Egg

[Capiert]

Please wait! (Under construction)

 

The egg orbit: (assumes)

 

1.

The planets move around the sun in an egg orbit,

not an ellipse.

 

(Implying Kepler's 1st law needs fine tuning,

being unacceptable (without),

but viewing his anti-thesis (as acceptable):

the planets do not move around in perfect circles,

but instead a distortion of that (circle)

we can see (=recognize) what he means

(even though he didn't say it right)

& so (his thesis) needs fine tuning,

to an egg.)

 

Nature is not so simple,

but instead lob_sided.

(Ellipses rarely occur,

but instead water drop(let)s

& egg shapes

are most common.)

 

2.

The period of a circular orbit

is Huygen's pendulum period

T=2*Pi*((R/ac)^0.5)

of radius R,

deriveable from Newton's

centrifugal_acceleration

ac=(vc^2)/r,

where

the (circular) tangential_speed

vc=2*Pi*r/T

is the circumference

cir=2*Pi*r

per period T.

 

An egg has only 1 focus

(near the smaller end);

unlike an ellipse

which has 2 focii).

 

The egg formula is derived from a (slanted) cone cut (intersection);

because an ellipse is drived from a slanted cylindrical cut.

Edited April 16, 2017 by Capiert

[Argent]

How do you account for the fact that planetary orbits are observed to be elliptical? (Bar variations accounted for by gravitational interactions.)

[Capiert]

Kepler's proposal of ellipse

is an approximation

& a suggestion

you've accepted.

If your teams will observe

more closely

you might find egg shapes.

Dealing with the large distances

& small apparent sizes (of planets & stars)

I'm quite sure

there is room for improvement

in the accuracy & tolerances.

 

I must admit

I've seen a few eggs

that were very difficult

to distinguish

between

the narrow

& wide ends,

because

they both (widthes, ends) looked rather similar.

Maximum width

is usually found

at half the length.

Edited April 16, 2017 by Capiert

[Strange]

Kepler's proposal of ellipse

is an approximation

& a suggestion

you've accepted.

If your teams will observe

more closely

you might find egg shapes.

 

 

Can you present the evidence that the orbits are egg-shaped?

 

Also, Can you show the required modifications to Newton's law of gravity?

 

Or is this just some random idea you have made up for no reason?

[swansont]

!

Moderator Note

Many orbits have been observed, so it should be no trouble to back this up with evidence. Do so, or we're done.

[Capiert]

Can you present the evidence that the orbits are egg-shaped?

Hi Strange.

I can present evidence

that the orbits are not symmetric

as stated above.

You've interpretted (modelled)

that to an ellipse;

& I haven't

(giving you that alternative).

 

Also, Can you show the required modifications to Newton's law of gravity?

We know the earth's free_fall acceleration is ge=G*Me/(Re^2)

where Newton's G & the earth's mass Me

are constants

for the radial distance Re

from the earth's center

to the earth's surface.

 

Or is this just some random idea you have made up for no reason?

This is an aside

to Swansont's task

to fit in the pull theme (thread)

that I cannot yet complete in 1 step

so I must attempt the 1st of 2 steps here.

E.g. I have an answer for a LEO

low earth orbit (e.g. skylab)

which makes "some" sense

but I do not have a complete solution

for the 2 body problem, yet.

Swansont placed a very tall order (to the moon).

 

Very ruffly, I get ~16.6 orbits per day for skylab,

considering the earth is also rotating

each day the synchronization means we loose 1

giving 15.6

compared to Wiki's 15.4 orbits per day.

Edited April 16, 2017 by Capiert

[Strange]

Hi Strange.

I can present evidence

that the orbits are not symmetric

as stated above.

 

 

Good. Go on then.

 

 

 

We know the earth's free_fall acceleration is ge=G*Me/(Re^2)

where Newton's G & the earth's mass Me

are constants

for the radial distance Re

from the earth's center

to the earth's surface.

 

Which results in an elliptical orbit.

 

So far: no evidence and contradicted by theory.

 

Fail.

[Capiert]

Good. Go on then (present that orbits are not symmetrical).

I think you might have misunderstood me.

The major point is a single focus (not an ambiguous double focii).

The traditional math does NOT fit either:

how can you derive an ellipse from a cone,

when a cylinder's cut gives the ellipse?

Your professors claim a cone('s cut) will give you that (ellipse)

but I get otherwise.

i.e. an egg shape.

Kepler assumed an ellipse,

& nobody has questioned that

because it's not far from the truth,

but I assumed otherwise

because I wanted a(n exclusive) single focus

(for the modelling).

2 different assumptions,

which is right?

The facts will tell.

 

 

Which results in an elliptical orbit.

I think you're mixing up Newton with Kepler.(?)

