Joint heat, eh? I hadn't thought about that. I assumed that out by the solar jump limit the heat from the K6 III star would be negligble. This is taking me outside my meager astronomical knowledge. Would it be possible to place Heya outside the tidelock zone of the M8 dwarf? What about visible light? Would the be enough for ordinary human operation in the daytime?
It should. The further from the M8D it is, the less its meager light will help, and the wider the range of effects will be.
K5 III should be 375☉ luminosity, and the DM should be about 0.01☉
375/x²+0.01/y²=(0.8 to 1.2) or so where X and Y are in AU.
orbit 8 is 19.6 AU, orbit 9 is 38.8
Orbit 0 is 0.2 AU, Orbit 1 is 0.4, orbit 2 is 0.7 and 3 is 1.0 AU
A moon will keep an orbit 0 world from tidelocking to the star.
So 375/x²+0.01/y²=1, solving using y=0.4
375/x²+0.01/0.4²=1
375/x²+0.01/0.16=1
375/x²+0.625=1
375/x²=1-0.625
375/x²=0.375
1/x²=0.001
x²=1/0.001
x²=1000
x=31.6 AU
For a cooler world, we need to solve for less; about 0.8Lre
the formula:
a/x² + b/y² = c
given
a in L☉ (Luminosity in Solar luminosities)
b in L☉
c in Lre (Luminosity received in earth units - 1L☉ at 1AU)
x distance from a in AU
y distance from b in AU
Note: luminosities grabbed by looking for stars of that type in the catalogues, not from Traveller sources.