But why an elliptical orbit

"oriel36" wrote in news:1129137707.959738.266710
@g44g2000cwa.googlegroups.com:

Your idol is nothing but a fraud who mangled so many astronomical
principles for his ballistic agenda applied to planetary motion that
the noble discipline can only recover with stern discipline and candor
to face the fact.

Pish, posh. When the underlying physics is completely unknown, you have to
simplify problems to find basic solutions. Once the simple problems are
understood, then you can try to build up more complex situations by
agglommerating known solutions. To expect any more of even such a genius
as Newton would be like expecting the ancient Greeks to fire an Apollo
rocket to the moon. You're both unrealistic and vain.

"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?

canopus56 wrote:
snip

This page may also help the thread top-poster:
http://www-astronomy.mps.ohio-state....t4/orbits.html

These lecture notes by an Ohio State professor note that to sustain a
exactly circular orbit, velocity of the smaller body must be, per
Newtonian gravity:

v_circular = Sqrt( ( G*M ) / r )

where r = radius, G is the gravitational constant, and m is the mass of
the larger first body.

If the initial velocity of the smaller body when captured is slightly
more than v_circular, the orbit will change into an ellipse. The
ellipse will grow larger until escape velocity is reached.


- Canopus56

John Schutkeker writes:

(Paul Schlyter) wrote in :

Another hypothetical case: if gravity would have varied as the inverse
*fifth* power of the distance, all orbits would have been spirals.

Are the orbits stable if gravity varies as the inverse 4th or 6th power of
the distance?

I'm fairly sure there are other powers with "closed" orbits, but I don't
remember if any are stable.

Andrew

John Schutkeker wrote:
1. Newtonian mechanics being exactly valid

2. Only two bodies are present in the universe

3. The bodies are point masses.

Actually, no. The bodies can have positive size if they are radially
symmetric, never touch, and are infinitely rigid. (Sure, that never
happens precisely, but neither are masses ever point masses.)

--
Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

In article 02,
John Schutkeker wrote:

(Paul Schlyter) wrote in :

Another hypothetical case: if gravity would have varied as the inverse
*fifth* power of the distance, all orbits would have been spirals.

Are the orbits stable if gravity varies as the inverse 4th or 6th power of
the distance?

No.

If gravity varies as r^(-n) then circular orbits are stable only if n 3

For other shapes of the orbits the stability criterion get much more complex.
Even under normal r^(-2) gravity a very elongated elliptical orbit with
an eccentricity sufficiently close to one is unstable, since it can easily
be perturbed into a parabolic or hyperbolic orbit.

--
----------------------------------------------------------------
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://stjarnhimlen.se/

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.

Regards,
Martin Brown

John Schutkeker wrote:
"oriel36" wrote in news:1129137707.959738.266710
@g44g2000cwa.googlegroups.com:

Your idol is nothing but a fraud who mangled so many astronomical
principles for his ballistic agenda applied to planetary motion that
the noble discipline can only recover with stern discipline and candor
to face the fact.

Pish, posh. When the underlying physics is completely unknown, you have to
simplify problems to find basic solutions. Once the simple problems are
understood, then you can try to build up more complex situations by
agglommerating known solutions. To expect any more of even such a genius
as Newton would be like expecting the ancient Greeks to fire an Apollo
rocket to the moon. You're both unrealistic and vain.

The criticism is justified based on the damage done to the relationship
between aial and orbital motion in searching for basic solutions that
are not required for planetary motion.

The transfer of Flamsteed's erroneous axial rotational/stellar
circumpolar equivalency to a Newtonian geocentric/heliocentric orbital
equivalency is an incredible feat of intellectual vandalism visited on
the original reasoning that inferred axial and orbital motions as
indepedent motions. For contemporary climatological purposes,it becomes
impossible to study the changing relationship between axial and orbital
motions asthe geometry of an orbit becomes more circular or more
elliptical.

You are simply wasting your time and everyone else's by adhering to the
awful Newtonian maneuvering in attempting to account for retrogrades in
beginning that practice of framehopping to the Sun in accounting for
the apparent backward arcs.

The great heliocentrists such as Copernicus ,Kepler and Galileo refered
the motions of the other planets to the orbital motion of the Earth or
rather dropped the reference where the motion of the planets are
plotted against the background stars.The sort of nonsense that retains
the background stars in a heliocentric framework can only appeal to
mathematical theorists who know no better or cataloguers who imagine
looking through a telescope qualifies one as an astronomer.

The Newtonian geocentric/heliocentric orbital equivalency derived
through Flamsteed's erroneous sidereal justification for axial rotation
completely destroys the relationship between axial and orbital motion
for climatological purposes,geological purposes,astronomical modelling
purposes and goodness knows how many different avenues.The price
humanity pays for designating Isaac and his work in celestial phenomena
as 'genius' means destroying completely the insights of
Copernicus,Kepler and Roemer.

I already give you the reasoning of Copernicus in how they inferred
heliocentricity through retrogrades,perhaps I will add Galileo's
explanation in support -


http://antwrp.gsfc.nasa.gov/apod/ima...2000_tezel.gif

[Here Salviati explains Jupiter's motion, then follows with:]



Now what is said here of Jupiter is to be understood of Saturn and Mars
also. In Saturn these retrogressions are somewhat more frequent than in
Jupiter, because its motion is slower than Jupiter's, so that the Earth
overtakes it in a shorter time. In Mars they are rarer, its motion
being faster than that of Jupiter, so that the Earth spends more time
in catching up with it. Next, as to Venus and Mercury, whose circles
are included within that of the Earth, stoppings and retrograde motions
appear in them also, due not to any motion that really exists in them,
but to the annual motion of the Earth. This is acutely demonstrated by
Copernicus . . .



You see, gentlemen, with what ease and simplicity the annual motion --
if made by the Earth -- lends itself to supplying reasons for the
apparent anomalies which are observed in the movements of the five
planets. . . . It removes them all and reduces these movements to
equable and regular motions; and it was Nicholas Copernicus who first
clarified for us the reasons for this marvelous effect." 1632, Dialogue
Concerning the Two Chief World Systems


Absolutely nothing supports the unethical maneuver of Newton in jumping
to the Sun to account for retrograde -

"For to the earth they appear sometimes direct, sometimes stationary,
nay, and sometimes retrograde. But from the sun they are always seen
direct..."

http://members.tripod.com/~gravitee/phaenomena.htm

BTW,it really is a matter of how many avenues for study wither before
the Newtonian approach but if nobody accepts the original heliocentric
reasoning in contrast to the dire Newtonian one,everyone is wasting
their time.

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'.

To Brian

The geologists are desperate to consider the Earth's Equatorial bulge
as a geological feature insofar as the Earth's crust is comprised of
component plates but they are stuck in a Newtonian world and unabler
to graft in the solution required to explain the Equatorial bulge and
plate motion.

Like Keplerian motion where orbital geometry can vary (in order to
explain ice ages and cyclical climate imbalances),it is not possible to
consider the Equatorial bulge from the point of view of a solid
Earth.If geologists can manage to ignore physicists and infer
differential rotation bands between Equiatorial and polar regions in
the mantle as explaing both the bulge and plate motion,they will do
everyone a favor.

All rotating bodies where a fluid is involved display differential
rotation but phsyicists make the Earth's mantle an exception and come
up with convection cells as explaing plate motion and nothing at all
with the Equatorial bulge.

Here is what differential rotation looks like -

http://www.astronomynotes.com/starsun/sun-rotation.gif