# Amateur Astronomy

#1141

I’m afraid I still don’t understand your point about “the only way the earth can heat itself to 300 K is to absorb energy at frequencies about 300THz (~ 1 um wavelength) which we havn’t a hope of doing on earth without using some clever tricks”. Most of the energy we absorb from the Sun is shorter than that, i.e. higher photon energy. Is that a problem?

It’s actually straightforward enough in principal. I came across it before when calculating the spectral index of quasars, which is just the log slope of their spectrum (and Wien’s Law is just about calculating where the slope is zero). It boils down to when you are converting from flux in a frequency band to flux in a wavelength band you have to remember to incorporate the derivative of wavelength with respect to frequency. The total flux in any bandpass is the same whether you are measuring by frequency or wavelength, so https://latex.codecogs.com/gif.latex?F_\nu\text{d}\nu%3DF_\lambda\text{d}\lambda which means:

https://latex.codecogs.com/gif.latex?F_\nu%3DF_\lambda\left%20|%20\frac{\text{d}\lambda}{\text{d}\nu}\right%20|%3D\frac{\lambda^2F_\lambda}{c}

#1142

the more higher energy photons the better, I thought it was the IR that was heating the earth even though the visible is where the sun is most efficient at radiating.

electric light bulbs and lasers is where I am going. “we” have to do something special to get light at the visible and IR. in both case blast a wire or semiconductors with current to get light out of them. there is no source for those wavelengths given the temperature of the earth.

the topic of blackbody radiation and quantum mechanics was my introduction to a university education. seeing all the summations, integrals , exponentials and having to take the lecturers word for it. began in first year with solving for probability densities in a hydrogen atom and finished in 4th year solving the spatial electromagnetic modes in a coaxial cable.

#1143

Ah, ok I see where you’re coming from. No, as I said the Earth (or any black body) will happily absorb high energy photons from the Sun and re-emit them as low energy ones. In fact the process began in the Sun with even higher energy gamma ray photons that are down-scattered to the optical by the time they reach the surface. This is the essence of entropy – high energy photons that can do useful work end up as waste heat. Fortunately we’re able to maintain our life processes by temporarily capturing a tiny proportion of them on their way to the cosmic heat bath. (EDIT: by sheer coincidence, just watched a great vid on this)

Brings back memories.

#1144

new crescent moon and venus in the western sky right now

#1145

A few posts back we were talking about gravitational potential energy as the integral of the gravitational force over a distance:

https://latex.codecogs.com/gif.latex?E_g%3D\int\frac{GMm}{r^2}\%2C\text{d}r%3D-\frac{GMm}{r}

Strictly speaking we should be taking a definite integral between two distances, i.e. two different values of r. But if we pretend one of the distances is infinite, at which point the potential energy goes to zero, we can use the above formula as a decent approximation. Basically, let’s suppose we drop something from “very far away” to the surface of the Earth. In that case the value of r in question is the radius of the Earth, as gravity for a spherical body works just as if all the matter was concentrated at its centre. That suggests that if the surface of the Earth hadn’t got in the way of the falling object, we could have liberated even more energy. And that is indeed the case. If we could squish the Earth down to half its size while keeping all its mass, we’d get:

https://latex.codecogs.com/gif.latex?-E_g%3D\frac{GMm}{\tfrac{1}{2}r_E}%3D2\frac{GMm}{r_E}

That means an object dropped from far away onto something half the size of Earth (but equally massive) would make a splat that was twice as energetic. If we could halve the size again we’d double the energy again. So how small can we go? We know that if we squish it down small and dense enough we’ll end up with a black hole, and the event horizon is as small as it gets for any object (at least as far as we can see from our part of the universe outside the black hole).

In the same post linked above we derived an expression for escape velocity:

https://latex.codecogs.com/gif.latex?v_e%3D\sqrt{\frac{2GM}{r}}

We can calculate the size of the event horizon of a black hole which, by definition is the point at which the escape velocity becomes equal to the speed of light. The distance at which this occurs is called the Schwarzschild radius:

