Equations, and stuff

Here’s some bizarre scientific equations to while away the time. Soon I will post about the 2010 cycling trip in Sweden and then as it proceeds, the 2017 trip that is about to happen.

Astronomy is always a source of, er, astronomical numbers. Very massive things (like, black holes) emit gravity waves as they move about. Well, so do less massive things, but then the gravity waves are harder to detect. I have to say “massive” rather than “heavy”, as things can only be heavy if they happen to be near the Earth. I tried to run a competition once, to gues the weight of the Great Melbourne Telescope’s clock-driving weight:

which in fact weighs about 229 kg. I was correctly told that its mass is 229 kg, it only weighs that because it happens to be near the Earth – it would weigh nothing if it were in outer space, although it would be expensive to get it there – and if it were taken to the North Pole it would weigh less. I got one helpful answer listing what its weight would be if it were on various other planets, and pointing out that it would weigh 216 milligrams less when at the top of its 10-foot vertical travel, just after the clock had been fully wound, minus 59 milligrams for the air it displaces, which is less dense if you go up 10 feet.

Two weighty questions – answers at end of this post – Supposing you have a meat pie for lunch, where would be the best place to find out how heavy it is? And where would be a good place to weigh a whale?

Anyway, back to gravity waves; I was at a talk about these the other day. With the very most sensitive apparatus working under the most delicate conditions, scientists were just about able to detect the gravity waves from two unusually large black holes that were orbiting one another. Here’s the mathematical equation giving the energy radiated by gravity waves from a pair of objects orbiting one another

You see “c” there, well that is the speed of light, and here it is being raised to the 5th power, so the numbers are pretty vicious. We need hardly bother with the factor of 32/5.

Now this power can be worked out for the Earth orbiting the Sun; and between them, they are radiating 200 watts into space by this means. (The Sun radiates more than that, from other processes). Now this perpetual loss of 200 watts is taken from the Earth’s orbital energy, causing the Earth to spiral in towards the Sun, and indeed eventually to fall right in, which will happen after a time of 3,000,000,000,000,000,000,000,000,000,000 years, given by :

Isn’t that reassuring? The brightness of galaxies on the surface of the night sky is measured in mJy.kpc2 (milliJansky square kiloparsec) and 1 mJy.kpc2 is about 9,521,540,000 kg metre-squared per second squared. Please do not confuse that with mJy per square kiloparsec, because one of those would be about 0.00000000000000000000000000000000000000000000000000000000000000000000105025 kg PER metre-squared second-squared. Woops.

This brings to mind a joke about cosmologists (who study the origin of the universe) – levity, not gravity. One of them was trying to calculate some sort of cosmological constant, and wanted some measurements done at a radio telescope, and the next day the engineers told him “We did a quick first set of measurements, and we estimated your constant as being between 6 and 7 – maybe 6.3, very roughly.” “That is a very encouraging result”, said the cosmologist, “please do some more measurements and refine it.” Four weeks later “We’ve done the accurate measurements and now your constant is determined to be 873,000 billion”. Cosmologist grins and says “That is an even MORE encouraging result”.

The Pythagorean Expectation in baseball is an attempt to predict the percentage of wins that a team should be getting, based on their past performance. One formula is: % = rs2 / (rs2 + ra2) where rs and ra = runs scored and runs allowed. Now some commentators applied this to basketball and use different exponents: Daryl Morey used the 14th powers, % = rs14 / (rs14 + ra14) and John Hollinger used 16th powers. Approximately. Thus, the New York Yankees in 2002 scored 897 points and allowed 697 points; so they should have won 89716 / (89716 + 69716) = 98.2% of their games. One day I’ll post about asymmetric cryptography, where the exponents go much, much higher but can still be brought back into the real world.

Ah yes. The best place to weigh a pie is somewhere over the rainbow; with reference to the song “Somewhere Over the Rainbow – Weigh a Pie …”; and whales should of course be weighed at a whale-weigh station. I’d better stop now; next post will be about my trip this weekend to Woomargama.


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