January 1995


Solar Eclipse Track Across Europe

HERE to get you thinking about future summer trips over the winter is a map which shows the path of the next Solar eclipse track across Europe in 1999 and the list below gives the times of first contact, mid total eclipse and final contact for a few spots along the track.  If you get your atlas out I'm sure you can follow the path across the countries.  I suspect that that these times will be published to a greater accuracy along with a better detailed map nearer the time.  But to get every one thinking about their holidays in 1999...
I for one will NOT be staying in the UK that year in August!  We all know what the weather will be doing in Cornwall in the middle of summer.  So if you opt to go abroad, where do you head for?  I think the best bet is to head East into Germany, Austria or even Hungary. Mid Europe has wonderfull clear skies in the Alps and it has an excellent chance of sunny skies, but the important thing to remember is that there is a superb motorway system so it's possible to drive to a clear sunny area if it looks cloudy in your original place.  Watching the weather forecasts will pay off in deciding to stay in one place or move.  This will be one eclipse that may be watched by more people than ever before, be one of them.

Ivor Clarke

                                                                                                           TIME IN U.T.
Location                             Place                                Height       Begin      Mid       End

-5°10" Long. 50°00"Lat.    Lands End        UK         50m          8.54      10.11    11.31
7°00" Long. 48°40"Lat.     Nr Metz           France     100m        9.09      10.31    11.53
9°30" Long. 48°10"Lat.     Nr Stuttgart    Germany  500m         9.13      10.35    11.57
11°30" Long. 47°50"Lat.   Nr Salzburg     Austria     1000m       9.16      10.38    12.01
19°00" Long. 46°00"Lat.   Nr Budapest    Hungary   50m          9.29      10.52    12.16
26°40" Long. 43°40"Lat.   Nr Bucharest   Romania   50m          9.44      11.08    12.31
38°00" Long. 39°00"Lat.   Nr Malatya      Turkey     1000m       10.11     11.33    12.56


THERE is an apocryphal tale told to young designers about the dangers of rigid thinking, which concerns the early years of NASA's space programme.
One of the APOLLO rockets, so the story goes, was made 6" taller than the earlier craft. When the time came to transport it from the construction site to the launch pad, the team hit an unforeseen problem.  The rocket, which for technical reasons had to be transported vertically, was a couple of inches too tall to pass under the bridges which lay along the route.
A quick calculation showed that even partial destruction and rebuilding of the bridges would cost millions of dollars.  The only other option they seemed to have, taking the rocket apart and re-assembling it at the launch site would cost at least as much.
A lot of intelligent people began to feel rather stupid.  In a last ditch attempt to avoid incurring the kind of expenses which do nobodies career much good.  The project called in a consultant who did not pretend to be an expert on space flight or on bridges . . . .
He did however, have an uncanny ability to solve problems.  Within minutes, this man hit upon a solution which cost not a cent.
He suggested they deflate the tyres of the transporter every time it had to go under one of the bridges. as soon as the rocket was safely through, the tyres could be reinflated.
Obvious?  Maybe, but for most people only in retrospect.


Naked Eye Variable Star Observing
by Vaughan Cooper

THE following notes may be of interest to members, not only to those who are beginners in finding their way around the night sky, but also those who are a little more experienced.

Once basic star and constellation recognition skills have been established it will now be possible to apply ones time in a slightly more serious manner; namely naked eye variable star observing.
I've prepared two charts to start you off, of the well known constellations, Cassiopeia and Gemini.  The object of the exercise is to estimate the magnitude of a variable against the stars listed whose magnitudes are stable and accurately calibrated and not too dissimilar to the total range of amplitude of the variable being studied.
For example, if you consider γ Cass. the variable star in Cassiopeia to be equal to β Cass., write down 2.2.  However if you feel γ is slightly fainter than β but may be a little brighter than 6 Cass. write down your magnitude estimation as 2.4 as this is half way between 6 and β in brightness along with the date and time and perhaps the quality of the seeing which might be judged by noting the faintest star magnitude visible overhead.  And its as straight forward as that...
Of cause the above notes are aimed at the very beginner who wishes to make a start in variable star observing.  For the more demanding and serious study of variable stars a little more time and attention to detailed will be needed and of course access to a telescope, which could put off the beginner variable star student, so I've purposely kept the procedure of studying γ Cass. and η Gemini very simple.

