But why an elliptical orbit

(Paul Schlyter) wrote in
:

True of course, but to a good first approximation the orbits are
ellipses (or some other kind of conic section: circle, parabola,
hyperbola).

And in the hypothetical case of

1. Newtonian mechanics being exactly valid

2. Only two bodies are present in the universe

3. The bodies are point masses.

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

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

Brian

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 explaining 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

You are all too impressed with yourselves and the sound of your own
voices to ever experience the excitement of a new avenue,plenty of
volume with no substance.I enjoy going through Newton for his
maneuvering is difficult to spot but eventually it is easy to deal with
him.People who are imposters to 'genius' are often like that and the
fact that Newton tried to imitate Kepler,Galileo,Roemer and Copernicus
and failed is no big deal as terrestial ballistics looks a good shot at
explaining planetary motion.

Brian Tung wrote:
(Sure, that never
happens precisely, but neither are masses ever point masses.)


Ahhh but you've never met my ex-wife now have you :^)


Bill

--

William R. Mattil : http://www.celestial-images.com

John Schutkeker wrote:

3. The bodies are point masses.

Like Brian said, this isn't necessary. In fact, that's one of the
things Newton had to invent calculus to prove.

Parts of the Earth closer to you pull on you more strongly, and parts
farther away pull more weakly. But when you add it all up, it's the
same as if all of the Earth's mass were concentrated at a point in its
center.

- Ernie http://home.comcast.net/~erniew

In article ,
Ernie Wright wrote:

John Schutkeker wrote:

3. The bodies are point masses.

Like Brian said, this isn't necessary. In fact, that's one of the
things Newton had to invent calculus to prove.

Parts of the Earth closer to you pull on you more strongly, and parts
farther away pull more weakly. But when you add it all up, it's the
same as if all of the Earth's mass were concentrated at a point in its
center.

- Ernie http://home.comcast.net/~erniew

Not quite! The Earth isn't a perfect sphere but is somewhat
ellipsoidal in its shape - that's why the equatorial radius is some
0.3% larger than the polar radius of the Earth. And that means
that the gravitational pull by the Earth isn't precisely equivalent
to the gravitational pull of a point mass at the Earth's center
having one Earth mass.

The Earth's non-spherical shape will cause perturbations in any
satellite orbiting the Earth. For the Moon (the Earth's natural
satellite) these perturbations are very small although noticeable
when high accuracy is needed. But for an artificial satellite in LEO
(Low Earth Orbit, a few hundred km above the Earth's surface) the
flattening of the Earth is the most important source of perturbations:
it causes larger perturbations on the satellite orbit than the Sun
or the Moon do.

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

On 2005-10-12, tt40 wrote:
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.

Orbits are elliptical because of the inverse square law of gravity and
Newton's three laws of motion. Isaac Newton worked it out in Principia
back in the 17th century.

--
The night is just the shadow of the Earth.

In article .com,
tt40 wrote:

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.

We could expand your question a bit and ask: why is the orbit always
a conic section? I.e. a circle, an ellipse, a parabola, or a hyperbola?
(in the absence of other distrubing gravitational forces that is - if
such forces are present, the orbit can get extremely complex. But let's
disregard that case for the moment).

OK, time to answer your question: the orbit is a conic section (the
ellipse being the most common case) because gravity is inversely
proportional to the square of the distance to the gravitating body.

If gravity had changed with distance in some other way, the orbits
would get different shapes. One hypothetical case often brought up
in basic courses in celestial mechanics is this: if gravity had been
inversely proportional to the fifth power of the distance, the
"orbits" would become spirals, i.e. all planets would then either
spiral into the Sun or spiral out into space. Needless to say, any
solar system would under such circumstances become very short-lived.


If you want to know why the inverse square law of gravity imposes
orbital shapes being conic secsions (ellipses, etc), you'll find
the answer to that in any good fundamental textbook abut celestial
mechanics, for instance this one: http://www.willbell.com/math/mc7.htm
Yes it requires some math to understand it. But if you don't want
to learn the needed math and read this (or some other, similar) book,
then you've denied yourself an explanation for this.


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

On Wed, 12 Oct 2005 12:13:25 GMT, (Paul Schlyter) wrote:

OK, time to answer your question: the orbit is a conic section (the
ellipse being the most common case) because gravity is inversely
proportional to the square of the distance to the gravitating body...

Perhaps that is a satisfying answer to somebody already familiar with
the mathematics behind orbital dynamics, but I suspect it doesn't help
the OP at all in his quest for a simple explanation of the shape of
orbits. I doubt most people find it intuitive that an inverse square
gravity law naturally leads to elliptical orbits. I'm afraid this is
just a case where most people need to trust the math (or the
mathematicians).

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com