Peter Riedt wrote:

On Wednesday, January 3, 2018 at 4:23:40 PM UTC+8, Libor 'Poutnik' St?í?
wrote:
Dne 03/01/2018 v 09:12 Libor 'Poutnik' St?í? napsal(a):
Dne 03/01/2018 v 04:21 Peter Riedt napsal(a):
The eccentricity constant of solar objects

The eccentricity constant X of solar objects can be calculated by the
formula .5*sqrt(4-3(a-b)^2/(a+b)^2) where a = the semi major axis and
b = the semi minor axis. The eccentricity constant X of nine planets
is equal to 1.0 as follows:

I'm curious:

Where does that formula come from?
What *is* the eccentricity constant in the first place)
How does it relate to e = sqrt(1-(b/a)^2) ?

You listed the semi minor axes (b) of the planets with 11 to 13
significant digits. Impressive!. Where did you get those numbers?
(I have a hunch...)

Even 8 digits for the semi major axes is quite a feat.

Why do you round off to one decimal? Just to prove a point?
Isn't it more interesting to explore the differences? 3 decimals?


So you say a circle has the eccentricity constant 1.0.
Interesting.

.5*sqrt(4-3(r-r)^2/(r+r)^2) = .5*sqrt(4) = 1

Similarly, any ellipse similar enough to a circle
like those of planets has this constant 1.0,
if rounded to 1 decimal place.

Actually, the eccentricity of a circle is 0 (zero).
Poutnik should maybe have pointed that out to you...


I have improved the formula to read 1-3(a-b)^2/(a+b)^2).

How does .5*sqrt(4-3(a-b)^2/(a+b)^2) simplfy to 1-3(a-b)^2/(a+b)^2) ?

Let's do the algebra. Oh bummer!

..5*sqrt(4) = 1 !!! Trust me, you'd fail any high school math test with
that one (pun not intended).

Orbits are subject to the Law of X.

What's the Law of X.?

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