A little background history

γ Cassiopeia is a peculiar variable star normally the 3rd brightest in Cassiopeia, regarded as a young star of around 9 million years old.
Because its a young star newly formed, we know from its spectrum that the star is rotating at a very high speed, as a result of this, along with other unknown reasons the star expels its outer atmosphere.  Now until 1936 it had shone steadily as a 3.0 mag. star, but early in that year it suddenly and unexpectedly started to brighten, this continued until May 1937 by which time it was of magnitude 1.4 making it slightly brighter than β Cass., and deepening in colour to an abnormal yellow tint.  Although a brightening of 1.5 magnitudes is not that unusual for a star, but when it happens to a 3rd mag. star, that star becomes one of the brightest stars in the entire sky.
During the later months of 1937 it faded rapidly with fluctuations of decreasing amplitude and by 1940 it had sunk to a lower level than from which it had started (about 2.8); here, more or less consistently remained.  My own observations show a steady magnitude of 2.2 over the last few years.  Very accurate measures have however shown that faint and quasi periodic variations still persist and there is no reason to suppose that its more spectacular performance may not one day be repeated.
A large number of spectroscopic observations were made during its outburst and these indicate that the star expelled its outer atmosphere and photospheric layers; ultimately this envelope became entirely detached from the star.
In 1965 γ Cass again showed signs of brightening but not to the same degree as occurred in the late 1930's

Frequency of Observation and Comparison Stars to use

Due to the very slow change in the magnitude γ needs to be kept under careful scrutiny and as such its on the BAA variable star priority list.  The frequency of the number of times you make a estimate of its brightness, some authorities suggest once or twice a week, but I find this far too frequent for my observing practice and so I limit it to only once or twice per month.

Suggested comparison stars;
α     And.       2.07
ε     Cyg        2.46
γ     Cygni     2.22
α    Pegasi     2.48
β    U. Major  2.35

Before leaving Cassiopeia the following may be of interest.

ρ Rho Cassiopeia, this star can be seen with the unaided eye on any clear night, however ρ was discovered to be variable by Miss Wells, an American lady working, I believe, at a professional observatory in 1901.

ρ Cass. a super giant star with a diameter of 600,000,000 miles, of intermediate spectral type.  Usually of 4.4 mag. and known to fade on very rare occasions to a 6.2 minima, the last known fade was during 1945 to 1947.  As its so faint for effective naked eye observations, binoculars are required for a proper study of it.

Comparison stars to use are;
χ      Cass     4.2
θ     Cass      4.5
λ     Cass      4.8
σ     Cass      4.9
γ     Cass      5.1

For positions of the comparison stars may I suggest you refer to Norton's star atlas for their positions in the sky.

ρ Cassiopeia is also on the priority list of the BAA variable star section and so worth monitoring.  At one time α Cass. was considered to be variable with a range of 2.2 to 2.8, but no definite period.  The discovery was made by W.R. Birt - (presume-able the same Birt, an English selenographer) in 1831.  However professional astronomers consider the alleged variability of α Cass. is almost wholly attributable to errors of observation. But could a be a star that varies at very infrequent intervals and with long periods of inactivity?

η Geminorum was discovered by Julius Schmidt during the last century along with many others he discovered during his long active observing life.  η Gem. is a semi-regular star with a range of 3.2 to 3.9, with a period of 233 days, so quite suitable for naked eye observation with a frequency of once every 7 to 10 days.  Over the long term if you are persistent enough you will notice a different pattern of variation both with amplitude and periodicity on each successive cycle as the years go by.

Comparison stars to use are;
μ    Gem.     2.8 (slight var.)
ε    Gem.     2.9
δ    Tau.      3.0
ξ    Gem.     3.3
λ    Gem.     3.6
υ    Gem.     4.1
1    Gem.     4.1

If any of the above is attempted, you will have gained some first hand experience of variable star observing and also improve your knowledge; like knowing the names and positions of the comparison stars listed, which otherwise you would never probably bother in getting to know.

