I'm trying to work out what the sky looks like on an Earth-like moon, in particular the length of day and apparent size of the other celestial bodies: the gas giant's size, the gas giant's other moon's size, and the relative size of the star). I'm kind of stuck on the numbers here. Maths is my weak point, so I stole Artifexian's formulas and tried a simulation on Universe Sandbox a little while ago, but it wouldn't tell me the length of day on the moons. I was left having to use my brain, but all I got was an internal blue screen. Can anyone help me?
I'm gonna give all my numbers down below, but here's the setting and the result I want: it's a system with two tidally-locked Earth-like moons orbiting a massive Gas Giant.
- How short can Moon A's orbit around its Gas Giant be? I.e., how short can its days be? I'm ideally aiming for 28 hours, but up to a week would be okay-ish (both sound extremely fast to me though. Jupiter's moons can go that fast, but they don't look very hospitable to me).
- How can I have people from Moon A sometimes see Moon B from close enough that you can see its cities lit at night? Is it even possible?
- How big do the gas giant and the star it orbits around look?
So this gas giant (8.3 Jovian masses) orbits a K-type star of 0.8 solar masses. (Though a friend told me that it'd be easier if the gas giant orbited a star hotter than the Sun, maybe a class F of 1.4 solar masses I don't really care either way. I've put in the numbers for both).
At least two of these moons are habitable.
Moon A is tidally locked and fairly close to 1 Earth mass. I don't really care for the mass or situation of Moon B as long as it's habitable. Both are on inclined planes, just because it's more believable. Now, I'd also like our gas giant AND Moon B to be visible to the naked eye from Moon A's sky. The gas giant should appear to be at least the size of Earth's moon, and Moon B's surface should be visible too, because I'd like for people on Moon A to see the cities lit at night on Moon B. Due to the tidal locking, the gas giant would have its different phases during the day and appear full during the night.
(Maybe relevant?) Both moons would have been terraformed to be habitable for humans, though Moon A already had somewhat primitive but intelligent forms of life (most of which were killed during the terraformation process).
If K-type Star (all numbers are relative to our Sun unless indicated otherwise)
- Star mass = 0.8 Sun masses
- Diameter = 0.8477
- Temperature = 0.8934 = 5156.7 Kelvin
- Lifetime = 1.75
- Habitability = 1.7155 AU
- Goldilock zone = between 95% and 137% of 1.7155, so between 0.68 and 0.7 AU = between 10 474 and 541 429 km
If F-type Star
Star mass = 1.4 Sun masses
Star luminosity = 3.8416
Diameter = 1.28
Temperature = 1.185
Lifetime = 0.43
Habitability = 1.96
Goldilock zone = between 95% and 137% of 1.96, so between 1.862 and 2.6852 AU
- Gas Giant mass: 8.3 Jovian masses
- Orbit: 0.68 AU from K-type star or 2.1 AU from F-type star? (I just went through the forum and learnt that tidal locking helps heat a moon, but I don't know how to account for that in the numbers)
- Length of orbit: No idea. Sandbox Sim won't tell me, and whenever I accelerate time in the simulation it sends my planets flying off into deep space...
- Velocity: 48.4 km/s (according to my simulation)
- Mass: 0.8 Earth mass
- Orbit around Gas Giant: 23.8 hours in my simulation (which sounds AWEFULLY fast! Is that even possible?)
- Velocity: 45.1 km/s
- Semimajor axis: 58 007 km (periapsis 24000; apoapsis 92000)
- Eccentricity: 0.59 (Inclination 77.44°; perihelion 178°; node 156°; mean 138°)
- Moon B mass: 1.4 Earth mass
- Orbit around Gas Giant: 2.40 days in my simulation.
- Velocity: 60.5 km/s
- Semimajor axis: 1.05M km
- Eccentricity: 0.061 (Inclination 0.40°; perihelion 305°; node 174°; mean 177°)
How many of these numbers seem off? I could send the Sandbox file if it helps, though I woudn't be surprised if the sim's rubbish too.
Many, many thanks! And sorry for the terribly messy post. (No wonder I kept sending my moons flying in Sandbox Simulator: I can't even keep my sentences in orbit.)