"tt40" wrote in news:1129087625.368615.299390
@g47g2000cwa.googlegroups.com:

In everything I've read about planets and elliptical orbits, I can't
ever recall any author (Feynman, Newton, 'Ask an Astronomer' etc.),
explaining exactly 'why' the orbit is elliptical. Oh sure there's been
lots of mathematics to explain the orbit and how it works, but most of
the explanations don't provide a definitive statement as to why it IS
elliptical.


Until someone can do the 'why', I'm going to assume that either:

1. it's because the Sun is in a rotation of it's own and all the
planets have to scoot to 'catch' up with it. But since the Sun is
moving too, the now-receding planet's momentum carries it further away
than it expected, so it maps out a stretched circle, longer than it
thought was necessary. So it's stretching the distance on the long-arm
of the orbit and has to scoot back in again, chasing that moving Sun.


No, the motion of the Sun through the galaxy is not relevant at all. Given
the law of gravity, F=GmM/r^2 and the Newton/Galileo laws of motion, a two
body situation results in only two possible closed orbits, either a circle
or ellipse. A circle is just a special case of an ellipse. To simplify
things, you normally use the center of mass of the Sun as the origin of the
coordinate system - that way you can work the equations without having to
worry about the motion of the Sun. Other orbits are possible of course, the
parabola and hyperbola are also valid orbits but they are not closed - i.e
the planet enters and leaves the system in one pass. It is very interesting
that any orbit in a two body system can be described by one of the above
conic sections. In the real solar system things are not quite as simple
because there are many bodies and they all interact with each other via
gravity. Nevertheless, ellipses still give a pretty reasonable
approximation for the motion of the planets as the inter planet
perturbations are fairly small. It's a different story when you have to do
astro-navigation such as the dance that JPL put the Cassini space probe
through - you need a lot of precision to do what they did and are still
doing with that.

It's a lot of fun to see how Newton figured all this out - especially if
you can read Latin, there are scans of the original editions of the
Principia online he

http://burndy.mit.edu/Collections/Ba...ine/Principia/

or

2. the minute gravitational tug of the planet pulls the Sun closer (out
of its 'fixed' position relative to the planet) which increases the
mutual gravitational attraction so that they are each attracted that
little bit stronger. But since the Plant is still in orbit, it follows
the short arm of the ellipse that little bit faster or a little more
energised. It then maps out the long-arm of the ellipse and
gravitational attraction recedes just a little bit, allowing it to
'stretch that circle'.

That is almost right in a hand waving sort of way.

Klazmon.






or

(this space left blank for the correct answer)

Greg