How far the Stars?

We had good teachers at the schools I went to, witness the fact that my old school friend Carl and I went on to get our Ph.Ds a few years later on :-) I particularly remember Sam, our physics teacher and Jeb, who taught us maths. Jeb had a special way of teaching us which I didn't understand until I was about 17. He rarely answered questions directly, but answered with another question back at us. He was teaching us to teach ourselves, a great help later at university and in life, as it turned out. So today's blog is giving you a sample anecdote of Jeb in action :-)

We schoolboys thought we could get Jeb off track easily, sidetracking him off the curriculum and getting him to talk about other stuff. I gave you an example last year. Little did we realise that he was showing us how to think and research for ourselves!

Let me use the abreviations S1,S2,S3,S4 for the schoolchildren, Jeb for the teacher:

Jeb : "Today we are going to talk about loxodromes, orthodromes (great circles), geodesics and navigation by geometry using a sextant to look at the stars..."

S1 (no homework done nor lesson prepared) : "How far away are the stars, sir?"

Jeb : "Hmm, that was first measured in the early 19th century. So, given the knowledge available in 1838, how would YOU set about measuring that?"

The whole class is now off and running, having successfully gotten Jeb off topic (?)
S2 : "Well the Catholic church thought the Earth was in the middle and all the stars were the same distance away..."
S3, interrupting : "No, Galileo Galilei (1564-1642) had shown 200 years earlier that the sun was in the centre and the other planets revolved around the sun, explaining their complicated orbits as seen from Earth..."

Jeb (leading us on) : "But the stars could still all be the same distance from the sun, remember they had the nested 'spheres within spheres' idea . . ."

S1 (doubtfully) : "But Kepler (also about 1600) knew about elliptical orbits..."
S2 (excitedly) : "And Newton (around 1700) did the maths and built the first reflecting telescope, Galileo had built the first refracting telescope."
S3 (thinking aloud) : "But if the stars were all the same distance from the sun, surely they would all look as bright as one another? And since they don't, they aren't!"
S4 (confused) : "So the stars could shine with different brightnesses if they are different sizes. Or the brighter ones are nearer. Or both..."

Jeb (coaching) : "How many stars are there?"

S3 : "Lots, space goes on for ever, so there are infinitely many stars"

Jeb (teasingly) : "That implies that whatever direction you look, you should see infinitely many stars, so the sky would be infinitely bright at night in all directions! But, firstly it's mostly black, and secondly what about the Milky Way?"

S1 (triumphantly) : "Not if there's some sort of black fog or dust in space, that would absorb the light, especially from far-away stars, so we come back to the idea that brighter stars are on average nearer. And the Milky Way merely implies an uneven distribution of stars, in a disc. If we look along the disc we see lots of stars (the Milky Way) and if we look at right angles we're looking out of the disc and only see a few!"

Jeb (summing up, and giving us a tip) : "OK, let's assume brighter stars are nearer. How does this help us measure their distance? Apart from Newton, who invented Calculus, most astronomers would have only known some geometry at that time."

S2 (cautiously) : "Weeeelll, you could look for any parallax between the bright stars (in the assumed foreground) and the dim stars (in the assumed background), measuring 6 months apart, when the Earth is on the other side of the sun???"
S3 (doubting Thomas) : "But they are called fixed stars, surely any proper motion would have been noticed over the centuries...."
S2 (firming up his argument) : "True, but we're not looking for a drift, we're looking for a cyclical parallax change. And it must be small otherwise people would have noticed it over the years."
S4 (jumping in) : "With their naked eyes? Remember telescopes had just been invented and Jeb said the distance to the stars was not measured until the early 19th century, therefore the parallax angle must be so small that they had to wait for sufficient advances in telescope technology."

Jeb (giving us a tip) : "What's the smallest angle you can resolve with a telescope?"

S1 (triumphantly : "We had that in Sam's physics class last term, the resolution angle in seconds of arc is about 116 divided by the diameter of the telescopes objective (mirror or lens) in millimetres, I remember that!"
S3 : "So Newtons's largest {2 inch (50mm)} telescope could resolve at most 2¼ seconds of arc. In the early 19th century they had refractors about a foot (250mm) across, they'd resolve about ½ second of arc. So you'd need a lot of measurements to reduce the statistical error..."

Jeb (testing our memories) : "How many?"

All (in chorus) : "Error reduces inversely proportional to the square root of the number of samples"
S1 : "that implies 2500 measurements, taken 6 months apart, to get 1/100th of a second of arc parallax".

Jeb (probing) : "What kind of instrument would you need?"

S2 (jumping in) : "Take 2 photos 6 months apart and then look to see where they don't exactly overlap..." S4 : "Objection, no photography back then!"
S1 (musing) : "Let's assume 1 focal length of about ten feet (300mm, say), then 5mm of parallax would be 1 minute of arc. So 1 arc-second would be under a tenth of a mm, so you'd need a micrometer at the focus to measure anything. Mechanical engineering in the early 19th century was pretty good and I imagine they had invented micrometers with screw-threads already."