Stars of Old, Stars of New
by Ivor Clarke

GO OUTSIDE on a clear night and look at the sky.  What you see is not necessary what actually is there, what you are seeing is mixed in your minds eye with all of the knowledge of the late 20th century's science of astronomy along with all of the wonderfully images beamed to us from distant space craft or the Hubble Space Telescope's new sharp views of the heavens.
You can't help it, you know what you're seeing when you look at a star, a misty patch of light of a distant galaxy or a nearby planet.  Turn your telescope on to the Moon and you can see the dust, the rocks, the craters, or look at the mare; flooded, not with water, but with long solidified lavas.  You know because we've been there and everyone has seen the films of the 12 astronauts bouncing around on our twin world we call the Moon.
We have all read in books and magazines what the worlds of the Moon and the planets are like. Mercury, moon like, roasted by the sun on one side and freezing on the other. Venus, Hell?  Mars, no Martians, just craters and dust with a little frozen water at the poles. Jupiter, nearly got to be a small star and would have had its very own solar system with its large and small moons.  Saturn, best looker in the system?
Going outward, the stars form not just groups of patterns of the ancient gods and goddess's, but complex systems of binary and triple systems, of clouds of gravitational linked suns rotating along with us around the rim of our Milky Way galaxy.  The stars to us, are dynamic objects: we understand how they burn, how long they live and how they are born and die.
Most of this knowledge has been gathered recently in the course of the last 300 years and most of all in the last 30 years as spacecraft have explored the planets and telescopes both on the ground and in orbit have looked at all the wavelengths in the electromagnetic spectrum.  30 years is a very short time in which a whole new universe has been created in the minds of men.  Of cause is was there all along just waiting to be discovered, but it took a lot of work and explaining for us to be able to understand it.  And it's most likely we have still got some things wrong.
But can we see the sky as the people 1000's of years ago did?  Yes, find a dark spot away from lights and just look up.  Clear your mind of what you know and look.  To the folk of long ago the stars brought order to there lives.  They where there every night and with each year repeated their movements night after night.  Some nights they would see a meteor or two flash across the sky or see a comet move from night to night across the star patterns.  But overall they knew the stars stayed still in the heavens.
With each season the same star patterns repeated themselves.  This predictability helped to organise the year, the time for planting and the time for harvest.  All over the world our ancestors built devices to measure the passing of time, at Stonehenge in England; Abu Simbel in Egypt; Chichén Itzá in Mexico; Angkor Wat in Cambodia; Chaco Canyon in New Mexico.  Some of these were sophisticated sundials to measure the longest day and the shortest, some of them could predict the eclipses of the Sun and Moon.
It was obvious to the superstitious that the stars along with the Sun and the Moon controlled man.  Early on in the history of astronomy the visible stars were given names as an aid to remembering and they were grouped into constellations.  Old stories and legends formed the base to the names in each country along with the 12 zodiac constellations through which the Sun and the Moon moved along with the five strange bright stars.
All the stars in the sky stay in place, that is except for the five points of light that don't. Could you spot the point of light which moves a little every night while all the rest stay still? I don't think I would for a long while.  Could you work out if the Sun went round the Earth or the Earth went round the Sun?  After all you can't feel any movement can you? And what about working out when is the longest day and the shortest, (easy with a fixed pole and some stones to mark the suns shadow).  But what about predicting an eclipse of the Sun or Moon without my computer?  Phew. . .
By following the motion across the sky for a few months of one of these strange wandering or vagabond stars called planets, they would see it move from constellation to constellation and occasionally do a strange slow loop-the-loop in the sky.  Also they varied in brightness slightly, dimmest near dawn and sunset and brightest when high in the sky at midnight.
