Perihelion has the SLOWEST orbit_speed, (but fastest angle_speed).(?)

[Capiert]

Perigee (e.g. perihelion, is the nearest distance to the sun, &)
 has the slowest orbit_speed, but fastest angle_speed (angular_velocity);
 &
 Apogee (e.g. Aphelion is the farthest distance (away) from the sun)
 has the fastest orbit_speed, & slowest angle_speed (angular_velocity).

I distinguish
 between orbit_speed (v_c=Cir/T=2*Pi*r/T);
 versus the angular_speed (theta/T);
 (Disclaimer:
 otherwise Kepler's 3rd law
 is NONSENSE
 (for me),
 who(m) I pity).
 

Tycho (Brahe)
 (only) measured
 planets'(_position):
 angles
 & time (dates);
 so we
 can calculate
 the(ir orbits) angular_speeds,
 e.g. how fast arcs (=angles).
 are swept.

To summarize (my interpretation):
1.
Kepler found
 that (planets') obits
 were NOT perfect circles
 (& (he simply) approximated that (orbit)
 to an ellipse (math)).
2.
Instead,
 an egg (shaped orbit)
 has only 1 focus (center),
 found near the smaller end.

(The conic_section
 was done (algebraically)
 from a cone

 (with its circular base sitting
 on the ground (y=0),
 & its apex (x,y=0,H=0,1) up
 at the top)

 having the same radius R=H=1
 equal to its height H
 (which seems to be the key
 to the results);
 & then normalizing
 by dividing
 by the egg's total (diagonal_)length L
 which starts at the cone's base_circumference (left_side, x,y=-1,0)
 going (diagonally up, to the right)
 thru the center axis (focus x,y=0,h)
 where the (partial) height (fraction) h
 is the eccentricity (Epsilon);
 (& continues till it pierces (out, thru) the cone's right side).
Your mathematicians
 should be capable
 of similar results.
If you DON'T believe me
 you can form bread dough
 & cut it, appropriately.)
 
Equal arcs (=angles) are swept [out]
 in equal times.
3.
A circular orbit
 uses (=has)
 the pendulum_period
 T=2*Pi*((r/g)^0.5), g=ac
 which is similar
 to Newton's centifugal_acceleration
 a_c=v_c²/r
 if a_c=g.
Why should an orbit_speed v_c
 increase
 with smaller radius?
E.g. For very small eccentricities?
(It does NOT, because..)
There is NO consistency,
 when extrapolating
 to large(r) eccentricities.
Nature does NOT abruptly change her laws;
 (but) men do.
Especially when they did NOT understand.

Edited January 17, 2023 by Capiert
A few details, update.

[Genady]

3 hours ago, Capiert said:

Perigee (e.g. perihelion, is the nearest distance to the sun, &)
 has the slowest orbit_speed, but fastest angle_speed (angular_velocity);
 &
 Apogee (e.g. Aphelion is the farthest distance (away) from the sun)

Apo(gee] and perigee _refer_

(to an) orbit (=around)

//Earth// (while?)

aphelion (and__)

perihelion ..&refer**.. (to_an!)

orbit around ((Sun---))

[Sensei]

@Capiert

https://www.google.com/search?q=earth+orbital+speed+at+perihelion

https://www.google.com/search?q=earth+orbital+speed+at+aphelion

Have you ever seen a pendulum ? Is its speed highest at the highest point (=far from the center of the Earth) ?

 

5 hours ago, Capiert said:

Nature does NOT abruptly change her laws;
 (but) men do.
Especially when they did NOT understand.

Edited January 17, 2023 by Sensei

[Capiert]

On 1/17/2023 at 1:06 PM, Sensei said:

@Capiert

https://www.google.com/search?q=earth+orbital+speed+at+perihelion

https://www.google.com/search?q=earth+orbital+speed+at+aphelion

Have you ever seen a pendulum ?

Yes.

On 1/17/2023 at 1:06 PM, Sensei said:

Is its speed highest at the highest point (=far from the center of the Earth) ?

No.
Did I say it was?

The (pendulum_)Period formula T
 does NOT mention height;
 & I am NOT discussing Pendulums (anyway);
 but instead Orbits
 which use the same (similar) formula.

I just wanted to point out
 their math similarity
 so you can quickly understand.
(Perhaps I said things wrong, in my haste?)

On 1/17/2023 at 11:28 AM, Genady said:

Apo(gee] and perigee _refer_

(to an) orbit (=around)

//Earth// (while?)

aphelion (and__)

perihelion ..&refer**.. (to_an!)

orbit around ((Sun---))

Thanks for the correction.
I could NOT find the vocabulary quick enough, on the fly.
I wanted to use something like Periside & Apside
 but forgot the (exact) spelling.
(So (unsure) I backed down, & (I) had to rush for something else ((&) that did NOT work).)
 

ERRATA: Typo.