Jeb (helping us ) : "Such an instrument is called a Heliometer, the world's largest one is in Vienna. One of you run over to the library and look it up. In the meantime, yes, that's the way it was done in 1838. The star that was measured was 61 Cygni, the parallax angle measured was about 0.313 arcseconds, which imples that the star 61 Cygni is about 10 light years away (or ~3=1/0.31 parsecs; parsec stands for parallax-second). And the man who made the measurement was the astronomer and mathematician called Friedrich Wilhelm Bessel. So tomorrow's lesson will be on Bessel functions; read up about them as your homework! And read all about loxodromes, orthodromes and geodesics too, because we missed doing that today! Class dismissed!"

Omne S: "Groan!"

What prompted me to post all this today? Well, firstly, Winston blogged again about the ways we learn, and secondly, I'd been talking to my friend Lothar (who is a head teacher) about what makes a good teacher. Thirdly we have the coincidence that the French branch of our extended family was involved, viz : the first application of the divided object-glass and the employment of double images in astronomical measures (i.e. the Heliometer) is due to Anne Jean Marie René Savary in 1743. And fourthly I was riding my motorcycle last month on a tour along the river Weser and rode through the town of Minden. As chance would have it I had to stop for a small celebratory parade outside the birthhouse of Bessel, who was born there 222 years ago on July 22. Now those are just too many coincidences for me NOT to blog about my first encounter with Herr Bessel and his unforgotten differential equations ;-)
Fifthly, and finally, it is the mission statement of this blog to dispense snippets of useful(?) information, even if I do get sidetracked a lot, like Jeb ostensibly did ;-)

Copyright ^© Stu Savory on 10th August 2006 at 06:10 CEST permalink Email

50,000 kms on a Yamaha FJR1300 tourer

Just the other week Haggiswurst and I had been conversing about motorcycle reliability; I'd said "Give me a Jap four over a Hardly-Ableson any day, they are much more reliable!". Then, last friday, the SNI'ce riding gang were teasing me about how the brake-lights on my FJR 1300 had locked permanently ON during one of our recent tours up into the Harz mountains. Although I kidded back "That's because I have to ride so slowly to let all you guys have a remote chance of keeping up ;-)" I decided to summarise the log-book of my Yamaha FJR 1300 which now has over 50,000 kms ( = 30,000 miles) on it after 5 years, the last 4 of which were mine.

The Yamaha FJR 1300 is a big, heavy (298 kg), shaft drive, comfortable tourer. The first owner had leased it for a year and put 17,000 km on the clock (well done!), so when I bought it, it was nicely run in and scratch-free. I've had it 4 years now, and it now has 53,000 on the clock. Subjectively, it has been pretty reliable, but my log-book shows it was in the workshop 17 times in those 4 years, albeit mostly for new tyres, it eats up the rear rubber in no time, a tyre per 2-3 months in summer :-(

The graph on the left shows mileage (well, kilometerage) versus date. The graph on the right shows the daily average ride over time, you can see the seasonal variation, the troughs in winter and the peaks in summer. You can also see the 50% increase since I retired nearly two years ago. But I don't ride much in winter at my age (62).

First, lets look at the issue of tyre usage. The first owner had used Metzeler Z4, a touring tyre. These gave on average 5,150 kms of touring use. Looking at the wear pattern, he hadn't been cornering as hard as I do, so the tread was still new at the edges but worn out in the centre. I didn't like the rain performance of the Z4 nor the way it 'stood up' in the corners under hard braking, so I changed to the bi-compound Bridgestone BT020 which has a better reputation in the rain. These lasted just 4992 kms, being a bit softer. But they were much better in the rain and didn't 'stand up' so much during corner braking. The second set of Bridgestone only lasted 4197 kms :-( the Bridgestone front tyres develop a 'herring-bone' pattern as they wear, due to the weight of the FJR under heavy braking. So after the third set of Bridgestone BT020 developed the same wear pattern at 4791 kms, I changed to Pirelli MTR23/24 in the hope of getting better mileage. The rear got 4674 kms and the front got 5400 kms

(no herring-bone wear because the MTR23 does not have the small-block pattern of the BT020. However, the grip of the Pirelli MTR23/24 was less than I liked, so I went to the opposite extreme and changed to Michelin Pilot Power, a soft sports tyre with lots of grip. The rear only lasted 4575 kms ;-( So now I'm keeping the Pilot Power on the front (for that superb grip, wet and dry) and have changed the rear tyre to a Pilot Road S which appears to be lasting longer ( 3641 kms so far and appears to be only ½ worn). The Pilot Road S has less grip than the Pilot Power, especially if the road is just a bit moist, but is quite controllable at the edges, it's OK for the FJR's torque :-)

Thus 8 of the 17 workshop visits were changes of tyres, so what were the other 9 ?

