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Transfer Orbit

Posted in Cute Problems, The Universe and Stuff with tags , on November 2, 2011 by telescoper

From time to time I like to post nice physics problems on here. Here is a quickie that I used to use in my first-year Astrophysical Concepts course which has now been discontinued, so I don’t need to keep it to myself it any longer.

A simple way to travel from one planet in the solar system to another is to inject a spacecraft into an elliptical transfer orbit, like the one shown by the dashed curve, which is described by Kepler’s Laws in the same way that the planetary orbits (solid curves) are.

Kepler’s Third Law states that the  period of an elliptical orbit is given by P^2 \propto a^3 where a is the semi-major axis of the ellipse. Assuming that the orbits of Earth and Mars are both approximately circular and the radius of Mars’ orbit is 50% larger than Earth’s, and without looking up any further data, calculate the time taken to travel in this way from Earth to Mars.

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Kielder Star Camp

Posted in The Universe and Stuff with tags , , , on October 27, 2011 by telescoper

I  came across a story in the Grauniad about the Kielder Forest Star Camp at which scores of amateur astronomers are gathering along with their tents this week to exploit the darkest skies in England.  The skies are pretty dark above  Cardiff right now, but that’s because of the thick cloud rather than lack of light pollution. I hope they have better weather in Kielder which, if you didn’t know, is in Northumberland. With an area of 250 square miles, Kielder Forest is  England’s largest forest (although it’s actually more of a plantation, being man-made under the auspices the Forestry Commission) and it surrounds Kielder Water, the largest man-made reservoir in the UK. Anyway, as the time-lapse video shows, it’s  a fine spot for astronomy when the clouds stay away; at the end you’ll see the excellent new Kielder Observatory too!

Good luck to all the participants (and, more importantly, clear skies…) .

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A Big Idea

Posted in The Universe and Stuff with tags , , , on October 25, 2011 by telescoper

I thought I’d share this, part of the Big Ideas series produced by Cardiff University, because it features our own Haley Gomez:

In the video Haley explains how enormous quantities of dust have been found by astronomers in the School of Physics & Astronomy. We just can’t get the cleaning staff, you see. In fact more recently there have also been discoveries of damp, mould, crumbling ceilings and broken windows.

I don’t want to steal Haley’s thunder in any way, but I should mention that an even more startling discovery has recently been made elsewhere in the School of Physics & Astronomy at Cardiff University. In my office, in fact.  Not  dust, but anti-dust!

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Death of a Cosmological Parameter

Posted in The Universe and Stuff with tags , , , on October 21, 2011 by telescoper

I’m sad to have to use the medium of this blog to report the tragic death of the Hubble parameter. It had been declining for some time and, despite appearing to pick up recently, the end was somewhat inevitable. Condolences to the other parameters, especially Ω (who was in a close relationship with H), on this sad loss.

The original photograph (and joke) may be found here.

 

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Baby Planet Pictures…

Posted in Astrohype, The Universe and Stuff with tags , , on October 20, 2011 by telescoper

My eye was caught this morning by this dramatic picture on the front page of the Guardian website, linked to a story about the discovery of a very young planet:

I wonder how many people looking at it thought that it was an actual picture of a planet actually forming? In fact the above graphic is just an “artist’s conception” of the view near the planet, which is called LkCa 15b. The real picture is considerably less dramatic:

What you see is (left) a disk of dust and gas surrounding a star cleverly made visible by masking out the light from the star, which is much brighter than the disk.  On the right you can see a blow up of the inner region of the system, which appears to show a Jupiter-like planet associated with an irregular blob of material, out of which it probably condensed and from which it may still be accreting.

The size of the picture on the right is worth noting. The angle indicated is 76 milli-arcseconds. This is the angle subtended by  the  width of a  human hair at distance of about 130 metres…

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The Physics of the Pole Vault

Posted in Education, The Universe and Stuff with tags , , , , , on October 17, 2011 by telescoper

At the RAS Club Dinner last Friday I chatted for a while with my former DPhil supervisor, John Barrow. I’m not sure how, but the topic came up about how helpful it is to use sports to teach physics. By coincidence he chose the same example as I have used in the past during first-year tutorials,  the pole vault.

Years ago I went to watch an athletics meeting at Gateshead Stadium and sat right next to the pole vault area. I can tell you that the height the vaulters reach is truly spectacular, especially when you’re close to the action. The current world record for the pole vault is 6.14m, in fact, set by the legendary Sergey Bubka in 1994, so the record hasn’t been broken for 17 years. Here’s a clip of him a few years earlier clearing a mere 6.10 metres (pretty comfortably, by the look of it)…

One might infer, from the fact that the record has not been broken for such a long time, that pole vaulters are working pretty much at the limit of what the human body can achieve. And a bit of physics will convince you of the same.

