Physics Stop

OrbitsMarcus WilsonNov 30

Going back to my comments on the Karman line (100 km about the earth’s surface), I think it’s worth commenting a bit ‘being in orbit’ means. We are familiar with the fact that if we drop something it accelerates downwards and hits the ground. If we throw something away from us, it will still accelerate downwards and hit the ground, but this time at some distance from us. If we throw it hard enough (and I mean, really hard), it will accelerate downwards, but, because the earth curves, by the time it has fallen the earth has dropped away too, so that it is still the same distance above the earth. It’s then in orbit, and will come back and hit you on the head (obstructions and atmosphere being absent).

Put more precisely, a circular orbit results when the acceleration due to gravity matches the centripetal acceleration required to move the object in a circle.

Orbits don’t have to be circular. Kepler worked out that the planets orbit the sun in ellipses, with the sun at one focus. Newton worked out that, if the sun exerted a force on a planet inversely proportional to the distance between the sun and the planet squared, then an elliptical orbit would necessarily result. (Well, actually the orbit could be circular, elliptical, parabolic or hyperbolic – these are all conic sections).

One curious result of orbit theory is that, the closer a particle is to the focus of its orbit (e.g. the closer a planet is to the sun; Mercury as opposed to Neptune – alas, Pluto no longer counts) the faster it goes. The same applies to satellites orbiting the earth as well. Satellites that are in lower orbit move faster.  These satellites have to contend with more atmosphere as well (remember the edge of space is not distinct, there are still a few air molecules up there). When a satellite hits an air molecule, it loses energy. It drops to a lower orbit (less potential energy) and so it speeds up. We don’t normally think of something that is gaining speed as losing energy, but, in the case of a satellite, that is the case.

To counteract air resistance, satellites have to be given little boosts of energy to keep them in orbit. Without it, they will progressively spiral inwards, until they burn up in the earth’s atmosphere, or, sometimes, hit the earth itself.

Dazed and confusedMarcus WilsonNov 27

Physicists love units. The best way to wind up a physicist is to tell him you were driving at 100 down the road.  One hundred what?  Just hope you don’t get pulled over by a traffic cop with a physics degree or he’ll ticket you for leaving your unit off, even if you were within the speed limit.

A unit is usually a very meaningful thing. One hundred kilometres an hour means, at that constant speed (and I mean speed not velocity, direction is irrelevant) you will travel one hundred kilometres in one hour.  An freefall acceleration of ten metres per second, per second (or 10 metres per second squared) means every second something is in free fall it gains ten metres per second of velocity. Easy.

Not quite.  In the area of stochastic physics, which I have worked with for several years, we have units that are metres per square-root second. What on earth is a square-root second?  It still confuses me no end. Sure, I can work with it, and write computer programmes to use equations that involve it, but quite grasping it in my mind is something I haven’t succeeded in doing.

I know I haven’t succeeded yet because I find it so hard to describe what’s happening to my summer students.

(N.B. It’s related to the random walk (‘drunkard’s walk) problem – where the root mean square distance you travel is proportional to the square root of time.)

However, not understanding a concept does not exclude you from using it.  I remember years ago working with Lagrange’s method of undetermined multipliers, (N.B. don’t click on this link unless you have a solid grasp of calculus) and being able to use it to work out problems, but not really having a clue as to WHY it worked. No text book seemed to help me. Then I remember one winter in Bedford walking to a bus stop and having a sudden flash of inspiration. At last I got it. It didn’t help solving problems, but it made the process that much less mysterious.

Maybe, just maybe, one day the same thing will happen with square-root units.

How to get publicityMarcus WilsonNov 26

For those of you wondering (and several have asked) how I managed to get a third of a page in the main section of last Sunday’s Sunday Star Times, the answer is simple.  Tell the press about whatever story you want them to know about.  Some journalists can be pretty good at digging up stories, but it helps them no end if you give them one, rather than hoping that they find it.  So, whatever you want to publicise, go and tell the media about it.

