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.


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


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):

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