Raindrops, stars and photons

July 29, 2013

Here is another one of those occasional posts with mazin facks bout stronomy. (See also Almost Nothing and A Dim Glimmer).

Today’s rambling is inspired by some fascinating tweets emitted by darkskyman aka Steve Owens of Dark Sky Diary fame. First I will give you the gist of Steve’s ‘believe it or not’ sequence. From the average rainfall in the UK last year (1.33m), the area of the UK (2.426×10^11 m^2), and the average volume of a raindrop (10^-9 m^3) he calculated that the total number of raindrops that fell on the UK was 10^20. That is a big big number. However, continues Steve, the number of stars in the Universe is approximately 10^23.

So as Steve told us ‘for every raindrop that hit the UK last year there are 1000 stars in the Universe’.

Very nice, but I found myself thinking – how does the rate of raindrops compare to the rate of photons? The average raindrop flux is 13 raindrops/m^2/s. Lets compare to the Sun. The solar constant is 1360 W/m^2. If we take the typical photon as being at about 500nm with energy hc/lamda = 4×10^-19J, we get roughly 3×10^21 photons/m^2/s.

So we get much much much more sunlight than rain! Woohee!

What about starlight? Well, as Mr Olbers pointed out, a Universe full of stars would make a sky as bright as the Sun in every direction. However, the Milky Way fades out, and the universe runs out too, in time and therefore space. So lets just get empirical. Cosmology types will often plot the ‘cosmic optical background’ at a level of about 10^-8 W/m^2/sr, about a factor of a thousand less than the CMB. However, that is the extragalactic background light;  the summed emission from nearby stars is in fact much more. According to my Trusty Allen, star light from the whole sky is equivalent to 460 V=0 stars, or one star of V=-6.7. The  apparent mag of the Sun is V=-26.7. So the scattered starlight is 20 magnitudes fainter or a factor of 10^8.

So in super-crude terms, starlight is giving us something like 3×10^13 photons/m^2/s. Still lots more than the 13 raindrops/m^2/s.

But what energy? Scaling down from the solar constant, starlight is giving us an energy flux of about 1.4×10^-5 W/m^2. What about raindrops? Each of those raindrops has mass 10^-6 kg. The terminal velocity of a raindrop depends on size, but at 1mm its about 4 m/s. So the KE per raindrop is about 8×10^-6 J and the energy flux is therefore 10^-5 W/m^2, about 6 times as much as starlight.

So… in particle count terms, the Sun wins hands down; starlight is down a factor of hundred million but still huge; and the raindrop count is pitiful, another factor of a trillion down.

In energy terms, the Sun still wins easily, with starlight a hundred millions times down; but the rain carries more energy than the starlight – just.

Please do check the maths… Anyhoo. Better do some real work today.

Riots, Purpose, and Science

August 11, 2011

Back from my hols. Brain getting back in gear. Pouring with rain here in the Burgh. So much grimmer than that nice Cornish drizzle.

So whats happening ? Astronomically not a lot. Courtesy of the inimitable Crowther, there is an interesting analysis of the Australia vs South Africa battle for SKA, from a financial point of view.

Meanwhile, in other news… London’s burning, and Manchester too. Its all a bit depressing, and its tempting to pontificate on The Cause Of It All, but best not to. My opinions are no better than anybody else’s. But listening to the debate did pluck a philosophical nerve…

(A) Some say we have to understand why young people are doing this – they are poor, disenfranchised, bored, etc. (B) Others say – no ! We mustn’t look for excuses, its just selfish and criminal. Now, the citizen in me goes for B, but the scientist in me goes for A. The problem is that people tend to blend the concepts of  reason and excuse. It should be possible to stand outside a system, and say objectively ” ahh.. here are the reasons it happened”, and still be able to go back inside and say “I don’t care why. Has to stop”.

So here is the philosophical tickler. Sometime recently (lost the link..) Hawking provocatively suggested that there is no need for God, because Science is a self-contained explanation of the Universe. It seems to me that big daddies in the sky with beards, or creation myths, or all-pervading spirits or essences, ain’t really the point. What is outside Science, that patently seems to exist, and is an everyday human fact of life, is purpose or intention. In fact for science to work, you more or less have to switch it off, as I sketched above.

Aristotle had causation by purpose (teleology) as one of his four categories of cause. But we modern scientists hold no truck with that. (What is this obsession with holding trucks ?) Does this mean that Science is an incomplete world view ? Or does it in fact suggest that intention is an illusion ? Of course this is standard Philosophy 101 stuff, all tied up with free will vs determinism etc. But whats the gut instinct of the working scientist ?