Where did Newton's F=G*M*m/(R^2)

state an ellipse, exclusively.

His formula can use either an ellipse or a (perfect) circle.

You seem to be jumping to conclusions.

Are you?

 

So far: no evidence and contradicted by theory.

Seems to pertend to you, sorry.

Which theory do you mean?

(Please be specific.)

 

Fail.

Seems to be (at least partially) on your side.

[Fuzzwood]

Are you confused by a circle vs an oval?

[Capiert]

No Fuzzwood.

 

 

The ellipse_info

can be converted to an egg (shape)

& visa versa.

 

The Egg's_length (Apsis)

l = periside + apside, e.g.

l = perihelion + aphelion

l = c + d

l = closest + distant (distance from the focus).

 

(If we let (the cone's base radius) r=1,

then (the cone's height)

h ~ Epsilon

is the eccentric

(of an ellipse).

But only if.)

 

The "closest" side (Periside, e.g. Perihelion)

c = ((r^2 + h^2)^0.5) * (r-h)/(r+h)

c = ((r^2 + h^2)^0.5) * e

 

Let (the cone's_base_radius) r=1,

& the height h=0..1 defines the (egg_)plane's slope_"height",

wrt the cone's center_axis Y,

h=0 produces a circle (symmetric: half & half, peri & ap);

h=1 produces minimum periside=zero, & maximum apside=all;

then, simplifies to

c = ((1^2 + h^2)^0.5) * (1-h)/(1+h)

c = ((1 + h^2)^0.5) * (1-h)/(1+h)

c = ((1-h)/(1+h)) * root (1 + h^2).

 

The "distant" side (Apside, e.g Aphelion)

d = ((r^2 + h^2)^0.5)

 

Again, let the cone's_base_radius r=1,

simplifies to

d = ((1^2 + h^2)^0.5)

d = ((1 + h^2)^0.5)

d = root (1 + h^2).

 

The closest ©

& distant (d)

distances

wrt the focus

are the apsis.

 

Radius

r = h * (d + c)/(d - c)

 

height (wrt the cone's height)

h = r * (d - c)/(d + c)

 

h = r * e

 

Numeric Eccentric

e = (d - c)/(d + c)

 

r = h / e.

Edited April 16, 2017 by Capiert

[Strange]

I think you might have misunderstood me.

 

 

Apparently.

 

You said you could present evidence but you haven't.

I think you're mixing up Newton with Kepler.(?)

 

 

Nope. I think you are confusing brainfarts with science.

 

 

 

 

Where did Newton's F=G*M*m/(R^2)

state an ellipse, exclusively.

His formula can use either an ellipse or a (perfect) circle.

 

A circle is (a special case of) an ellipse.

http://radio.astro.gla.ac.uk/a1dynamics/ellproof.pdf

 

You cannot derive your egg shape from Newton's laws, can you?

[Capiert]

Apparently.

 

You said you could present evidence but you haven't.

 

Nope. I think you are confusing brainfarts with science.

I think you've missed the math connection

between proclaimed ellipses

from cones.

Did you?

There is none.

 

A circle is (a special case of) an ellipse.

http://radio.astro.gla.ac.uk/a1dynamics/ellproof.pdf

What does not examinable mean? & for curiousity only?

It sounds like a good joke (for proof, a bit weak?).

But "the answer (my friend) is blowing in the wind."

 

You cannot derive your egg shape from Newton's laws, can you?

I didn't derive the egg shape from Newton's laws.

Did anyone say I must?

I derived it (the egg shape) from a cone cut.

I don't think I can (derive the egg shape from Newton's laws), either.

Can you?

Edited April 16, 2017 by Capiert

[Strange]

I don't think I can (derive the egg shape from Newton's laws), either.

 

 

So, no evidence and you agree that it doesn't fit with existing (well-tested) theory.

 

Sounds like it is wrong then.

 

 

 

Can you?

 

No reason why I (or anyone else) should. It is your half-baked idea, it is up to you to support it.

[Capiert]

So, no evidence and you agree that it doesn't fit with existing (well-tested) theory.

 

Sounds like it is wrong then.

 

 

 

No reason why I (or anyone else) should. It is your half-baked idea, it is up to you to support it.

What do you need?

How should it (the evidence) look like?

e.g. a small example.

[swansont]

I derived it (the egg shape) from a cone cut.

!

Moderator Note

Then you did it wrong. A cone is symmetrical, and you are "deriving" an asymmetry that doesn't exist.

 

This might help

http://math2.org/math/algebra/conics.htm

 

No evidence, no thread.

[Klaynos]

For the interested reader, you can derive Kepler's orbits from Newtonian gravity (which is what was requested of op).

 

You can read how to do this here: http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/KeplersLaws.htm