Basically, the pole is a device that converts the horizontal kinetic energy of the vaulter \frac{1}{2} m v^2,  as he/she runs in, to the gravitational potential energy m g h acquired at the apex of his/her  vertical motion, i.e. at the top of the vault.

Now assume that the approach is at the speed of a sprinter, i.e. about 10 ms^{-1}, and work out the height h = v^2/2g that the vaulter can gain if the kinetic energy is converted with 100% efficiency. Since g = 9.8 ms^{-2} the answer turns out to be about 5 metres.

This suggests that  6.15 metres should not just be at, but beyond, the limit of a human vaulter,  unless the pole were super-elastic. However, there are two things that help. The first is that the centre of mass of the combined vaulter-plus-pole does not start at ground level; it is at a height of a bit less than 1m for an an average-sized person.  Nor does the centre of mass of the vaulter-pole combination reach 6.15 metres. The pole does not go over the bar, but it’s pretty light so that probably doesn’t make much difference. However, it’s not  obvious that the centre of mass of the vaulter actually passes over the bar.  That certainly doesn’t happen in the high jump – owing to the flexibility of the jumper’s back the arc is such that the centre of mass remains under the bar while the different parts of the jumper’s body go over it.

Moreover, it’s not just the kinetic energy of the vaulter that’s involved. A human can in fact jump vertically from a standing position, using elastic energy stored in muscles. One can’t jump very high like that, but it seems likely to me that this accounts for a few tens of centimetres.

Anyway, it is clear that pole vaulters are remarkably efficient athletes. And not a little brave either – as someone who is scared of heights I can tell you that I’d be absolutely terrifed being shot up to 6.15 metres on the end of  a bendy stick, even with something soft to land on!

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Another day, another tutorial…

Posted in Education, The Universe and Stuff with tags , , , , on October 13, 2011 by telescoper

Oh what fun it is to derive the Bohr radius. At least the camera on my Blackberry works!

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Wave your hands and think of Astronomy….

Posted in The Universe and Stuff with tags on October 12, 2011 by telescoper

Here’s a short video presentation in which it is demonstrated that astronomers like to move their hands while talking. It’s frightfully amusing, but I can’t help thinking it would have been even better if the musical accompaniment had been, well, musical. Anyway, keep watching until 2:17 or thereabouts and you’ll see that I have a small part.

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Einstein and your Gas Bill

Posted in History, Television, The Universe and Stuff with tags , , , , , on October 11, 2011 by telescoper

Taking refuge in my office this lunchtime for a sandwich and a cup of coffee I turned to the latest edition of Physics World and came across an funny little story about a physicist (who is completely new to me) with the splendid name of Fritz Hasenöhrl.

The news story relates to a paper on the arXiv, part of the abstract of which I’ve copied below:

In 1904 Austrian physicist Fritz Hasenohrl (1874-1915) examined blackbody radiation in a reflecting cavity. By calculating the work necessary to keep the cavity moving at a constant velocity against the radiation pressure he concluded that to a moving observer the energy of the radiation would appear to increase by an amount E=(3/8)mc^2, which in early 1905 he corrected to E=(3/4)mc^2…

Since I’ve been doing a bit of dimensional analysis with first-year students, I’m a bit surprised that the authors of this paper read so much into the fact that Hasenöhrl’s formula bears a superficial resemblance to Einstein’s most famous formula E=mc^2, probably the best known and at the same time worst understood equation in physics. In fact any physicist worth his or her salt no matter how incorrect their reasoning would have to get something like E =\alpha mc^2, with \alpha some dimensionless number, simply because the answer has to have the correct dimensions to be an energy.

Expressing energy in terms of the basic dimensions mass M, length L and time T is probability easiest to do when you think of mechanical work (force×distance). Since Newton’s laws give a force equal to mass×acceleration, a force has dimensions MLT^{-2}, so work (a form of energy) has dimensions ML^{2}T^{-2}. Now try to make this out of a combination of a mass (M) and a velocity (LT^{-1}) and you’ll find that it has to be mass×velocity2. You can’t get the dimensionless constant this way, but the combination of m and c must be the way it is in Einstein’s formula.

Anyway, all this suddenly reminded me of a day long ago when I appeared on peak-time television in the consumer affairs programme Watchdog, explaining – or, rather, attempting to explain – the physics behind the way gas bills are calculated. Apparently someone had written in to the programme asking why it was that they weren’t just being charged for the volume of gas that had flowed through their meter, but that the cost involved a complicated calculation involving something called the calorific value of the gas.

The answer is fairly obvious, actually. The idea is that to make competition fairer between different forms of energy (particularly gas and electricity) the bills should be for the amount of energy you have used rather than the amount of gas. Since the source of fuel varies from day to day so does its chemical composition and hence the amount of energy that can be extracted from it when it is burned. Gas companies therefore monitor the calorific value, using it to convert the amount of gas you have used into an amount of energy.

