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Charles Beck edited PH1 stable?.tex
almost 9 years ago
Commit id: 7e938c57bda4b8e0e417447d4827a9dcbcb793df
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diff --git a/PH1 stable?.tex b/PH1 stable?.tex
index a118707..457cb38 100644
--- a/PH1 stable?.tex
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We will define $\mu _1 =0.4366$ as the mass ratio between Binary 1 & Binary 2 and $\mu _2 =0.000262$ as the mass ratio between the Planet and Binary 1.
Using equation $(7)$ again, we get $a_c =[0.464+(-0.380)0.4366 +(-.631)0.539+(.586)0.4366 (0.539) +$
$.15(0.539^2 ) +(-0.198)(0.4366) (0.539^2 ) ]*1000 = 253.192 $
For inner orbits we again assume that semimajor axes smaller than the critical semimajor axis is stable and $.634 \stackrel{\checkmark}{<} 253$ which means the planet is stable!
Next, we will calculate the critical semimajor axis of the outer binary using equation $(8)$ to get: $a_c =1.6+5.10.5+(-2.22)0.5^2 +4.12 (0.000262) +(-4.27)(0.5) (0.000262)+$
$(-5.09)(0.000262^2 ) +4.61(0.5^2 )(0.000262^2 )$