A Question of Magnitude

Posted in Cute Problems, Education, The Universe and Stuff with tags , , , on January 30, 2016 by telescoper

A frequent complaint raised by students of Astronomy is that astronomers insist on using funny units. Chief among them is the use of magnitudes to quanitify the brightness of an object. Why not use the observed intensity (or brightness or flux) of the light from the star, which can be expressed straightforwardly in SI units, instead of faffing around with a clunky logarithmic measure? The reason we use the magnitude scale is primarily historical and based on the fact that the eye’s response to light is more-or-less logarithmic and that in the days before calculators it was easier to deal with very large and very small numbers using logarithms.Most relevant calculations involve divisions and multiplications which become subtractions and additions when you use logarithmic quantities.

It was Norman Pogson who first suggested that a magnitude scale be defined such that a difference of five magnitudes should correspond to a factor of 100 in actual brightess. This was because the brightest naked-eye stars – those of first magnitude – are about 100 times brighter than the faintest naked-eye stars, which are of sixth magnitude. That was in 1856 and we’ve been stuck with it ever since!

Although the magnitude system may appear strange, it’s not really that hard to use when you get used to it. A beginner really just needs to know a few key things:

  1.  Bright things have lower magnitudes (e.g. first magnitude stars are brighter than second magnitude stars);
  2.  If two stars have apparent magnitudes m_1 and m_2 respectively then m_2-M_1=2.5\log_{10} (I_1/I_2) where I_1 and I_2 are respectively the fluxes received from the two stars;
  3. The intensity of light falls off with the square of the distance from the source;
  4.  The absolute magnitude is the apparent magnitude a star would have if it were 10 parsecs from the observer;
  5. Most stars have roughly black-body spectra so their total intrinsic luminosity depends on the product of their surface area (i.e. on the square of the radius) and the fourth power of the surface temperature.

Got it?

To test your understanding you could try these little problems. To warm up you might look at I posted the first of them a while ago. Anyway, here we go:

  1. A binary system at a distance of 100 pc has such a small separation between its component stars that it is unresolved by a telescope. If the apparent visual magnitude of the combined image of the system is 10.5, and one star is known to have an absolute visual magnitude of 9.0, what is the absolute visual magnitude of the other star?
  2. Two stars are observed to have the same surface temperature, but their apparent visual magnitudes differ by 5. If the fainter star is known to be twice as far away as the brighter one, what is the ratio of the radii of the two stars?
  3. A binary system consists of a red giant star and a main-sequence star of the same intrinsic luminosity. The red giant has a radius 50 times that of the main-sequence star. (i) If the main-sequence star has a surface temperature of 10,000 K, what is the surface tempature of the red giant star? (ii) If the two stars can’t be resolved the combined system has an apparent magnitude of 12, what are the apparent magnitudes the two component stars would have if they could be observed separately?

Answers through the comments box please! The first correct entry wins a year’s free subscription to the Open Journal of Astrophysics…

 

 

Wouldn’t you just die without Mahler?

Posted in Film, Music with tags , , , on January 30, 2016 by telescoper

I was listening to BBC Radio 3 last night. The evening concert happened to feature Mahler’s wonderful 4th Symphony, so obviously I turned the volume up. All of which reminded me of this scene from the film Educating Rita,  featuring Julie Walters and Maureen Lipman. Fortunately in my case nobody rang the doorbell. I am not to be disturbed when listening to old Gustav.

 

Comets, by Kandinsky

Posted in Art on January 29, 2016 by telescoper

image

The last time I posted a work of astronomically-themed art by Wassily Kandinsky it proved unexpectedly  popular so here’s another one, called Comets. This is also a lithograph and also dates from around 1938.

Mathematicians at Work

Posted in Poetry with tags , , on January 29, 2016 by telescoper

hunker down on their hands and knees
and sniff the problem
poke it with ungentle fingers
rub it raw with steel wool
wad it up in a ball and cackle
then pound it flat with little mallets
watch it rise like dough (uh oh)
resume its original shape
screech, swing at it with hatchets
spatter the walls with oozing fragments
stare horrified at the shattered bits
reassembling themselves, jump up
attack the problem with icepicks
gouge holes six inches deep
and seven inches across
(chew the mangled matter
spit it out and belch) kick the thing
into a corner, remove their belts
and beat it senseless, walk off
with the answer in their pockets.

by Judith Saunders

Critical Opalescence in Carbon Dioxide

Posted in The Universe and Stuff with tags on January 28, 2016 by telescoper

Fascinating demonstration of critical opalescence..

Protons for Breakfast Blog

One feature of the teaching at Dalhousie University’s Physics Department is a laudable emphasis on demonstrations.

Visiting Professor Tom Duck there, I was delighted to be shown a demonstration I had heard of, but never seen: the phenomenon of critical opalescence in carbon dioxide.

I have written about critical opalescence previously on this blog (here) and with more pictures (here), so I won’t repeat most of that.

In my previous articles I described the phenomenon in two immiscible liquids which is an exact analogy for the physics of critical opalescence in a pure substance. But it’s not what physics students read about in text books.

Michael: What are you going on about?

The phenomenon occurs when one heats a liquid in a container with a small amount of free space.

  • As the liquid heats up, it expands causing its density to fall.
  • The liquid also evaporates causing the vapour (gas) pressure to…

View original post 338 more words

Hit and Run in Brighton

Posted in Brighton with tags , , on January 27, 2016 by telescoper

I was having a drink with friends on campus last night and the subject came up of a terrible hit-and-run incident in Kemptown on 14th July. I hadn’t heard about it until then. The location of this incident was Montague Place in Kemptown, which is due a couple of hundred yards from my flat . The police issued a video obtained from CCTV cameras and appealed for witnesses. Apparently this bore fruit and two people were arrested yesterday. Rumours are circulating that the car involved was stolen.

I’m including the horrific video here. The man who was hit suffered serious head injuries, but is apparently recovering well. He’s extremely lucky to have survived. If you watch the video I’m sure you will agree that he is very fortunate. Please be aware that this is extremely shocking to watch so don’t click it you’re squeamish. I’m showing it here because it’s a graphic illustration of what a speeding car can do to a human being. Cars frequently travel at ridiculous speeds around Kemptown. This is what can happen when people drive like maniacs.

If the persons arrested are guilty I hope they get very severe punishment.

 

Stormy Weather (Billie Holiday)

Posted in Jazz with tags , on January 26, 2016 by telescoper

 

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