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Ellipses

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Flash
154521.  Wed Mar 07, 2007 7:28 am Reply with quote

I wonder whether we could get an elliptical billiard table into the studio, put two balls on the focus points, and invite a panellist to strike one ball and not hit the other ("oh, come on ... all you have to do is miss!"). We'd shoot it from above.

Anyone got any ideas where we could find one?

 
suze
154561.  Wed Mar 07, 2007 9:08 am Reply with quote

By the simple expedient of asking Google, it seems that they exist and you too can have an elliptical billiard table for just $338.99!

Although shipping from Korea would likely be extra.

http://www.mathlove.com/new3/tools/detail.php?pid=TTA0A

 
Flash
154573.  Wed Mar 07, 2007 10:27 am Reply with quote

Thanks, suze. That seems to be a desktop model sold as a maths teaching aid, which might be OK. I've e-mailed them to see if they have a UK outlet.

Presumably such a thing is only ever going to be made as a teaching aid, because a game at which it's impossible to miss would have a short-lived appeal even in this age of instant gratification, so no-one would make one.

 
Gray
154606.  Wed Mar 07, 2007 12:14 pm Reply with quote

Flash wrote:
OK, thanks. My difficulty is this: because the gravitational field of a body is uniform in all directions, my intuition tells me to expect an orbit to settle into a circle unless it is perturbed by some extraneous force. But I think we've gone into this as far as we need to for present purposes.

Oh go on, just a little further...

To change from an elliptical orbit to a circular one would actually require a force on the body, because you'd need to change its velocity at some crucial point.

 
dr.bob
154813.  Thu Mar 08, 2007 5:01 am Reply with quote

Indeedy. Unless the velocity was exactly right to start with, an elliptical orbit will ensue. To change this to a circular orbit requires an external force since, as Newton pointed out, an object travelling in a straight line with no external forces yadda yadda yadda.

Sometimes orbits can be changed due to tidal effects, but I think the orbiting bodies have to be relatively close to each other (e.g. the Earth and Moon where tidal effects are causing the Moon to steadily move further away from the Earth)

 
Gray
154988.  Thu Mar 08, 2007 10:19 am Reply with quote

When Saturn 5 put Apollo 11 into (circular) Earth orbit, they did a couple of 'turns' and then fired a huge rocket at just the right moment (and just the right amount) to turn their circular orbit into an elliptical one whose other focus was The Moon.

And all with slide rules.

 
dr.bob
155038.  Thu Mar 08, 2007 11:38 am Reply with quote

Gray wrote:
And all with slide rules.


Slide rules have probably been responsible for some of the greatest breakthroughs in science over the years.

Besides, orbital dynamics isn't that complicated :)

 
Gray
155333.  Fri Mar 09, 2007 10:17 am Reply with quote

It's hardly brain surgery.

And Tsiolkovsky did in Russian, even...

 
Flash
155345.  Fri Mar 09, 2007 11:12 am Reply with quote

Is this a possible question:

Which is harder - rocket science or brain surgery?

Belongs in an 'experts' thread, perhaps.

 
eggshaped
156025.  Tue Mar 13, 2007 6:39 am Reply with quote

Sorry to bring this up again, but I had a thought on the drive home last night that the reason orbits are elliptical is that the sun is not standing still.

If the Sun was still and the planets went round in a circular orbit, then the orbit of the Sun around the centre of the milky way would cause slight changes in the planets' orbits which would cause ellipses.

I know that's not what all you guys said above, so I'm sure it's not correct, but it would make a much neater answer if it were - so I say we go against all scientific theory just to make things easier to understand.

 
Flash
156035.  Tue Mar 13, 2007 7:01 am Reply with quote

There's a song by Jewel called "What's Simple Is True" which I must let you have.

Here's a different question: an ellipse is a conic section. Does each ellipse mathematically imply a single apex to the cone, if you see what I mean? Or, given an ellipse, could you postulate any number of imaginary cones of which it could be a section?

Don't take any time on this query as it is plainly no use to us at all. It's just that if there is a single point in space which is the apex of our ellipse, I think it would be a good place to start looking for God - the God of this planet, anyway.

 
Gray
156061.  Tue Mar 13, 2007 7:45 am Reply with quote

A particular ellipse defines only a single geometry of cone (with a single apex). However, that apex could be in any of four different places, two above the plane, and two below.



In (b), above, the apex could be pointing rightwards, downwards and leftwards, and would still make the same ellipse when intersecting that plane (assuming the plane is inclined at 45 there).

The only section that generally reveals God to anyone is generally one that puts one in an asylum...

 
eggshaped
156392.  Wed Mar 14, 2007 6:19 am Reply with quote

The earth's orbit gets more and less elliptical through time.

There was a theory, accepted from the 1920s to the 1950s that these eccentricities in the Earth's orbit caused ice ages, however the theory fell out of favour as the figures didn't quite add up.

However Jose Rial, a professor of geophysics at the University of North Carolina at Chapel Hill, writing in Science, has brought the theory back, by claiming that the figures do add up after all.

Simply put, the original "Milankovich variation" theory claimed that there should be 100,000 and 430,000 year cycles in Ice ages, and while the 100,000 year one was clear, the 430,000 one was no-where to be seen. However Rial claims that the evidence is there, but was difficult to spot because the two cycles interefere with each other in the same way that two radio waves might cause interference.

Source

 
Flash
156607.  Wed Mar 14, 2007 4:43 pm Reply with quote

If God is in four different places at once, as Gray claims, then I have no time for him. Imagine if it had been three, though - how spooky would that have been?

 
Gray
156621.  Wed Mar 14, 2007 6:25 pm Reply with quote

Quote:
but was difficult to spot because the two cycles interefere with each other in the same way that two radio waves might cause interference.

I think Fourier analysis has been around for long enough to distinguish two interacting frequencies...

The Precession of the Equinoxes comes up with other cycles that affect climate as well:
Quote:
Over longer time periods, that is, millions of years, it appears that precession is quasiperiodic at around 25,700 years, however, it will not remain so. According to Ward, when the distance of the Moon, which is continuously increasing from tidal effects, will have gone from the current 60.3 to approximately 66.5 Earth radii in about 1,500 million years, resonances from planetary effects will push precession to 49,000 years at first, and then, when the Moon reaches 68 Earth radii in about 2,000 million years, to 69,000 years.

http://en.wikipedia.org/wiki/Precession_of_the_equinoxes

 

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