As the Earth was the centre of their universe, all of the sky revolved around it.  First was the Moon then Mercury and Venus followed by the Sun in their transparent spheres; then the three outer planets until you came to the last sphere of stars.  Simple.  All the orbits of the planets where perfect circles claimed Pythagoras in the 6th century BC.  No one thought otherwise for nearly 2000 years!
However, even the Egyptians knew that Mars could travel backwards and the name they gave it meant "who travels backwards".  In each of the outer spheres it was reasoned, was another smaller planet sphere called an epicycle so that the planet could turn independently.  For Ptolemy this solved the problem of the retrograde motion of the planets, and for 1500 years no one tried to change it!
But what were the planets?  If you look at them they look like bright stars, just points of light.  Mars does look a pink colour and Jupiter creamy, while brilliant Venus is a diamond in the sky.  The stars also have colours, red Betelgeuse, blue Rigel, yellow Capella.  On most evenings the stars twinkle and shake slightly while the planets seem to stay still. Why?  Was it possible that the planets had a solid form?  When Venus is near Earth in the morning or evening sky it is seen as a crescent with a diameter of up to 62 seconds of arc. Is it possible to see its thin crescent shape like a new Moon but 30 times smaller in the twilight sky?  Venus is the only planet that it may be possible for the unaided human eye to see as a shape.
The other planets have an even smaller angular diameter, which is below the resolution of the human eye see unaided.  How else could they be detected as having a form?  Well if, say, Jupiter or Saturn, both of which have an opposition diameter of over 40" were to pass behind a distant building, pole or rock when near opposition it would not suddenly blink out as would a star in similar circumstances but would quickly fade, within about 1 second, as it disappeared.  On reappearance it would fade up in a similar amount of time.  None of the stars in the sky do this, on meeting an eclipsing object they wink out in an instance as befits a distant point light source.  Did the ancient astronomers of Babylonia, Egypt or Greece know this?  In almost all cases they seemed to think of these bodies as something special.  Something which could effect the lives of men.  The planet Jupiter was thought to be the King of the planets, how did they know it was the largest planet?  Venus and Mars complemented each other being the Goddess of Love and the God of War.
Then in the 16th century, Tycho Brahe spent 25 years plotting as accurately as possible without telescopic help, the positions of the stars and planets.  This work helped Kepler prove that Copernicus was right about the Sun being at the centre of the Solar System, but wrong about the orbits of the planets being circles.  Kepler believed that the planets had solid bodies and he seems to have been one of the first since antiquity to propose they were made of stuff like the Earth.  The orbits of the planets were shown to be ellipses, moving fastest when nearest the Sun and slower when furthest away.  It took another 66 years before Isaac Newton published his theory of gravitation and explained why the planets moved in such paths.
In 1610 Galileo Galilei looked through his new telescope at Jupiter and saw that it was a body with 4 stars near it.  From night to night he observed them with his blurred 15x telescope.  He drew in his notebook the movements of the four moons showing them changing position as they orbited the planet.  He was less surprised by the planet having a body than he was at seeing that other moons could orbit a planet other than Earth.  This proved that the Earth could not be the centre of all orbital movement and showed that the Copernicus system with the Sun at the centre was correct.
Later that year Galileo looked at Saturn and was surprised with what he thought he was seeing: a triple planet or one with two very large moons.  When he next looked a year later, they had gone!  The rings had closed up and so his primitive telescope could not resolve them.  He found this very disturbing, but a year later the planet's triple nature was visible again.  It was nearly 50 years later before Christiaan Huygens had a good enough telescope to be able to see the rings clearly.
Today we have a fairly good idea of what the solar system is like, but to the people of yesterday it was all a wondrous mystery unlikely ever to be resolved.  If some of the old philosophers came back today, and looked at our present state-of-the-art telescopes, what would they make of it?  It would astound them I'm sure, would it increase their fascination of the heavens?