(The article, thankfully minus the photos, is available on stuff.co.nz, click here.) The cafe scientifique in question went really well – Alison Campbell and I did a session on some of those bizarre science stories that crop up from time to time. We didn’t get onto the zombies, but, in case you didn’t know, or need a reminder, that was one of the more ‘interesting’ bits of scientific research published this year – click on the link. And as for the fruit bats, Alison handled it very well indeed.

Blink and you miss itMarcus WilsonNov 24

First collisions in the Large Hadron Collider

http://press.web.cern.ch/press/PressReleases/Releases2009/PR17.09E.html

Only at a ‘paltry’ 0.45 TeV per beam (CERN are wanting to ramp that up to about 3.5 TeV per beam over the next few months) but one can really now say that the LHC ‘works’.

The final frontierMarcus WilsonNov 24

New Zealand is, hopefully, just a few days away from becoming a space-nation. The private company Rocket Lab  (what a great name – I like names that describe what a business actually does) aims to put up its Atea-1 rocket from Great Mercury Island sometime around November 30th. The payload will reach an altitude of 120 km before returning to earth and being recovered.

But how high do you have to put something to get it into space?  The earth’s atmosphere does not have a well-defined edge – atmospheric pressure decays roughly exponentially as altitude increases. At about 6 km altitude, the pressure is about half what it is on the earth’s surface; and it approximately halves for every further 6 km you go up. So it doesn’t take long for there to be little left. The lowest layer of the atmosphere is the troposphere (to about 10 km in altitude, but rather variable); here it gets colder as you go upwards. Passenger jets typically cruise at around 10 km in altitude.

Above the troposphere is the stratosphere; this goes to about 50 km in altitude and curiously temperature increases again as you go upwards. However, with so little air pressure, temperature starts to become somewhat less meaningful. With pressure so low at 50 km, the top of the stratosphere is not accessible to conventional aircraft (jet or propellor), but has been reached by rocket plane.

Beyond the stratosphere is the mesosphere (temperature decreases with height again), and beyond that is the thermosphere (temperature, for what it’s worth, does a reverse again and now increases with height.) There’s not much air left at all, and at 100 km the Karman line marks an arbitrary boundary as the ‘edge of space’. Karman calculated that at about that altitude a place would have to travel so fast to gain enough lift from its wings it would be in orbit.  The Karman line is where the Federation Aeronautique Internationale sets the boundary for ‘space’, and it is where the Atea-1 rocket will have to reach before it is recognized as reaching space.

You heard it hear secondMarcus WilsonNov 22

I’ve got better things to do at the weekend than following CERN’s tweets about the LHC. Consequently this posting is about 24 hours out of date. Oh well. The LHC has circulating beams in it again, with not a time-travelling baguette in sight.

http://press.web.cern.ch/press/PressReleases/Releases2009/PR16.09E.html

Prisoner’s DilemmaMarcus WilsonNov 20

Writing my last post on public transport etiquette prompted me to recall William Poundstone’s excellent book an game theory, ‘Prisoner’s Dilemma’.  Poundstone, in a very accessible manner, discusses the ideas behing game theory (a branch of mathematics developed by John Von Neuman), illustrating it terrifyingly with examples from the Cold War.

Deciding whether to get on the first bus, the crowded one that is already late, thus delaying it further, or waiting for the second, that is nearly empty and running ahead of time, is a dilemma. Do the former, and you’ll get to work a little quicker than you would if you did the latter. Do the second, and your journey takes a bit longer, but it is to the benefit of everyone else on the first bus, who aren’t delayed further by your boarding. The choice is yours. Our mathematician friends in Mexico are obviously going to try a publicity campaign for people to do the latter.

Bus problemsMarcus WilsonNov 18

There are a significant number of people who view scientists as boffins in white coats who lock themselves in their labs for twelve hours a day while they invent things that are entirely useless to anybody.  This view is somewhat stereotyped, and I hope my blog goes a small way to changing it. (Am I succeeding? – you tell me please).

So needless to say when I find scientific articles that basically support the boffin picture, I tend to put my head in my hands and wonder why I bother.