# A Stable Red Giant Trinary System

In an alternate universe, we have a spot in the Orion Arm where we have nine Earth-like planets orbiting three red giants. Judging from the size and luminosity of each star, it's been conferred that each of the stars has been a red giant for 542 million years, which means it doesn't have as much time left (although, as this article suggests, depending on the original solar mass, some red giants can live to twice as long as Earth's current age!)

This map is a basic simplification more on the structure than the distance. Essentially, the center of the system is a binary of red giants orbited by a third, solitary red giant.

I imagine that the binary orbits each other from a distance of four AUs, but is that far enough for the stars to orbit each other without crushing under their own gravitational weight? And how far would the third star have to orbit the binary to ensure both gravitational stability and a wide enough habitable zone for nine Earth-like planets?

• What are the masses of each star?
– L.Dutch
Aug 31, 2019 at 13:35
• @L.Dutch - that's the trick here. Red giants fall within a given mass range. The inner 2 are so close that perturbation from the outer one will probably pull them into each other. Aug 31, 2019 at 15:22

Quoting from this answer on a very similar question:

First order approximation:

Distances and mass ratios have to be large.

I am afraid this is not the case for your system of red giants:

A red giant is a luminous giant star of low or intermediate mass (roughly 0.3–8 solar masses (M☉)) in a late phase of stellar evolution.

If the masses of the 3 stars were perfectly identical, the center of mass would be at about 1/3 of the distance between the couple and the lone star. Changing the masses won't change that figure too much: in the extreme case, given by the inner couple having both stars at 8 solar masses and the lone one being at 0.3 solar masses, the center of mass would be at 0.018 times the distance of the lone star from the center of the couple.

I suspect that it is enough to destabilize the system. Especially when you throw in the 9 planets.