Damarian's Parameters: What are they?

Question

For Damarian, I have its system starting to be worked out, and I even have the basics of Checuti and how Damarian orbits around its mother planet. (Link to my first question about this system is included)

Improvements on the System:

• Checuti now orbits around the K-type star (Finally decided, hopefully this doesn't mess it up too much)

• No more G-type stars (Don't last long enough for my taste), but the M and K type stars are still there.

• The K-type star (Think I'll call is Kenser) is 0.65 solar masses, and the M-type (Müla) is 0.3 solar masses, and Müla orbits Kenser about 15 AU from it, which I hope should be fine (Alpha Centauri A & B orbit a central gravity well 11 AU apart, and Alpha A is a G-type, and Alpha B is a K, so it should be fine).

• Damarian will be tidally locked to Checuti, but it orbits pretty frickin' fast, allowing its day to be about 50 Earth hours (2 Earth days, 2 Earth hours) despite how far away it is from Checuti.

• Checuti, at the recommendation of M. A. Golding (Who answered the accepted answer), is now much denser than Jupiter but roughly the same diameter. I'm thinking on about 5-6 times Jupiter's mass, and roughly 1.02 times the diameter. If these dimensions are off, please tell me which should change (Pretty sure the diameter would be roughly the same, but barely bigger?).

• Damarian will most likely have trapped a few of its sister moons into its Lagrangian points, which are these fancy schmancy points in space where, should an astronomical object be big enough, gets permanently trapped by a larger body, as long as it's not smacked hard enough to move it out of its Lagrangian point. For clarification, I'm expecting a moon will get stuck in either the L4 or L5 points (L4 leads the world literally, L5 is behind the planet).

How the system was made:

Roughly 6.5 billion years ago, a supermassive star went supernova about 4 light years away from a nebula. When the blast hit the nebula, the force of it created such high heat and energy that a bubble of hydrogen collapsed on itself and turned into a protostar: This was Kenser and Müla in their earliest years. A couple million years later, the force of the fusion in Kenüla (The Damrian scientist's name for the protostar) was so great that it ripped itself apart, and the smaller piece flew about 15 AU and started orbiting at that spot. This was Müla, and the other was Kenser. Smaller pieces were either sucked in or were destroyed. One, however, survived. This was Checuti, and it was too small to fuse hydrogen, so it cooled down. It immediately collected smaller bits and pieces that eventually became its moons and, later, rings, The largest moon would become Damarian, and it had a denser-than-water, lighter-than-iron magnetic fluid that froze at its surface to become Damarian's surface.

Don't worry if the age is older than our Solar system, K and M type stars live longer than our star, Kenser's still got 11.5-27.5 billion years left, and Müla's got 93.5 billion left.

I'd like it if an answerer gave me roughly how far away from Checuti's star, in AU (Decimals are fine), how far away Damarian should orbit, in kilometers (I'm using metric due to it being the superior measuring system), and whether Damarian's orbit would be able to stay within the habitable zone without being Roche'd into oblivion or being slingshot away from Checuti.

Note: If there's any reason at all why a K-type star wouldn't be able to support Checuti and Damarian, please let me know so that I can revise.

UPDATE: If you are wondering what the normal temperature range of Damarian should be, I'd like it to be from -5 Celsius to 35 Celsius, or a smaller range of Earth's (-25 to 45 in the same unit). I'm positive Damarian wouldn't be capable of more extremes.

Answer 1

The answer by user 177107 to the question:

https://astronomy.stackexchange.com/questions/40746/how-would-the-characteristics-of-a-habitable-planet-change-with-stars-of-differe[1]

has a table with the characteristics of various types of stars, including the distance from a star where a planet would receive exactly as much radiation from that star as the Earth receives from the Sun, and the year of a planet's orbit at that distance.

Your star Mula has 0.3 solar mass, and so would be somewhere between a M5V and a M2V in mass. Since Checuti and Damarian don't orbit around Mula but orbit around the larger star Kenser, the properties of Mula don't matter much.

Your star Kenser has 0.65 of the mass of the Sun. Thus it should be between a K8v and a K5V, and the distance from Kenser where a world would receive exactly as much radiation from Kenser as Earth gets from the Sun would be beween 0.281 AU and 0.406 AU, with an orbital period of about 70.95 to 114.84 Earth days.

An Astronomical Unit or AU is 149,597,870.7 kilometers, so the orbit of Checti and Damarian should be between about 42,037,001.67 and 60,736,735.5 kilometers from Kenser.

If Damarian has an orbital period (and thus a day) of 50 Earth hours or 2.08333 Earth days, The Damarian year will be between 34.056 and 55.1232 Damarian days long, and thus the Damarian calendar will be different than stated in your previous question.

But possibly Checuti and Dmarian obit Kenser at a different distance than the one where they receive exactly as much radiation from Kenser as Earth receives from the Sun.

There have been many different calculations of the inner and outer limits of the Sun's circumstellar habitable zone, and consierable variation in the limits that were calculated.

https://en.wikipedia.org/wiki/Circumstellar_habitable_zone#Solar_System_estimates[2]

However, a giant moon orbiting a giant planet could get signficent heating from light refelcted from the planet and from tidal heating. in somecases a moon could even be overheated and suffer a runawy greenhouse effect. Thus it is possible that Damarian receives a significent proportion of its heat from its relationship with Checkuti and is warmer than it would be at that distanc efrom Kenser if it orbited alone.

Also, your questions do not describe conditions on Damarian in qreat detail so I don't know how warm it is supposed to be.

So perhaps the Damarian year could be about 384.25 Dmaraian days, or about 800.519 Earth days, or about 2.1917 Earth years, long. That would be about 6.97 to 11.2828 times a year 70.95 to 114.84 Earth days days long.

Earth orbits the Sun at a distance of 1 AU and has a year one Earth year long, and asteroid 65 Cybele orbits the Sun at a distance of 3.4283 AU and has a year 6.35 Earth years long. An object at Cybele's distance from the Sun should receive 0.08502 times as much radiation as Earth receives from the Sun.

Earth orbits the Sun at a distance of 1 AU and has a year one Earth year long, and Jupiter orbits the Sun at a distance of 5.2044 AU and has a year 11.862 Earth years long. A world orbiting the Sun at 5 AU would receive 0.04 as much radiation as Earth gets, and would be much colder than Earth.

So if the distance from Kenser where Damarian would receive exactly as much radiation as Earth receives from the Sun is between about 0.281 AU and 0.406 AU, a world orbiting about 3.4 to 5 times as far from Kenser would have a distance of about 0.9554 to 2.03 AU, or about 142,925,805.7 to 303,683,677.5 kilometers

And at that distance Damarian would receive about 0.08502 to 0.04 times as much radation from Kenser as Earth recieves from the Sun, and so would be much colder than Earth, unless it receives many times as much heat from reflected light and tidal heating as it gets from Kenser.

But as I said, I don't know what sort of surface conditions or surface temperature is desired for Damarian.