initial SMA: 0.85085 (stable value)

hot->cold: 1570499988.7500882
cold->hot: 1710291616.7414923
hot->cold: 1844299546.5057061

time spent in cold orbit: 139791627.99140406
time spent in hot orbit:  134007929.7642138
length of omicycle:       273799557.75561786

real scale:

time spent in cold orbit: 442059942.27578574 s = 14.0083335 years
time spent in hot orbit:  423770282.57878655 s = 13.4287567 years
length of omicycle:       865830224.8545723  s = 27.4370902 years

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initial SMA: 0.8471375

cold->hot: 77686296.633566573 seconds
hot->cold: 226829361.17928717 seconds
cold->hot: 382573123.37788111 seconds

time spent in hot orbit:  149143064.54572058 s
time spent in cold orbit: 155743762.19859394 s
length of omicycle:       304886826.74431455 s

real scale:

time spent in hot orbit:  471631781.1819829 s  = 14.9454285 years
time spent in cold orbit: 492505019.91119015 s = 15.6068757 years
length of omicycle:       964136801.0931731 s  = 30.5523042 years

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length of originally given omicycle = 29.4081984 years
average of the two omicycles we've simulated = 28.9946972 years
double weighted average = 29.5138995
so try for:
(0.8471375 + 0.8471375 + 0.85085) / 3 = 0.848375 au sma

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initial sma: 0.848375 au