My angle_speed example
 was a ruff quick random (hash) mixture (example);
 NOT a (formal) formula.
Just to give a (vague) ruff idea (comparison).
I had originally intended something like
~theta/t, ~360°/T
 but I found a general formula getting too complicated,
 for the application I wanted.
So I wrongly settled for a condensation
theta[/t, ~360°]/T -> theta/T (when theta=360°),
 where that (particular) T was any kind of time
 NOT intended to be (just only) a period,
 but as a quick comparison
 to what a (real) Period should hint at.
Sorry. (Trying to pack too much info,
 into too little space,
to keep things short.)

My angle_speed (formula, of choice)
 should be called "frequency"
 f=(theta/t)*(1 [cycle]/360°) =1/T
 for the angle theta in (units) [degree(s)]=[°];
 t is an amount of time (duration, e.g. difference in time)
 in (units) [second(s)];
 & period T is the (amount of) time (duration), per cycle.

There are several ways
 to express angle
 & (thus, also) angle_speed.

More info in that thread
 "Angle_speed f(?)"
 if you need it.

Edited January 20, 2023 by Capiert

[Capiert]

On 1/17/2023 at 1:06 PM, Sensei said:

@Capiert

https://www.google.com/search?q=earth+orbital+speed+at+perihelion

https://www.google.com/search?q=earth+orbital+speed+at+aphelion

Sensei
Thanks for the links
 but (I suspect) you missed my point (=speculation).

I'm saying Kepler's 3rd law is wrong for an Orbit_speed;
 & (=but instead) it should (=might) apply to an angular_speed.

Btw.
Is there any (Foto) evidence that orbits
 are (suppose to be) elliptical?
I know he empirically determined T~Ra^1.5.

On 1/17/2023 at 1:06 PM, Sensei said:

Have you ever seen a pendulum ?

Yes.

On 1/17/2023 at 1:06 PM, Sensei said:

Is its speed highest at the highest point (=far from the center of the Earth) ?

No.
Did I say it was?

(The pendulum(s) I saw
 was NOT orbiting
 around the Earth.)

The (pendulum_)Period formula T
 does NOT mention height;
 & I am NOT discussing Pendulums (anyway);
 but instead Orbits
 which use the same (similar) formula.

I just wanted to point out
 their math similarity
 so you can quickly understand.
(Perhaps I said things wrong, in my haste?)

On 1/17/2023 at 11:28 AM, Genady said:

Apo(gee] and perigee _refer_

(to an) orbit (=around)

//Earth// (while?)

aphelion (and__)

perihelion ..&refer**.. (to_an!)

orbit around ((Sun---))

Thanks for the correction.
I could NOT find the vocabulary quick enough, on the fly.
I wanted to use something like Periside & Apside
 but forgot the (exact) spelling.
(So (unsure) I backed down, & (I) had to rush for something else ((&) that did NOT work).)
 

ERRATA: Typo.

My angle_speed example
 was a ruff quick random (hash) mixture (example);
 NOT a (formal) formula.
Just to give a (vague) ruff idea (comparison).
I had originally intended something like
~theta/t, ~360°/T
 but I found a general formula getting too complicated,
 for the application I wanted.
So I wrongly settled for a condensation
 theta[/t, ~360°]/T -> theta/T (when theta=360°),
 where that (particular) T was any kind of time
 NOT intended to be (just only) a period,
 but as a quick comparison
 to what a (real) Period should hint at.
Sorry. (Trying to pack too much info,
 into too little space,
to keep things short.)

My angle_speed (formula, of choice)
 should be called "frequency"
 f=(theta/t)*(1 [cycle]/360°) =1/T
 for the angle theta in (units) [degree(s)]=[°];
 t is an amount of time (duration, e.g. difference in time)
 in (units) [second(s)];
 & period T is the (amount of) time (duration), per cycle.

There are several ways
 to express angle
 & (thus, also) angle_speed.

More info in that thread
 "Angle_speed f(?)"
 if you need it.

Edited January 20, 2023 by Capiert

[Sensei]

4 hours ago, Capiert said:

Did I say it was?

Don't you see your error?

Did you see and read articles from my links? (below attached 2nd time)

On 1/17/2023 at 1:06 PM, Sensei said:

https://www.google.com/search?q=earth+orbital+speed+at+perihelion

https://www.google.com/search?q=earth+orbital+speed+at+aphelion

 

[swansont]

For a circle, v=wr (w is angular speed), and this will be a good approximation for a low-eccentricity ellipse.

There is no way to have v be a minimum but w be a maximum for an orbit.

If you think Kepler’s laws are wrong, you must provide the evidence. Nobody has to justify it. 

Quote

Why should an orbit_speed v_c
 increase
 with smaller radius?

Conservation of energy tells you it must be so. As r decreases, the PE becomes more negative. KE must increase. The sum must remain constant, since no work is being done on the system.