You can bet it would.

The Interplanetary Dangerous Sports Club

by Mike Frost

(The physics in this story is valid, I think, but the engineering may be a bit dodgy)

Every so often, when I'm in England, I drop in on my old college bar to catch up on my friends who stayed behind at university.  There aren't so many left these days - the people who stayed on to do research have now got their doctorates, and most of them have moved on to other universities.  One or two have even left the solar system!  But there's usually somebody I recognise.
This time it was Clive, playing shoot-em-up on the video machine.
"Care for a drink?" I asked.  Silly question.  Have you ever known a student turn down the offer of a drink?  Even a post-doc.  Post-doctoral research is a curious half-way house, between being a penniless student and a salaried scientist - three years of full time research paid for by an enhanced grant, with no guarantee of work at the end.  Post-docs tend to fall into two categories.  There are those careerists, conscientious scientists, who gaze with envy on their more fortunate colleagues with a permanent university position. Then there is the second category, aimless delinquents marking time, working only to support their out of hours activities.  These characters are at university for one reason only - the subsidised sports.
Clive fell into the second category.
"The research?  Boring.... But you should see what the Dangerous Sports Club are getting up to!"
Our university had a reputation for producing the most daring, lunatic, dangerous sportsmen of them all.  Paragliding, scuba diving, white hole rafting.... they had tried them all.  Chuck the ruksaks in the back of the warp drive and head up the hyperway for the week-end....
"So what are you up to these days?" I asked.
He took a sip of beer. "Geostationary abseiling."
"What on Earth is that?"
"Not on Earth," Clive explained, "In orbit!  It's the cheapest way to see a planet.  All those rockets and shuttles; they're such an expensive way to leave a planet's surface.  All that fuel wasted, simply getting your spacecraft up to escape velocity.  If we landed our spacecraft on a planet's surface, we'd never be able to afford the fuel to take off again."
"But you have to reach escape velocity," I pointed out, "otherwise you wouldn't make it into outer space.  That's what escape velocity means."
He looked at me with the piteous expression reserved for those with lower degrees.
"Come on Frosty, you know your Newtonian dynamics better than that.  Escape velocity is the speed you need to fire a bullet at, so that it escapes to outer space.  Like, for example, on Earth, if you fire a bullet straight up at seven miles a second, it won't come back.  It has enough energy to escape Earth's gravity completely.  But you don't have to go at escape velocity to escape, provided you keep on accelerating up.  Take the space shuttle.  That goes pretty fast, but it doesn't quite need to reach seven miles a second.  If you're prepared to take your time, you can go up as slowly as you like.  It's so much more efficient - and a lot less bumpy!"
I wasn't convinced.  "Why doesn't the shuttle fly out to space at ten miles an hour, then, if that's so efficient?" I asked, sarcastically.
"Because it has to carry it's own fuel supply - so it can't hang around.  Rockets are inherently a bad way of going into space because they are self contained.  So we ..." (he motioned proudly to himself), "don't bother taking a rocket to the surface of a planet.  We park our spaceship twenty thousand miles up.  Then we sling a rope out the airlock and abseil down it."
I nearly swallowed my pint. "Long rope!"
He nodded.  "VERY long rope.  It's only now in me twenty second century that we've got the materials to make the rope.  Your average nylon climbing rope would snap under it's own weight after we'd paid out about ten miles of rope.  Fortunately my chemistry department came up with something a bit more, erm, durable".
"Let's get this straight.  You lower yourselves down from space on a rope to go and explore a new planet, because it's the cheapest way to get up and down.  So why don't you burn up when you hit the atmosphere?"
"Because we're not going very fast.  Look, most of the hassle with rockets and space ships is because they're travelling fast when they hit the atmosphere.  They are dropping from low orbit - in the Earth's case that means that they are orbiting the Earth in about 90 minutes.  They then have to enter an atmosphere that's going round once every twenty four hours.  They have to use the atmosphere to brake themselves down to landing speed. But we're not interested in coming in fast - at least, not when we're abseiling! What we do is find an orbit much higher up - twenty thousand miles higher up - where the orbital period is precisely one day.  For earth we call that the geostationary orbit - it's where all the communication satellites go, because they stay fixed above a single point on the equator.  So we park in high orbit, lower the rope, slide down it, and take a look around, find the nearest pub.  Come closing time, we clip the karabiner on the end of the rope and then 'wind me up Scotty'!"
