But why an elliptical orbit

Martin Brown wrote in news:dil51b$hl6$1
@news7.svr.pol.co.uk:

tt40 wrote:
Phew, I'm overwhelmed by the considerable and considered lengths that
respondents have made on this topic. (Of course it's tempting to be a
smart-alec and ask 'Yes, but why an ellipse?' as if to off-handedly
tilt at the signficance of mathematics in answering my question, but
that would lazy and disingenuous).

** To clarify, as was requested by some, the extended version of my
question is 'Why an ellipse and not a circle?' And thanks to those who
recognised this -- an imprecision on my part. **

OK That is actually a much easier question to answer. A circle is just a
very special case of an ellipse with exactly zero eccentricity.

If you set your planet off with exactly the right speed and exactly
perpendicular to the sun-planet line and at exactly the right velocity
then you will indeed get a circle. But these are a very special set of
initial conditions - do anything else and you will get an ellipse,
parabola or hyperbola depending on exactly how much velocity (kinetic
energy) you supply.

If the planet is at the right position for a circular orbit, with the
right speed, but moving in slightly the wrong direction it will get
closer or further from the sun and accelerate or decelerate accordingly
to conserve angular momentum.

If it is at the right position, moving in the right direction, but at
slightly the wrong speed it will not follow the circle either.

That's my hand waving English language approximation to why most orbits
are an ellipse and not a circle. I am sure it could be refined, as could
the following home experiment:

You can demonstrate a crude analogue of this at home by making a conical
pendulum. A weight hung on a string from the ceiling move it off from
the vertical by say 30 degrees and then push it to try and get it to
move around in a circle. You will quickly discover how hard it is to get
the initial conditions right for a perfect circular orbit.

The mathematical details are slightly different, but you basically have
a tame test particle orbitting under the influence of a central force
and can explore how it behaves when set off with different velocities.

It is a fascinating topic and I wish I understood (read 'could
configure my life so I had the time to learn') the maths.

There are several cute planetary orbit simulators on the web that will
let you set up some of the more famous scenarios and watch them evolve.

Just to add a little to this. In the real solar system, the planets are of
course perturbed by each other. A planet starting out in an exactly
circular orbit would not stay that way for long. In the case of the Earth
the other planets cause the Earth's orbit to slowly change over time. The
changes include the precession of the major axis and also a slow cyclic
change in the eccentricity. Periodically, the Earth's orbit does become
pretty much circular. You can look up Milankovitch cycles to find out more
about that.

Klazmon.






Regards,
Martin Brown

tt40 wrote:
Phew, I'm overwhelmed by the considerable and considered lengths that
respondents have made on this topic. (Of course it's tempting to be a
smart-alec and ask 'Yes, but why an ellipse?' as if to off-handedly
tilt at the signficance of mathematics in answering my question, but
that would lazy and disingenuous).

** To clarify, as was requested by some, the extended version of my
question is 'Why an ellipse and not a circle?' And thanks to those who
recognised this -- an imprecision on my part. **

It is a fascinating topic and I wish I understood (read 'could
configure my life so I had the time to learn') the maths.

Sorry that I've only had time to skim the thread, can't wait to read it
all in detail.

Greg.

It is no longer possible to isolate the elliptical geometry of orbital
motion as attempt to persuade people that it is a larger version of
terrestial ballistics.

For over a 100 years,geologists and climatologists have found that mid
latitude glaciation or ice ages contain the clues for a variation in
the shape of the planet's orbit from more to less elliptical.Because
the relationship between axial and orbital motion changes depending on
whether the geometry is more elliptical or less,the regretable feature
of the Newtonian scheme is that no such variation can be considered.

Newtonian physicists have axial and orbital motion sharing a common
axis when both motions are actually independent of each other -

http://www.pfm.howard.edu/astronomy/...S/AACHCIR0.JPG

Because they insist of a constant orbital displacement,if you extend
the orbital geometry to an ellipse,you will witness an assault on the
eyes for under such a justification ,the Earth would travel faster at
the aphelion !,Go ahead and try it.

The moral is don't be desperate for elliptical orbital causes and
certainly not terrestial ballistics or the silly and grandiose named
'unioversal laws of gravitation'.

"oriel36" wrote in news:1129198172.871900.182650
@g14g2000cwa.googlegroups.com:

Looks like there is a crack in your pot. You should get it mended.

Klazmon


SNIP

"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.

What I've always wondered is whether it is possible to separate the
elliptical orbits into two components, the way elliptically polarized light
can be separated into counter-rotating beams of circularly polarized light.

What, for instance, remains of a low eccentricity orbit if the circular
orbit is subtracted?

John Schutkeker wrote:
"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.


What I've always wondered is whether it is possible to separate the
elliptical orbits into two components, the way elliptically polarized light
can be separated into counter-rotating beams of circularly polarized light.

What, for instance, remains of a low eccentricity orbit if the circular
orbit is subtracted?

To first order, what remains is an elliptical epicycle, centered on the
circular position. The radial excursion must be a*e, for the perihelion
distance is a(1-e) and the aphelion distance is a(1+e). The downtrack
excursion is twice this, because (again to first order) the true anomaly
f = M + 2e sin M (where M is the mean anomaly).

-- Bill Owen