But why an elliptical orbit

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.

canopus56 wrote:

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.

Note that this is just a solution for v in the eccentricity equation I
posted earlier,

e = (rv^2 / GM) - 1

Set e = 0 (the eccentricity of a circle) and you find

rv^2 = GM

which implies that you can find not only the right v for a given r, but
also an r for a given v.

v = sqrt( GM / r )
r = GM / v^2

I'm not a physicist, so I don't know if that's physically right, but I
don't know why it wouldn't be, either.

The equation for escape velocity is yet another solution of the same
relation, but this time with e = 1 (the eccentricity of a parabola):

rv^2 / GM - 1 = 1
rv^2 = 2GM

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

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

canopus56 wrote:

I always thought it is was because gravitational attraction between
two bodies was the result of two force vectors, not one.

The second smaller body has an orbital speed (angular momentum)
combined with its mass. The causes the second smaller body to pull the
larger body slightly off-center. Conversely, the larger body generates
sufficient gravitational force to still hold the smaller orbiting body
in place. As a consequence, a smaller body and larger body always orbit
a common dynamical center, offset from the true gravitational center of
gravity of the larger body.

It sounds like you're saying that, for example, the sun is pulled to one
focus of an ellipse by the gravity of each planet. That's not right.

Mars's distance from the sun varies by 40 million kilometers, almost 30
solar diameters.

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

Brian Tung wrote:

Ernie, I'm going to try an explanation, and you tell me how far off I
get.

I'm not really smart enough to do that, but it has a very satisfying
geometric, ancient Greek quality. It feels more like an explanation
than the algebra can. On a Web page, you could substitute diagrams for
a lot of the text, which would help a lot.

In order to vary the ratio of the rope lengths AP:BP, you have to rotate
the plank that A and B are fixed to. Does the plank's angle of rotation
have any physical significance?

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

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

Brian Tung wrote:

I (Brian Tung) wrote:

Ernie, I'm going to try an explanation, and you tell me how far off I
get. It's not going to be a rigorous explanation, but I'll try to make
it specific to the ellipse. Warning: This may use no complicated math,
but it is *long*.

OK, it was long, and not very well written, but I think it basically has
a seed of truth to it. At some point, I'm going to try to polish it a
bit and see if it can be made understandable.

The other classical way to draw an ellipse with 2 nails in a board and a
loop of string may be helpful as a concrete demonstration at home.

Drive the two nails into a flat piece of wood, place a closed loop of
string over them both, and keeping the string loop in tension trace with
a pencil around the ellipse. Same construction as your Chinese toy
example, but much easier to do at home.

A circle being the special case where both pins are in the same place
(and usually drawn by using compasses).

Regards,
Martin Brown

Ernie Wright wrote:
I'm not really smart enough to do that, but it has a very satisfying
geometric, ancient Greek quality. It feels more like an explanation
than the algebra can. On a Web page, you could substitute diagrams for
a lot of the text, which would help a lot.

Yes, I plan to put it on the Web.

In order to vary the ratio of the rope lengths AP:BP, you have to rotate
the plank that A and B are fixed to. Does the plank's angle of rotation
have any physical significance?

Hmm, none that I can think of, but that doesn't mean much.

--
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

Martin Brown wrote:
The other classical way to draw an ellipse with 2 nails in a board and a
loop of string may be helpful as a concrete demonstration at home.

Drive the two nails into a flat piece of wood, place a closed loop of
string over them both, and keeping the string loop in tension trace with
a pencil around the ellipse. Same construction as your Chinese toy
example, but much easier to do at home.

The purpose of using the Chinese toy example is to bring forces into
play. The spindle is at rest because of a balance between the forces
exerted by the two sections of rope and gravity. Since gravity pulls
straight down, the vector sum of the two rope tensions must be straight
up.

I assumed anyone caring about the demonstration would know that you can
draw an ellipse with two nails and a length of string.

--
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

I have given you an abundance of material relating to how Kepler
transfered geocentric observations to heliocentric renderings of those
observations.All the contemplative astronomer has to do is apply the
geocentric observations to a heliocentric rendering by considering the
Earth's annual orbital path hence the accuracy of Kepler -

"The proportion existing between the periodic times of any two planets
is exactly the sesquiplicate proportion of the mean distances of the
orbits, or as generally given,the squares of the periodic times are
proportional to the cubes of the mean distances." Kepler


It would be really stupid to retain the background stars however that
is exactly what this Newton guy did -

"PH=C6NOMENON IV.
That the fixed stars being at rest, the periodic times of the five
primary planets, and (whether of the sun about the earth, or) of the
earth about the sun, are in the sesquiplicate proportion of their mean
distances from the sun.


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


Now there is nothing stopping a good mathematical theorist from
recognising just how severe the limitations are with Newton's mangled
version for planetary motion,nay,how utterly ridiculous it becomes in
contrast to the original heliocentric reasoning and contemporary
observations of the Earth from space.

Kepler was right about the 'inferior tribunal of geometers' ,given that
you take great satisfaction from removing geometry entirely from
astronomy,it is far worse now than in Kepler's era.