https://latex.codecogs.com/gif.latex?v_e%3Dc%3D\sqrt{\frac{2GM}{r_\text{S}}}

https://latex.codecogs.com/gif.latex?\Rightarrow%20r_\text{S}%3D\frac{2GM}{c^2}

Now, the speed of light is a big number, and its square is even bigger. So the implication is that when an object is collapsed to such a high density that it becomes a black hole, it’s pretty small. And so it is – if we collapsed the Earth to that density it would be less than a centimetre across. That’s more than half a billion times smaller than the Earth’s actual size. So now imagine we put that size into our formula for gravitational potential energy. Dropping an object onto black hole Earth would release half a billion times more energy than dropping it onto real Earth. In general, the gravitational potential energy from dropping an object of mass m onto a black hole of mass M is got by just assuming the Schwarzschild radius:

https://latex.codecogs.com/gif.latex?-E_g%3D\frac{GMm}{r_\text{S}}%3D\frac{GMm}{\frac{2GM}{c^2}}%3D\frac{mc^2}{2}

Ok, if there’s one thing most people know about Einstein’s theory of Special Relativity it’s the famous mass-energy equation, https://latex.codecogs.com/gif.latex?E%3Dmc^2. That’s the amount of energy we would get if the object could be totally converted into energy. (It generally can’t, which we’ll come back to in a minute). So we can see from the above equation that dropping matter into a black hole liberates energy equivalent to half the total mass-energy of the object dropped. I say “liberated” but what I mean is the object’s potential energy is converted into kinetic energy as the object accelerates in free fall, and is then swallowed up by the black hole as it falls through the event horizon.

Except, in reality, a black hole is never going to be just sitting there waiting to gobble up lone objects. Material that came near the black hole in the past would have had its own tangential velocity which sent it into an orbit around the black hole instead of falling straight in. As more and more material falls in on these tangential trajectories it builds up into a swirling disc called an accretion disc. Our lone object will only fall until it smashes into the accretion disc.

Planets orbiting a star like our Sun will continue merrily on their way forever (more or less). But an accretion disc is a different kind of beast. It is not a single solid object but a swirling mass of gas. The orbital speed changes as you get closer to any gravitating body, so the gas in the accretion disc experiences a drag or shear force from the gas adjacent to it at bigger and smaller distances from the black hole. This creates friction and that, of course, heats the gas up. So now we’ve managed to convert some of our gravitational potential energy into kinetic energy and then into heat. This doesn’t change the overall equation. 50% of our object’s mass energy still gets liberated, but now instead of carrying it to oblivion inside the black hole, it is instead radiated away as heat and light. It loses kinetic energy as it goes, which means it does slowly spiral into the black hole, radiating more and more energy as it falls.

Let’s think about this for a moment. We know the Sun converts matter into energy by nuclear fusion, but fusion only converts a very small fraction of the matter. The only way to completely annihilate matter is to bring equal amounts of matter and antimatter together. In hydrogen fusion we stick four protons together to make a helium nucleus. Each proton has mass 1.007825 amu, while the helium nucleus has mass 4.00260 amu. That means we lost 0.02870 amu somewhere, and that’s what has been converted into energy. If you take it as a fraction, 0.7% of the mass is converted into energy.

This is amazing. It means that if we drop hydrogen into a black hole we get seventy times more energy out of it than if we fused it into helium. (In practice it’s more like 20 to 40 because of certain complications, but let’s not quibble). And if the black hole has an accretion disc – which all of them inevitably do – that energy will be radiated away instead of falling into the black hole. This has the paradoxical consequence that a “black” hole from which even light can’t escape is actually incredibly bright if we include its accretion disc.

Stars have a maximum brightness. This is because of the relationship between the star’s initial mass and its energy output. The bigger the mass, the more gravity crushes it, so the more it heats up and the higher the fusion rate in its core. As we make bigger stars, the energy output goes up much faster than the mass increase. That’s why big stars die younger – they use up their fuel quicker. As we know, the stable lifetime of a star results from the (temporary) balance between gravity trying to crush it, and the fusion energy trying to explode it. But because the energy scales faster than the mass, there’s a limiting mass above which the energy output is so great that gravity cannot contain the radiation pressure and the star explodes. Our Sun is below this limit by a factor of 30,000 (worked out by Sir Arthur Eddington a century ago). But giant stars called Wolf-Rayets are tearing themselves apart by this process.