Of those nine, four were for regular Yamaha services at 20, 30, 40 and 50,000 kms respectively. One, just after I bought it, was to add an alarm system and heated grips for cold-season riding. Another to fix the scratch damage after I fell off in june '05 :-(

Apart from replacing both brake light switches at 52,400 kms the only other, but persistently annoying, unreliability has been the battery. I'm now on my fourth battery in the four years I've owned the FJR! Since I use the bike sometimes in winter, I don't take the battery out for winter storage. Due probably to low winter usage and a creeping current somewhere, the batteries tend to deep-discharge and then not hold a charge again. So now I've mounted a charger on the bike to charge the (bloody inaccessible!) battery when it's in the garage in winter. I'm hoping this will pay off, because the special-shape original Yamaha batteries are really expensive. They are not regular under-seat batteries, but special ones fitted into the fairing near the steering head (meant to keep more weight forward).

Nevertheless, I'm very pleased with this bike. It's a sit-up-and-beg tourer rather than the bend-down-and-stretch-over-the-tank sport bike I had previously (a Suzuki TL1000S), but that's OK for me, 'cos I'm an old biker (62) now :-) The wife likes it too, 'cos it has a wide and comfy rear seat. With the cases fitted (see photo at the top) , it is ideal for touring two-up; with 140+ hp it will pull 250+ km/h two-up, more than countries other than Germany will allow. It corners well, although with two up it scrapes the pegs in the corners quite often despite the extra suspension pre-load ;-)

My good friend Fast Alex rides a 900cc Fireblade , so let's see how our bikes stack up, using some testnumbers from "Motorrad" magazine, and letting you compare :-

Now you've read the technical report, go look at the magnificent photos which Dusty Davis took when he rode his FJR from Silicon Valley to the US East Coast and back. Here's the blog of his trip. Boy, reading that makes me eager to get back in the saddle!

Copyright ^© Stu Savory on 8th August 2006 at 06:08 CEST permalink Email

---

Sunday, August 6, 2006

Suitcase Nooks

F righteningly, this "Little Boy" pictured left appears to be planning a trip east, to be followed 3 days later by his dick of a VP, the "Fat Man". Since both are hard cases, we have to worry about what they are packing?

It's a Strangelove that W has for suitcase nooks and crannies, where you can hide Heavy Metal.

Those hard-shell suitcases leave you wondering what to pack in the nooks, maybe an 'Apocalypse Now' CD? Certainly neither is a Rock'n'Roll or Honky Tonk fan, so I'd be scared to hear they were packing any Heavy Metal - especially if it were U₂₃₅ or Pu₂₃₉ :-(

Michelle Goodrich once asked me if I get scared about the Middle East situation getting out of control, so I quipped "Meg, I do!"; I'm not sure she got the pun though. It is but a short way from Nazereth to Armageddon.

PS: Today is August 6th, a day of remembrance, not only in Japan.

Copyright ^© Stu Savory on 6th August 2006 at 08:15 CEST permalink Email

---

Thursday, August 3, 2006

Four DVD tips for you Bikers & Headbangers

1. Long Way Round : Starting in London(UK) in April of 2004, Boorman and McGregor rode around the world on sponsored motorcycles (BMW 1150 GS) via Europe, Ukraine, Russia, Kasachstan, Mongolia, Siberia, Alaska, Canada and USA to reach New York 115 days later. The 3 DVD set documents the difficulties they and their support team ( lorries and SUVs) had, but shows magnificent scenery and friendly people all over the world. Well worth watching for all 4 ½ hours.
2. ELP C'est La Vie : Headbanging Rock at its finest. Includes Nutrocker, Pictures of an Exhibition and Knife Edge. One DVD, runs for 1 ½ hours of Dolby 5.1 :-)
3. Woodstock : Director's Cut. One DVD, runs over 3 ½ hours of Dolby 5.1 :-)
4. One Man's Island : Another M/C documentary. In 2002 Canadian Mark Gardiner gave up his job, home and life-savings to race in the Isle of Man TT, the world's greatest and most difficult motorcycle race, before his illness forbade him from doing so. The documentary is of an obsessive quest to fulfill his boyhood dream. He finished in both the Junior and the 600cc Production Race with lap times similar to Bill Ivy's 125cc record lap in the '60s. But that is NO small achievement, I certainly couldn't have done that any more! Just one DVD which runs for 100 minutes, only in English, no subtitles. Order it via his website.

Copyright ^© Stu Savory on 3rd August 2006 at 06:03 CEST permalink Email

---

Tuesday, August 1, 2006

The Art of Udalrike Hamelmann

An artist friend, Udalrike Hamelmann celebrated her 60th birthday recently with an exhibition of some of her more recent paintings at the old abbey in Willebadessen. She threw a great party there too, as she has a wide circle of friends. Like a Venn diagramm, her circle of friends intersects lightly with ours, so I got to meet people again whom I hadn't seen in quite a while, e.g. Wilfried Hauenschild who worked on my AI research team about 20 years ago. Then another guy came up, telling me I'd taught him to fly a couple of decades ago, and we got to meet the youngest Douglas Adams fan in the county ;-)

Udalrike's abstract paintings often involve projective geometry and emphasize the intensity of the oil colours used. Go look at her website for more info :-)

Currently though, I'm going through a space-art phase of the pix I like; artists like Chesley Bonestell and (here in Germany) Michael Boehme are two of my favourites :-)

I've collaged a sample here, from all three artists :-

. . .

Copyright ^© Stu Savory on 1st August 2006 at 06:01 CEST permalink Email

---