# Is there a computer simulation that anyone knows of that describes the loss of a moon as it's orbit extends beyond the Hill Sphere of the planet?

Let's imagine a moon orbiting a planet at 75000km distance (assume circular orbit). Now let's say that the Hill Sphere of this planet only extends to 78,000km (small planet in the habitable zone of a small star).

As with the moon/Earth situation, this moon is slowly drifting farther away from the planet. (ie Deimos and Mars).

What factors effect the time frame of this moon being lost so that it would be in orbit of the star and not the planet.

Does anybody know of a computer simulation showing this happen? Wondering what the trajectory and duration of the transition period would look like.

• I wonder if the eccentricity of the orbit of the moon changes as the star has a greater and greater effect. Keep in mind that the Hill Sphere shrinks by a factor of (1 - e) with eccentricty. Conservation laws would have to be maintained at all times. – Jack R. Woods Sep 25 '17 at 21:33
• Not an answer, but a fun, loosely related semi-orbit: jpl.nasa.gov/news/news.php?feature=6537 – userLTK Sep 25 '17 at 22:34
• I'm not sure how up to snuff your programming abilities are, but if you limit yourself to a moon, planet, and star, I can't imagine it would be too terribly difficult to use an RK4 solver to write such a simulation yourself. – zephyr Sep 26 '17 at 12:44
• @JackR.Woods zephyr's comment is of course correct. But what happens depends on the exact conditions. It's a chaotic system which means that two starting points that are extremely similar (even a few kilometers or less) can have very different outcomes. – uhoh Mar 15 '19 at 5:18