What about black holes? The same Eddington limit applies to their accretion discs. But whereas in the case of a star it is the mass of the star which must contain the pressure, in an accretion disc it is the mass of the black hole which keeps things in place. Want a brighter accretion disc? Just get yourself a bigger black hole. And there’s really no limit to how big a black hole can grow as long as it has matter to feed on. So when we see a black hole that is ten trillion times brighter than the Sun – which is far from unheard of – we can work out from the Eddington limit that it must be at least 300 million times as massive as the Sun. Indeed, we see black holes that are a billion solar masses and above, with the record being closer to ten billion. These are the brightest objects in the universe and can be seen from literally the other side of the known universe. They are the supermassive black holes that lurk at the centres of galaxies. Every galaxy has one, but many have already eaten up everything in their vicinity and have gone quiet for the time being. The ones that are still active are the outrageously luminous objects we call quasars.

#1146

Hi PS, would you mind answering a query of mine.

With the big bang, the universe experienced inflation.
During this phase, it expanded at faster than the speed of light.

Forward to today and we know that the universe is expanding at an ever increasing pace.
So it’s expanding faster today than yesterday etc.
But (obviously) not at, or beyond, the speed of light.

So given we know that the universe is expanding at an increasing pace, am I correct in thinking at some point after the initial phase of inflation, the rate of growth must have either slowed down considerably (or stopped/contracted), only to accelerate again ?

Or were conditions under which the big bang occurred so different to today that you simply cannot compare them ?

#1147

Great questions mr_a, I’ve been meaning to do a post on this. Still trying to find time to do it, so I’ll give the short answer. Yes, according to the current observations the universe expanded quickly initially, then the rate of expansion slowed down, then it accelerated again.

When I get the time I’ll write a post on why we can’t really say “the universe expanded faster than the speed of light” or that it is not doing so today. This is not being picky – it’s crucial to understanding what’s going on and will set the scene for some hard core cosmology later.

#1148

Really appreciate that.

#1149

I’ll get back to cosmology soon. But couldn’t help noticing Jupiter looking very pretty tonight. It’s around magnitude -2.5, about two thirds of the maximum brightness it ever gets to. That’s because it’s close to opposition, i.e. on the opposite side to us from the Sun, as you can see from this plan view of the Solar System:

The other thing Jupiter is doing at the moment is retrograde motion. The plan view is good for picturing this too. Draw a line from Earth through Jupiter to the constellations beyond. Now remember two things: first, that all the planets are moving anticlockwise around the Sun on this view from above the North Pole and second, that the inner planets move faster than the outer ones, so the Earth is currently overtaking Jupiter on the inside. As it does so, that line through Jupiter will be sweeping clockwise through the constellations.

But once we complete another quarter or so of our orbit we’ll be moving more or less directly away from Jupiter so the line will stop changing direction. Shortly thereafter it will begin to sweep the opposite direction, anticlockwise around the zodiacal constellations. That’s the more usual, and causes Jupiter to appear to move westward through the constellations. But from early March until mid July 2018 Jupiter is moving eastward in a retrograde motion. Jupiter is at opposition on May 8th (but curiously not at its closest to Earth until a day or two later).

If you want to visualise how the Solar System is moving, look at the above view on theplanetstoday.com. You can pop open a little control panel and run things forward at high speed to see Jupiter pass through opposition. Unfortunately you’ll have to imagine the Earth-Jupiter-constellations line in your minds eye.

#1150

What have the Romans ever done for us?

One thing they definitely didn’t do is give us astronomy. Ok, they mucked around with the calendar a bit, but modern astronomers’ use of Julian dates has only the most tenuous connection to the calendar named after Julius Caesar. In any case we have evidence of carefully constructed solar and lunar calendars going back 10,000 years and being incrementally refined – the idea certainly didn’t originate with the Romans. No, the Romans were good at breaking things, but when it came to culture and science they borrowed most of their ideas from the Greek world which they “inherited” (a.k.a plundered).

One way we can interpret the development of an idea is to study etymology – to see where the words came from. There’s an interesting and funny insight into our words for domesticated animals in English. Sheep, cow, and pig are all west Germanic words. Mutton (mouton), beef (boeuf) and pork (porc) all come from French. It’s been suggested that our English words for the animals came from the Saxons who farmed them, while the words for the meat came from their Norman overlords who ate them!

