Questions about the potential characteristics of a hypothetical Planet 9
So, I'm writing a story. Most of the main story is set near Planet 9, which has finally been found somewhere far out in the outer solar system.
So first, I’ve been working on determining the probable characteristics of Planet 9.
In line with predictions, it’s an ice giant (a gas-rich sub-Neptune composed of an icy-rocky core with a H-He rich envelope) which is approx 7 earth masses.
The most recent article I can find on the topic from <PERSON> and <PERSON> seems to predict that Planet 9’s perihelion is likely 340(+80/−70) AU, that its aphelion is likely 560(+260/-140) AU, and that the semi-major axis is 460(+160/-100) AU. Unless I am sorely misunderstanding this paper (and I could be), the numbers provided seem to be a range of numbers which they think Planet 9 could fall into.
https://iopscience.iop.org/article/10.3847/1538-3881/ac32dd/pdf
I’ll assume that the perihelion is 340 AU and that the aphelion is a bit further out - 750 AU.
The semi-major axis is half of the major axis, which is the sum of the perihelion and aphelion.
So semi-major axis = (perihelion+aphelion)/2.
The orbital eccentricity is the ratio between the difference and the sum of the perihelion and the aphelion.
So eccentricity = (aphelion - perihelion)/(aphelion + perihelion).
So, after crunching the numbers based on these initial assumptions: Its perihelion is 340 AU, its aphelion is 750 AU, its semi-major axis is 545 AU, and its orbital eccentricity is 0.38.
Now, in order to estimate the orbital period, I’ve applied <PERSON>’s third law of planetary motion for a quick back-of-the-box calculation. If we measure the period (T) in years and the semi-major axis (a) in AU we can use a^3 = T^2.
545 cubed is 161,878,625. 710
The square root of that gives us an orbital period of approximately 12,723 years.
I have a few concerns. I'd like to know if my numbers are solid here, and if they are consistent with Planet 9's hypothesised characteristics given what we know.
Furthermore, I'm planning for it to have two main moons. One is approximately the size and mass of Ganymede, with similar gravity, whereas the other is the size and mass of Charon.
I have no clue if I can give it moons that large and still have it remain consistent with their models for Planet 9, but I’m unfortunately not well-versed enough in this to tell. If someone could help with this, that would be fantastic.
Finally, I have a question regarding how to calculate its diameter. I'm not yet sure how I would yet go about doing that. 710