On Thursday, January 4, 2018 at 4:19:46 AM UTC+8, Libor 'Poutnik' StÅ™Ã*ž wrote:
Dne 03/01/2018 v 21:00 Libor 'Poutnik' StÅ™Ã*ž napsal(a):
Dne 03/01/2018 v 16:18 Peter Riedt napsal(a):
On Wednesday, January 3, 2018 at 4:23:40 PM UTC+8, Libor 'Poutnik' StÅ™Ã*ž wrote:
Dne 03/01/2018 v 09:12 Libor 'Poutnik' StÅ™Ã*ž 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:


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.


I have improved the formula to read 1-3(a-b)^2/(a+b)^2). All objects in
closed orbits around the sun have an X constant between .8 and 1. Halley's comet has an X of about .85. A circular orbit has an X constant of 1. Orbits are subject to the Law of X.

Where is the improvement wrt the eccentricity e = sqrt(1-(b/a)^2 ) ?

P.S.: As that has the very particular geometrical meaning
of relative position of an ellipse focus on the major semi-axis.

--
Poutnik ( The Pilgrim, Der Wanderer )

A wise man guards words he says,
as they say about him more,
than he says about the subject.

I have simplified the formula by removing the sqrt part.