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Returning to the powerful clarkean civilisation in this question What compounds could be used to dye a gas giant the colour of a rainbow?

These same artistically inclined omnipotent beings have created an impossibly perfect binary Star system composed of a red and blue supergiant of exactly the same mass, orbiting at 24 AU, over 240 years, and both rotating every 24 hours. to finish, system’s creator left their signature inscribed on an asteroid positioned in orbit around these two stars.

However, I was considering this “signature asteroid” occupying another position: the Star system’s barycentre, which (since the stars are the same mass) is in the exact centre. Could an object occupy this position, and how?

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    $\begingroup$ It can occupy that position, of course, it is not forbidden. But if won't stay there, because there is no force keeping it there. The tiniest slighest push and it's gone. $\endgroup$
    – AlexP
    Jan 5, 2023 at 15:52
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    $\begingroup$ "orbiting at 24 AU, over 240 years," pretty sure supergiants at that distance will have orbits shorter than 240 years. MUCH shorter, since Pluto-Sol at near 40 AU has about that orbit period but only a tiny fraction of the system mass... $\endgroup$
    – Zeiss Ikon
    Jan 5, 2023 at 19:11
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    $\begingroup$ Also, the stars won't stay same mass for long (red will be pre-supernova and ejecting planetary nebula gas, while the blue will be burning mass far faster to produce energy to radiate -- I can't say which will lose mass faster, but they won't be the same rate). $\endgroup$
    – Zeiss Ikon
    Jan 5, 2023 at 19:26
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    $\begingroup$ You can't get a red supergiant to rotate in 24 hours. The rotational velocity at the equator will be well above the star's escape velocity, and it will come apart. Example: Epsilon Pegasi is about 7.25 solar masses, 211 solar radi. That's 147Mkm radius, 921Mkm circumference, speed at equator is about 10,600km/sec, but its escape velocity is only about 115km/sec. $\endgroup$ Jan 5, 2023 at 19:44
  • $\begingroup$ similar? worldbuilding.stackexchange.com/questions/213485/… $\endgroup$
    – Willk
    Jan 6, 2023 at 0:18

2 Answers 2

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Could an object occupy this position, and how?

Yes, and with difficulty.

Of course an object can occupy that position. The trouble is station keeping. Where it is, the gravitational pull of the two stars exactly balance (the radiation and solar wind pressure do not, but that's secondary).

What if the asteroid is nudged a few centimeters out of position by any one of several phenomena (for one, the Yarkowsky effect)? Consider also that the two stars will have different mass loss ratios, so the barycenter is bound to move - it won't stay in the geometric middle.

When the asteroid is slightly nearer to star A than star B, the pull of A will be felt more strongly, and the asteroid will tend to drift even closer to A. At the same time B's pull, that might avert the fall, will become weaker. So, the asteroid will start falling towards A.

To avoid this, you need some sort of attitude control and station-keeping machinery. The most economic way would be to modulate the asteroid's reflectivity and radiancy, in effect converting it into a sort of statite. The asteroid will reflect the weaker red star's light, and absorb the brighter one's, determining a net thrust towards the brighter star; and this must be enough to balance the brighter star's stronger radiant push. If the asteroid finds itself "falling" towards the blue star, it will start reflecting back its light; if it finds itself falling towards the red star, it will stop reflecting the blue star.

To be able to do this, the surface to mass ratio of the asteroid must be pretty high, which means the asteroid needs to be hollow or made out of some sort of foamy stone, like pumice.

Also, of course, it will require a source of energy, actuators, mechanical and electronic command and control systems. In short, it will need to be more like a space station than a simple asteroid.

On the other hand, the Ancient Race might have done this differently - they might have incorporated a sizeable black hole inside the asteroid, so that the two stars are actually orbiting the black hole. This is also an unstable configuration (the two stars will tend to "fall" on each other, unless the black hole gravitational field is somehow both made asymmetric, and made to rotate at the same rate as the two stars, trapping them inside two gravitational "pits"). It can be partially stabilized... but you need more stars to do that. And it will gall the slimy blue blobs from Mars :-)

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In a (basically) two-body system, the barycenter is also (conveniently) the L1 Lagrangian point. Plenty is known about lagragian points and the stability of things floating around at them.

Here's a diagram of the 5 Lagrange points for the Earth/Sun system, but this can be generalised to any two massive bodies including your stars. The arrows show the direction of gravitational potential, eg. the direction you'll be pulled or pushed if you're even the slighest fraction off the centre of a point.

A diagram of the gravitational potential around the Earth and the Sun, showing the 5 Lagrange points, showing how things can be accelerated towards or away from a point if they're not precisely resting upon it

(image credit: Xander89 via Wikimedia)

The L1 between two bodies isn't a stable position... this is basically because if you happen to float in slightly the wrong direction, gravitational influences will pull you away from the L1 point and into a more conventional orbit That floating-away can be triggered by even a miniscule difference in light pressure or solar wind from the two stars or an errant fleck of space-dust. The L2 and L3 points have the same issue. If the bodies are about the same mass, the L4 or 5 points aren't safe either either (for more complicated reasons that don't need to be detailed here).

However, there are things called halo orbits where an object follows a regular repeating path around a Lagrange point instead of just hoping to float there stationry:

A halo orbit animation. The shape is more of a criss-crossed lissajous rather than the conventional circular or elliptical form

(an animation of the halo orbit about the Sun-Earth L2 point followed by the WMAP satellite. Image credit Phoenix7777 via Wikimedia)

These are also not entirely stable, but in a mere 2-and-a-bit-body system built by godlike superpowers the stability could be handwaved over longer timescales without needing active station keeping of the sort merely human spacecraft use. I wouldn't expect it to stay put for billions of years, but that's OK because supergiant stars have short lifetimes which can be under a million years for the largest examples, so maybe a bit of clever orbit injection will keep your signature asteroid in place for long enough before everything goes foom anyway.

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