Speaking of Norman overlords, the Norman conquest of Britain happened to coincide roughly with the period of the First Crusade. An interesting juxtaposition of events occurred when a young Saxon lad called Adelard was born in the (Roman) city of Bath fifteen years after the Norman invasion. His father was probably a pig-farming tenant of the porc-eating bishop of Wells ( ). That bishop was John of Tours – a Norman, obviously – who extended his influence by taking over the rich cathedral city of Bath on the death of its Saxon abbot, Aelfsige. John can’t have been uneducated since he was doctor to William the Conqueror before becoming bishop. But he was no scholar, and became a rich benefactor of scholarship rather than a practitioner. Somehow the young Adelard ended up being sponsored to study in Bath abbey, and thereafter in the bishop’s original home city of Tours. His travels didn’t end with France though. He was not a soldier, but the opening up of routes to the Middle East in the footsteps of the Crusaders enabled him to go and study there. Adelard would have spoken Old English, French and Latin due to his studies. But in the Middle East he learned Arabic. And thus it was that he made the first translation of Euclid’s Elements into Latin, not from Greek but from Arabic. That’s how the medieval West got possibly the most important book of mathematics in the history of the world.

The language of astronomy is littered with Latin, Greek, and Arabic etymology. Like the animals and their meat, the language from which we derive our words depends on who was using them, and for what. The routes by which classical learning found its way to the modern West involve a tortured history of Islamic conquest, Christian crusades, Venetian trade with the Byzantine world and much more. We should also not forget that it didn’t all come from the Greeks – Islamic expansion and trade with Persia, India and China resulted in the importation of mathematics and technology that had never been known in the West, including Greece. And even the Greeks inherited their astronomy from the Sumerians and Babylonians.

So somehow we’ve ended up with names for the constellations that are both Greek and Roman. That’s partly down to the fact that Ptolemy was a 2nd century Greco-Roman living in Egypt. The constellations are figures from Greek mythology, and the names were established in the Greek world at least several hundred years before Ptolemy. They were certainly around by 370 BC when Eudoxus wrote his Phaenomena. But our current usage is mostly due to the use of Latin in medieval Europe (plus much later IAU exasperation with people inventing new constellations like the Telephone and the Hot Air Balloon – I kid you not).

Ptolemy’s famous astronomical work is known by its Arabic name – the Almagest – because, like Euclid’s Elements it was through translation from Arabic to Latin that it arrived in Europe. In that case the Latin translation was by Gerard of Cremona, a 12th century Italian working in Toledo which had been recaptured from the Muslim caliphate about the same time that Adelard was born in Bath. (By the way, recalling the domestic animals, all the Spanish terms in sheep-rearing are derived from Arabic because of the historical association). There is, of course, an even older history of translation. The 8th century Abassid Caliph Al-Mansur moved the capital of his Islamic caliphate from Damascus to Baghdad. In doing so, and in establishing a library there, a huge translation effort was needed from Syriac, Greek and Persian into Arabic. Personally I find it weird and wonderful thinking of an 8th century Syriac scholar working for a Muslim overlord, translating an (even then) ancient Greek scientific treatise from Aramaic into Arabic, which had been previously translated from Greek to Aramaic by his Coptic Christian ancestors. The continuity is amazing but it’s no wonder we ended up with a mishmash! Nevertheless, for the constellation names it was the medieval Latin that stuck.

Curiously, though, for the names of the stars themselves we’ve ended up with mostly Arabic. Some of the words are just Arabic translations of Greek, though some are of genuinely Arabian origin. And some are both – the variable star Algol is Arabic al-ghoul, a demon who winks at you from the sky. But in Greek it was the eye of the Gorgon. The Arabs took the Greek idea but used an Arabic monster. And we’ve got some pure Greek names too, like Arcturus, the Bear Watcher.

In many cases, the Greek words made it relatively unchanged into Latin, even when they came via Arabic. The planets are planetas in Latin, completely unchanged from the Greek word. The galaxy is galaxia when used technically, but Via Lactea when used colloquially or poetically. We can see this in English too, with the first recorded use of the word coming from Chaucer:

See yonder, lo, the Galaxyë
Which men clepeth the Milky Wey,
For hit is whyt.

There’s certainly poetry in the idea of a “way” trodden by the gods, but there’s always been a technical distinction, ever since Democritus first hypothesised two and half millennia ago that is was a mass of stars and not Hera’s breast milk. There’s been some very entertaining speculation since, such as Plutarch in the 1st century suggesting that the Milky Way was literally cosmic screen burn-in, from the original path of the Sun ! And by the way, the Greeks didn’t call it the Milky Way but the Milky Circle, Kyklos Galaxias. That’s because they knew it engirdled the spherical Earth. The modern conceit that former ignorant generations thought the Earth was flat is almost completely unfounded, at least as far as most of the last three thousand years is concerned.