I had the feeling I was being wound up myself. "Have you really done this, or are you having me on?"
He looked hurt. "Course we did!  We wanted to start on Earth, but air traffic control weren't too keen on a twenty-two thousand mile rope.  So we switched to Mars.  The Martian day's also about twenty four hours but the gravity is a lot weaker, so the Martio-stationary orbit's only about eight thousand miles off the surface.  Also the atmosphere's a lot thinner, so we can really come down the rope fast!  When you start out from orbit, you're weightless, so the first few hundred miles you have to pull yourself along. But you gradually feel your weight increasing as you drop towards the surface - and if you don't don't check your speed you'll just go SPLAT! into the surface."  He checked his hands." I got pretty bad friction bums on that drop".
"And after Mars?"
"Jupiter, of course.  MUCH stronger gravity, but it spins a lot faster.  The Jovo-stationary point is a good hundred thousand miles above the atmosphere, but it looks a lot closer. One hell of a view, I can tell you!  But there was no surface to land on and the atmosphere wasn't very good - hydrogen and methane - which soured the beer.  So we didn't stay there very long.  Tell you the truth, abseiling was cheap, but we weren't getting much of a thrill out of it - not enough danger, you know.  So we left the solar system for our next drop..."
He paused, to let me buy him another beer.   "Go on", I said, "where next?"
"The Crab Nebula!"
"The Crab!  That's a Neutron Star.  That's really dangerous."
"We know that now," he grinned, "actually, we knew it then, that's why we went.  Nobody had ever landed on a Neutron Star, we wanted to be the first.  We'd figured out the radiation was pretty intense, so we had our lead lined suits on, but we hadn't really appreciated how strong the gravity would be..."
"I'll bet!" I said.  "Neutron stars are, what, twenty miles across...?"
"Ten miles, actually.  They're what's left after a supernova.  The whole outer shell of a star gets blown off in one gynormous explosion, but the core of the star collapses into this incredibly dense neutron star.  Ten miles across and the mass of the sun!  And spinning thirty times a second.  You can imagine how close the neutro-stationary orbit had to be to that!...."
"So what was it like to land on a neutron star?"
He looked at his pint shiftily.   "We didn't make it.   Like I say, we hadn't thought through the effects of the gravity.  We knew our winch was strong enough to wind someone up from the surface of the neutron star, but what we hadn't figured on was the tidal effects. You see, when you are so close to such a small but strong field, the gravity varies very appreciably even between your head and your feet.  It's like being stretched on the rack! We couldn't even park in Neutro-stationary orbit - we had to pull out of our descent and escape before we got shredded.  Fortunately our pilot, Shorty, was less affected by the tidal forces than anyone else and he rescued us.  Being a six inch tall Arcturan isn't much fun climbing the Eiger but it sure helps in a differential gravity field!
Anyway..." he finished, sipping his pint," apparently there's not much to see on the surface, the highest mountains are less than a millimetre high because of the gravity.  A pity we didn't make it, but it was one hell of a ride.  Almost as good as Alton Towers!"
"Sounds like it..." I said appreciatively, "so what next?"
"Tomorrow" he said proudly, "we leave for M87..."
"What, the Glasgow ring-road?"
"No stupid, the active galaxy!  We're going to abseil down a black hole!"
This time I did swallow on my pint.  "A black hole?!  Are you crazy?  This time you will shred yourself for certain!"
"You really are out of touch, aren't you?  Look, if we were going down a small black hole, say in the galactic centre, we'd be in trouble, because the gravity would be too intense, like the neutron star only worse.  But we're going to visit a black hole the size of a galaxy.  At the centre, the singularity, the gravity is infinite and we wouldn't stand a chance.  But at the outer boundary, the event horizon, you'd hardly even notice the gravity.  And no-one's ever been inside an event horizon."
Something was beginning to worry me. "You can't return from beyond the event horizon. That's why we call them BLACK holes.  The escape velocity is faster than the speed of light".
He didn't look worried.  "Haven't you been listening?  We don't need to travel at the escape velocity - we've got a rope to pull us out!"
"I don't think that matters.  Once you venture past the event horizon, you might think you're OK but you can never escape."
"Don't worry", he said, trying to be reassuring, "there's no problem.  We're not going to stay around, we're not trying to visit the singularity.  We're just going to slide down a rope into a big black hole, take a few pictures, and then climb back out again.  What could be simpler?"
"But light can't escape from a black hole!" I said desperately.  He drained his pint.
"Light doesn't have a rope.  We do."


