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The eccentricity constant of solar objects



 
 
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Old January 12th 18, 11:48 PM posted to sci.astro
Peter Riedt
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Default The eccentricity constant of solar objects

On Friday, January 12, 2018 at 10:52:32 PM UTC+8, Paul B. Andersen wrote:
Den 08.01.2018 01.16, skrev Peter Riedt:
On Monday, January 8, 2018 at 4:44:46 AM UTC+8, Anders Eklöf wrote:
Peter Riedt wrote:

On Sunday, January 7, 2018 at 7:08:23 AM UTC+8, Anders Eklöf wrote:
Peter Riedt wrote:

Your points are valid. However, the formula using .5*sqrt(4)... produces
the same result as using 1-3....

No - they don't, except for a circle.

For Mercury 5*sqrt(4-3(a-b)^2/(a+b)^2) gives 0,999956 and
1-3(a-b)^2/(a+b)^2) gives 0.999650.

The difference doesn't look big, but the devation from 1 differs by an
order of magnitude.

The comet Halley produces .85 for X.

Only with 1-3(a-b)^2/(a+b)^2) as you listed.
Just try using .5*sqrt(4-3(a-b)^2/(a+b)^2) instead.

Since I don't have your values for a and b I can't check.




The values for the semi major axis were obtained from Princeton.edu
and the values for the semi minor axis were calculated by me with
the formula semi minor axis = semi major axis * sqrt(1-e^2):

So, since you use the eccentricity e to calculate the semi major axis,
what is the point of introducing a new "eccentricity constant" X?

1. What is the geometrical mening of X?
2. In what way is it useful?


smajora smina e
MER 57,909,231,029 56,672,064,712 0.2056
VEN 108,209,525,401 108,207,023,568 0.0068
EAR 149,598,319,494 149,577,457,301 0.0167
MAR 227,943,771,564 226,947,353,141 0.0934
JUP 778,342,761,465 777,430,569,626 0.0484
SAT 1,426,714,892,866 1,424,617,764,212 0.0542
URA 2,870,633,540,862 2,867,434,101,795 0.0472
NEP 4,498,393,012,162 4,498,226,658,512 0.0086
PLU 5,906,438,090,764 5,720,709,449,730 0.2488

The two formulas for X differ indeed:

.05*sqrt(4-3(a-b)^2/(a+b)^2) 1-3(a-b)^2/(a+b)^2)
MER 0.999956281 0.999650256
VEN 1.000000000 1.000000000
EAR 0.999999998 0.999999985
MAR 0.999998201 0.999985606
JUP 0.999999871 0.999998969
SAT 0.999999797 0.999998377
URA 0.999999883 0.999999067
NEP 1.000000000 0.999999999
PLU 0.999904311 0.999234522

So much for you simplification of the formula.
Can you still not see where the error is?
You say my points are valid, and choose to ignore them.

--
I recommend Macs to my friends, and Windows machines
to those whom I don't mind billing by the hour


X is more useful than SR and GR which cannot calculate any real elements of solar orbits.


A very strange idea.

X = X(e) = √(4-3⋅(1-√(1-e²))²/(1+√(1-e²))²)/2

e = 0.00 X = 1.0000000000
e = 0.04 X = 0.9999999399
e = 0.08 X = 0.9999990338
e = 0.12 X = 0.9999950691
e = 0.16 X = 0.9999842377
e = 0.20 X = 0.9999609449
e = 0.24 X = 0.9999175202
e = 0.28 X = 0.9998438029
e = 0.32 X = 0.9997265649
e = 0.36 X = 0.9995487110
e = 0.40 X = 0.9992881691
e = 0.44 X = 0.9989163362
e = 0.48 X = 0.9983958716
e = 0.52 X = 0.9976775062
e = 0.56 X = 0.9966953251
e = 0.60 X = 0.9953596037
e = 0.64 X = 0.9935455742
e = 0.68 X = 0.9910751195
e = 0.72 X = 0.9876855065
e = 0.76 X = 0.9829727662
e = 0.80 X = 0.9762812095
e = 0.84 X = 0.9664653233
e = 0.88 X = 0.9512997861
e = 0.92 X = 0.9256679486
e = 0.96 X = 0.8733242883
e = 1.00 X = 0.5000000000

So you have made a function which evaluates to something
very close to 1 for most eccentricities.
What's the point with that?

Wouldn't the function X = 1.0 be equal useful?

What does X tell us about the planetary orbits?

Mercury e = 0.2056 X = 0.9999562811
Venus e = 0.0086 X = 0.9999999999
Earth e = 0.0167 X = 0.9999999982
Mars e = 0.0934 X = 0.9999982007
Jupiter e = 0.0484 X = 0.9999998711
Saturn e = 0.0541 X = 0.9999997986
Uranus e = 0.0472 X = 0.9999998834
Neptun e = 0.0086 X = 0.9999999999
Pluto e = 0.2488 X = 0.9999043107

You said:
"X is more useful than SR and GR which cannot
calculate any real elements of solar orbits."

Can you please explain what elements of solar orbits
you can calculate using X?

--
Paul

https://paulba.no/


A very good analysis by you. X may not be used to calculate solar orbits but it shows the various eccentricities of orbits are close to a constant.
 




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