On the programme I was confronted by the curmudgeonly Edward Enfield (father of comedian Harry Enfield) who took the line that it was all unnecessarily complicated and that the bill should just be for the amount of gas used, rather in the same way that petrol is sold. When I tried to explain that the way it was done was really fairer, because  it was really the energy that mattered, it quickly became obvious that he didn’t really understand what energy was or how it was defined.  He didn’t even get the difference between energy and power. I suspect that goes for many members of the general public.

It was all a bit tongue-in-cheek, but I enjoyed the sparring. Eventually he came out with a question about why energy was given by E=mc^2 rather than mc^3 or something else. So I launched into an explanation of dimensional analysis and why mc^3 couldn’t be an energy because it has the wrong dimensions. His eyes glazed over. The shoot ended. My splendidly erudite and logically rigorous exposition of dimensional analysis never made it into the broadcast programme.

My brief career on BBC1 was over.

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Have you been Drexlered?

Posted in The Universe and Stuff with tags , , , , on October 10, 2011 by telescoper

Every time something interesting is announced in astrophysics or cosmology – which is quite often, these days – I get an email from a chap called Jerome Drexler. Last week’s announcement of the 2011 Nobel Prize for Physics  proved to be no exception and this morning I got yet another message.

It’s interesting that Drexler always writes about himself in the third person, e.g.

Beginning in 2002, Bell Labs-educated (under a three year
fellowship) applied physicist Jerome Drexler utilized this same astronomical set of non-homogeneous-expansion-rate data in conjunction with his dark matter cosmology to find a compatible explanation for the accelerating expansion of our universe. The compatible explanation he discovered did not use either Friedmann’s solutions or the General Theory of Relativity, which rely entirely on gravitational forces. The successful results from his endeavor are reported in Chapter 21 of Drexler’s March 2008 paperback book entitled “Discovering Postmodern Cosmology” and in Chapter F of his October 2009 paperback book “Our Universe via Drexler Dark Matter.”

Indeed, having read a few of Drexler’s publications – none of which has actually appeared in an authentic scientific journal – it seems that his output will be of much greater interest to psychologists than physicists. Drexler, you see, insists that the dark matter, whose presence astronomers have inferred from the dynamics of self-gravitating systems, exists in the form of highly relativistic protons.

There are many problems with this suggestion, most of which will be obvious to anyone with first-year undergraduate knowledge of physics. Most important of all is the fact that protons are charged and therefore accelerate in the presence of a magnetic field. Protons accelerating in the Milky Way’s magnetic field would produce copious electromagnetic radiation and would not therefore be at all dark! Still, we don’t want a little bit of basic physics get in the way of a mania for self-promotion.

Incidentally, it’s not a crazy idea that dark matter could be charged but, if it is, it must consist of particles with mass many thousands of times greater than that of a proton. That way their inertia will keep their acceleration low and restrict the radiation they produce.

I’ve often thought that it might be an interestingly novel way of teaching physics to get students to unpick contributions like this. I’ve got a filing cabinet full of similar “alternative” theories of the Universe and from time to time give one to a student to find fault with. Usually it doesn’t take long. Sometimes they’re wrong, sometimes they’re not even that. I’ll therefore leave it to my highly educated and knowledgeable readership to suggest other failings of the Drexler Universe.

I don’t know what I did to deserve the honour of being placed on Drexler’s mailing list and in any case suspect that I’m just one among many recipients of his missives. I’m sure others have tried to convince him that his model doesn’t make any sense from the point of view of physics, but I’m sure that their attempts have fallen on stony ground. It’s another aspect of the psychology of such individuals that it is inconceivable to them (a) that they could be wrong about anything and (b) that anyone else might know more than they do. Real scientists have quite the opposite attitude.

Here’s how Jerome Drexler describes himself on his email:

Jerome Drexler is a former member of the technical staff and group supervisor at Bell Labs, former research professor in physics at New Jersey Institute of Technology (NJIT), founder and former Chairman and chief scientist of LaserCard Corp. (Nasdaq: LCRD). He has been awarded 76 U.S. patents (see Google Scholar), honorary Doctor of Science degrees from NJIT and Upsala College, a degree of Honorary Fellow of Israel’s Technion, an Alfred P. Sloan Fellowship at Stanford University, a three-year Bell Labs graduate study fellowship in applied physics, the 1990 “Inventor of the Year Award” for Silicon Valley and recognition as the original inventor in 1978 of the now widely-used digital optical disk “Laser Optical Storage System” and the LaserCard(R) nanotech data memory used in six countries. He is a member of the Board of Overseers of New Jersey Institute of Technology and an Honorary Life Member of the Technion-Israel Institute of Technology Board of Governors.

Anyone know any more about Professor Doctor Mr Drexler? If so, the comments box awaits your contribution…

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