase the force as necessary to keep the stone in its orbit (unless you exceed some breaking strain). That’s because, microscopically, the electric forces between atoms in the cords push back ever more strongly as fibres are squeezed together.
The gravitational force between a planet and its moon, or a star and a planet, depends only on the masses involved and the distance between them. An orbiting body must be going at exactly the right speed so that the centripetal force required to keep it on its curved path is exactly that provided by gravity. Unlike the sling, for a given orbital distance, there is only one orbital speed that will work.
Now let’s talk about energy. An object’s kinetic energy is determine by its speed and mass. But an object separated from a gravitating body also has potential energy which can be turned into kinetic energy. Push a car up hill and it gains potential energy. Let it roll back down and it converts that energy back into kinetic energy. An orbiting body has potential energy too – the energy that could be released by dropping it toward its parent. Interestingly, that energy depends on the same parameters (mass and distance) as its kinetic energy, so it is instructive to compare the two. The maths isn’t too important , only the final result:
It turns out that for any object in a circular gravitational orbit, its kinetic energy is always exactly half its potential energy. The two quantities are treated as opposite in sign.
Now, you probably know that most celestial orbits are not circular, but elliptical. In such an orbit the speed and distance from the parent vary along the orbit. But each orbit is like rolling a car down one hill and back up another. Potential and kinetic energy are traded, one for the other, so that their total always stays the same. (Conservation of energy is a very important physical principle, but not one we’ll dwell on here). We also find the very general relationship that:
It’s similar to the case for a circular orbit but here the angle brackets signify the average energy along the orbit. Every two-body gravitational orbit of whatever elliptical shape obeys this general relationship. We’ll give it a name – the virial theorem (from vis, Latin for energy).
Let’s complicate things even further. Most orbits involve more than two bodies. In the case of our solar system the central mass of the Sun dwarfs the relatively tiny masses of the planets, and for many purposes we can treat each Sun-planet pair as an independent orbit in calculations. We can do this with spiral galaxies too. In those types of galaxies, the stars move on roughly circular orbits around the centre. If we measure the orbital speed of a star at a given distance from the galactic centre, certain symmetries about Newton’s gravitational equation become useful. All the mass of the galaxy outside the orbit of the star can be handily ignored, while all the mass internal to the star’s orbit behaves like one giant Sun at the centre. So if we can just measure the speed of a number of stars at various radii, we can estimate the whole galaxy mass.
But now consider a globular cluster of a million stars, or an elliptical galaxy of hundreds of billions of stars. Individual stars buzz around in random directions, making the orbital calculus a nightmare. Every star orbits some common centre of gravity under the combined gravitational influence of all the other stars. Tracking the changing potential of each star with respect to each other star is beyond the power of any super-computer. Even though we have great trouble calculating, or even simulating, that number of orbits, we find that our virial theorem still holds for the whole ensemble:
We are now referring to the total kinetic energy of the whole system, and the total potential energy calculated by considering each star paired with each other star. We no longer have to do the individual calculations to be able to glean some very useful information. I mentioned that the orbits in an elliptical galaxy are random. That’s because these giant galaxies evolve from mergers of smaller galaxies after complex tidal interactions. What we mean by random (if you remember your statistics) is that the energies and ellipticity of the orbits follow a Gaussian or normal distribution. And every normal distribution is characterised by just two parameters – its mean value, and its standard deviation. (We may also refer to the variance, or square of the standard deviation. Either way, we are just talking about how widely dispersed the values are around the mean).
With a bit of mathematical juggling we can derive a wonderfully simply equation that leads to the mass of an elliptical galaxy:
This relates the mass of the galaxy internal to a given radius to the velocity dispersion of the stars measured at that radius. It makes the mass calculation for elliptical galaxies just as simple as for spiral ones.
In case you’re wondering how we measure the velocities and velocity dispersions of stars in a faraway galaxy, we use spectroscopy. I’ve mentioned before that it’s the Swiss army knife in the astronomer’s armory. In this case, the known spectral lines of hydrogen in a galaxy’s spectrum are Doppler shifted to give us the velocities of the stars. And if we have stars moving in random directions, the spectral lines are broadened around their average position to give us the velocity dispersion.
Above left: hydrogen Balmer lines at their normal positions (top) and Doppler shifted by a recessional velocity (bottom); right: the spectrum of a galaxy (bottom) compared to a template star (top) showing both an overall Doppler velocity shift and a broadening due to velocity dispersion.
In a nutshell, this is how we measure the masses of galaxies. There are other techniques too, so we call this type of mass measurement from the movement of stars the dynamical mass of the galaxy. It’s the background to an interesting bit of astronomy news this week. But that’ll have to be another post.
I never understood how space vehicles use a ‘slingshot’ effect though. I can’t get past that they must somehow experience a balance of gravity as they go past, and thus never actually make a velocity net-gain.
Can anyone help me there?
You’re absolutely right, from the point of view of the slingshotting planet the spacecraft approaches at an accelerating speed and leaves with an equal and opposite deceleration. (The direction is usually different, which means the velocity is different, but we needn’t quibble about that – the speed is the same for any given distance on the inbound or outbound trajectory).
The point of the slingshot is to change the speed relative to the Sun. It does this by stealing some of the planet’s orbital energy and transferring it to the spacecraft. If you’re trying to escape the solar system it’s your speed relative to the Sun which is all-important. The Wikipedia article has a good depiction of the planet frame versus the solar frame:
It also has an analogy that I find very useful: