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As a follow up of the comments here: Why was the Rosetta probe programmed to "auto shutoff" at the moment of hitting the surface?

I'm fairly convince that a satellite cannot maintain an orbit above a comet, being quickly ousted or crashing by

  1. The comet pressure
  2. The effect of other bodies perturbing the orbit

Not helping is the very irregular gravity field of the comet.

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Comet 67P/Churyumov–Gerasimenko has a mass of about 9.982 gigatonnes, a semimajor axis of 3.4630 AU, and an eccentricity of 0.64102. If it was a point mass, it's Hill sphere would be about 221 km. The Hill sphere is an approximation regarding the volume within which orbits are stable. A more reasonable limit is 1/3 to 1/2 the Hill sphere radius, or 74 to 110 km. I'll use 100 km as a nice round number.

67P is anything but a point mass. The highly non-spherical nature of its gravitational field will definitely be felt at ~100 km from the center of mass. This would make the issues with lunar mascons tiny in comparison.

Plus it's a comet. It emits gases and sometimes boulders when it is close to perihelion. The odds of not being plumed or hit while the comet is near perihelion are astronomically low. Even if a body orbiting the comet isn't plumed or hit by a boulder, the non-gravitational forces on the comet itself will almost certainly be enough to make any orbit about the comet unstable.

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