Galileo, in Siderius Nuncius (The Starry Messenger), seems to mix and match Latin and Greek, even referring to the Milky Circle in Latin when he claims to have solved “altercationes insuper de Galaxia, seu de Lacteo circulo” (“disputes about the Galaxy, known as the Milky circle”). He was the first to confirm Democritus’ speculation with his own eyes.

And now I’ve blabbed on so long I’ve forgotten what the point was. Oh yeah … Latin, Greek and Arabic, all essential to astronomy … without any help from the Romans.

#1151

Brilliant

#1152

I concur brilliant!

Speaketh of Io, its an angry moon , latest JIRAM picture facebook.com/ScienceAlert/p … 6455322518

#1153

Wow! I knew it was volcanic, didn’t realise it was so active. It looks set to burst!

#1154

This evening had it all for the aesthetic sky watcher – ultramarine water in Dublin bay with crystal clear sky, fading to almost-green in the west-north-west above an icepop orange sunset, with Venus blazing down at magnitude -4. Turning around, something was twinkling brightly high up (Arcturus, magnitude 0, as I found out later) as if to call attention to the eastern horizon where a perfectly full moon (yeah ok, 98.6% full) was rising. And later, below it, Jupiter graced the sky again. So beautiful.

#1155

I went to bed about 1am last night and had a look at the moon before I did so and noticed an extremely bright star between 7 to 8 o’clock in relation to the moon. Could this’ve been Jupiter?

#1156

Yep, that’s exactly what it was. This was the view looking south at 1am this morning – lines are ten degree intervals:

#1157

Thanks PS

#1158

Astronomy is not immune to jobs being replaced by robots, although so far it’s not the astronomers themselves. The Sloan Digital Sky Survey has been mapping the sky for eighteen years now, and taking spectra through hand-plugged aluminium masks. Here’s a time lapse of a plate plugger at work:

If you’re interested in how this fits into the overall survey, here’s a recap from a vid I posted three years ago. The plates are mentioned between 2:15 and 3:30 :

And here’s how the plates are made:

Anyway, the fifth iteration of the survey has just entered the planning stage, for execution starting in 2020. Instead of the plugged aluminium masks, the spectrograph fibres will now be positioned “on the fly” at the telescope’s prime focus by five hundred tiny robots. (The fibre-fed spectrograph on ESO’s Very Large Telescope at Paranal in Chile has been doing this for a few years already). Instead of having to swap plates, the robots just move to the next programmed position as required, eliminating both the pluggers and the swappers (you can see the dolly used for plate swapping at 1:00 in the second video above).

PS. Since the start of its fourth iteration, the survey has been using two telescopes – the 2.5m shown above at the Apache Point Observatory in New Mexico, and the Du Pont 2.5m scope at Las Campanas Observatory in Chile, to get full coverage of the Milky Way from both hemispheres. Some very interesting stuff about the volume holographic grating in the spectrograph there from this enthusiastic snapchatting young astronomer/engineer:

As she says, the survey (at least, the APOGEE part of it) is mapping the chemical evolution of the Milky Way to see how it got enriched with the sort of stuff we’re made of. If things fall into place this summer I hope to be writing one very tiny sliver of the software that will be figuring it all out.

#1159

the two most recent big discoveries were detected through automation, the gravitational waves and oumamoua . For the gravitational waves the system was setup and running and within one day the software detected what they were looking for. oumamoua showed up as a smudge on an image and the software detected it and told the astronomers to go back and search for similar images, they did found there was something there and then they all directed their telescopes at that point in space.

#1160

In fairness, everything is found by automation these days. There are very few activities in professional astronomy that don’t rely heavily on software. Nobody sits in the observer’s cage on a telescope anymore. I was thinking more of things to do with the physical telescope setup that can be automated. There’s an increasing number of fully robotic telescopes around the world now. The biggest telescopes will probably need full time operations stuff for many more years. But, for instance, there’s a four metre class telescope under construction on La Palma which will be a fully lights out operation. The 2.5m used by the SDSS at Apache Point still has people required every day to load and unload the spectrograph plates, but I imagine every other aspect of dome control etc. can be automated. With the robotic spectrograph I’m not sure there’s any further need for anyone to leave the control room (which could be anywhere).