I was very worried that night.  Try as I might, couldn't convince Clive of the foolhardiness of his plans.  His brush with death on the descent to the neutron star convinced him he had a charmed life.  My attempts to explain the impossibility of escaping a black hole were met with protestations that I didn't understand the mathematics of gravity.  In that, Clive was right.  I knew enough about Newton's theory of gravity to understand that reaching escape velocity isn't necessary to reach orbit - escape velocity is simply the start speed needed for a projectile to escape a planet's gravitational pull.  But when the escape velocity reached the speed of light, as it did in the case of a black hole, Newton's theories of gravity weren't good enough.  I had to turn to Einstein's theories of gravity, and they were altogether more complicated.  I spent the whole night poring over my old lecture notes, and in the morning I set off at a pace for the spaceport.
I had to call the travel agents for Clive's flight details - a local shuttle to the galactic centre, then long haul toward the Virgo cluster and finally a local charter into M87.  I was very late to arrive at the space port before the shuttle departed.  I had to talk my way through departures and sprinted down the corridor.  Passengers were boarding the shuttle as I arrived at the departure gate, but I checked with the stewardess and Clive was not yet on board.  Ten minutes to take-off and he was nowhere to be seen.  Where could he possibly be?


"Oh hi Frosty!  Mine's a G and T," said Clive blearily from the spaceport bar stool, "meet the rest of the gang - that's Shorty under the table.  Come to wave goodbye?"
"Clive," I said, wearily, "it's absolutely vital you listen to me.  That shuttle goes in five minutes and you mustn't be on it!"
"Five minutes?!"   Clive looked at his watch, "Come on gang, drink up!"
As they donned their day-sacks I tried to argue with them.   "Listen!  Once you get gravity as strong as a black hole, the rules are different.  Space itself is bent, and at the event horizon the bend snaps off - once you're past the event horizon, there are no paths back through space-time." 
Maybe there was a flicker of doubt from Clive, but he was still mostly bravado, "What about the rope, then?  Does it snap at the event horizon?  I don't think so.  The tidal forces aren't strong enough.  What will break the rope and stop it pulling me out, Mike?"
We were nearly at the departure gate.  I only had one thing left to try.  "Where is your black-hole-stationary orbit going to be, Clive?  I told you space curves near a black hole - you can't even stay close to the event horizon for long.  Just outside the event horizon there's a region where light itself orbits the black hole.  Imagine that, Clive!  Inside that, the best you can ever do is a very rapid fly-by, not quite touching the event horizon.  If you linger at all you won't be able to leave.  You can't lower the rope, Clive, you don't have time — you have to be away."
Finally, finally, Clive took notice.  Maybe his experiences at the Neutron Star, trying to reach an orbit suicidally close to the intense gravity, convinced him of the logic of my argument.  He motioned to his gang to stop by the gate.
"What you're saying is, we can never go inside the black hole, and live to tell the tale: but, there are some really interesting things to see near the event horizon, provided we dive in really fast and stay there as short a time as possible...?"
I nodded, speechless.  He grinned.
"Let's go BUNGEE JUMPING, guys!"
And with that they were through the departure gate and off...


General Certificate of Education Examination


Two and a half hours

Answer Questions 1 and 2 and THREE other questions

1. Write a short essay on any two of the following:

(a) The measurement of time by the Sun.

(b) The discovery of planets beyond Jupiter.

(c) The scientific and other uses of artificial Earth satellites.

(d) The Milky Way.

(14 marks)

2. Use the information in the Table to answer all the sections (a) to

(g). In each case make your reasoning clear.

Star             Parallax     Right           Declination      Apparent      Absolute
Surface         seconds    Ascension                          visual           visual            temperature  of arc                                              magnitude    magnitude
                                   h   m           °   '
Rigel             0.004        05 10        -08 19             +0.1              -7.0
Betelgeuse     0.005       05 50         -07 23             +0.4             -5.9
Pollux            0.093       07 39        +28 16             +1.2             +1.0
Regulus         0.038       10 03        +12 27             +1.3              -0.8
Deneb           0.002       20 38        +44 55             +1.3              -7.2

(a) Name the star which is furthest from the Sun.

(b) Calculate the distance of Rigel from the Sun, in parsecs.

(c) Explain what is meant by saying that the absolute visual magnitude of Regulus is —0.8.

(d) Although Rigel and Regulus have nearly the same surface temperature, the absolute magnitude of Rigel is very different from that of Regulus.  Explain this.

(e) Explain why Betelgeuse is known as a 'red giant'.

These stars are observed from an observatory at 52° 00' N, 05° 00' W on 1972 February 21.  At 21h 00m UT on this date, the Greenwich sidereal time is 07h 00m.

(f) Name the star which is nearest to the observer's meridian at 21h 00m UT on this date.

(g) Show that from this observatory Deneb is circumpolar.

(19 marks)

3. What factors determine

(a) the escape velocity from a planet,

(b) the time taken for a satellite to revolve once in a circular orbit about a planet?

Jupiter's satellite V describes its orbit about Jupiter in 12h.

Calculate the period of satellite IV, Callisto, the radius of whose orbit is ten times greater than that of satellite V.

(14 marks)

4. Explain why Mercury is a difficult planet to observe from Earth.  State, with reasons, the time of year at which Mercury can be best seen in the evening after sunset.

Describe our present knowledge of the atmosphere and surface of Mercury.

(14 marks)

5. Describe how you would make observations of the variation in the light emitted by a typical Cepheid variable which has a period of about ten days. Show by means of a labelled diagram the results you would expect to obtain.

Explain how the variations in the light received from any one type of variable can be accounted for.

(14 marks)

6. For what reasons do you accept that the Sun is a typical star?

Describe the general appearance of the spectrum of the Sun.

Explain what information can be gained from a study of the spectrum.

(14 marks)

7. Describe with a ray diagram the simple refracting telescope.

Label your diagram, and show the paths of three rays of light from a distant object through the instrument.

Explain the relative advantages of reflecting and refracting telescopes of the same aperture. Why are the largest telescopes always reflectors?

(14 marks)

8. Write an account of the contributions which were made by Copernicus, Tycho Brahe and Galileo to our understanding of the Solar System.

(14 marks)

9. Give an account of the methods used to send an unmanned probe to make a soft landing on Mars. Describe briefly the information which is likely to be gained.  Mention the main difficulties to be overcome, both in sending the probe, and in receiving information from it.

(14 marks)

10. The times of the principal phases of the Moon in 1971 December were: Full 2d 08h; Last Quarter 9d 16h;

New 17d 18h; First Quarter 25d 02h; Full 31d 20h.

Explain how the phases are caused, and why the intervals between successive phases are not the same.

State the dates in 1971 December on which you would expect spring tides to occur.  State the times on December 9 at which you would expect high tides to occur in the open ocean. Give your reasons in both cases.

(14 marks)

Understanding Binoculars


Magnification is the increase in a subject's apparent size over unaided observation.  A subject 700 meters away seen with 7x magnification appears as it would from 100 meters
with the naked eye.  Magnifications under 5x are generally not powerful enough for outdoor use.  When magnification exceeds l2x, hand movement makes the image unstable and viewing becomes uncomfortable.  Magnifications of 6x to 9x are best for general use.

Field of View

The real field of view is the angle of the viewing field measured from the central point of the objective lens.  The apparent field of view is how wide that field of view appears to the eye, and is obtained by multiplying the real field of view by the magnification of the binoculars.  The field of view at 1000m is the width of the visible area at a distance of 1000 meters.

Objective Diameter

The effective aperture is the inside diameter (in mm) of the objective (front) lens frame.  The larger the objective diameter, the greater the resolving power and the brighter the image.  But large-diameter objective lenses make binoculars heavier, so 50mm is the general limit for manual operation.

Exit Pupil

The exit pupil is the image formed by the eyepiece lenses.  The diameter of the exit pupil (in mm) is the effective aperture divided by magnification.  The diameter of the human eye pupil varies from 2-3mm in daylight to 7mm in the dark.  An exit pupil of 7mm gives maximum light to the dilated eye and is ideal for use in the dark.


The relative brightness value is obtained by squaring the diameter of the exit pupil. The greater the relative brightness, the brighter the image.  However, this value doesn't correspond exactly to increases in brightness over the naked eye, because the light coming through the binoculars is 100% effective only if the exit pupil is the same diameter as the pupil of the eye.

Eye Relief

Eye relief is the distance between the eyepiece and the eyepoint.  Longer eye relief (high eyepoint) allows for rubber eyecups and eyeglasses.  Eyeglass wearers simply fold back the collapsible eyecups.

ED Lens

Extra-low Dispersion (ED) glass virtually eliminates chromatic aberration to provide higher resolution, contrast and colour balance.


Coating is also important to image brightness.  When light passes through a lens, some is reflected by the front and rear surfaces of the lens and lost.  This light causes flare or ghosts, reducing the sharpness and contrast of the image.  Vacuum-vaporize coating puts a thin, transparent film on the lens surface to minimise this effect by as much as half.

Binocular Operation

Pupil Distance
Adjust the distance between the eyepieces, while looking at a distant object, until the right and left viewfields coincide to form a circle.  The pupil distance scale helps you remember the setting.

Focusing Binoculars
First adjust the pupil distance. Using your left eye, focus on a distant subject with the central focusing knob.  Then use your right eye to focus on the same subject with the diopter adjustment ring.  The index helps you remember the setting.
(Diopter adjustment)
Thereafter, just turn the central focusing ring to focus.