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uhoh
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If the orbiting body's mass is a significant fraction of the central body's mass, the weak stability boundaries can be more dramatic.

Call the mass of the central body + orbiting body 1. Call the orbiting body's mass µ. Then the central body would have mass 1-µ.

Here are pairs arranged in order of µ

Pluto/Charon 1.043E-01
Earth/Moon 1.216E-02
Sun/Jupiter 9.545E-04
Sun/Saturn 2.856E-04
Saturn/Titan 2.374E-04
Jupiter/Ganymede 7.789E-05
Jupiter/Callisto 5.684E-05
Sun/Neptune 5.153E-05
Jupiter/Io 4.700E-05
Sun/Uranus 4.366E-05
Jupiter/Europa 2.526E-05
Saturn/Rhea 4.046E-06
Sun/Earth 3.039E-06
Sun/Venus 2.448E-06
Saturn/Dione 1.935E-06
Saturn/Tethys 1.091E-06
Sun/Mars 3.229E-07
Saturn/Enceladus 1.935E-07
Sun/Mercury 1.659E-07
Saturn/Mimas 7.037E-08
Mars/Phobos 1.682E-08
Sun/Pluto& Charon 7.149E-09
Mars/Deimos 2.803E-09
Sun/Ceres 4.741E-10

Pluto/Charon      1.043E-01  
Earth/Moon        1.216E-02  
Sun/Jupiter       9.545E-04  
Sun/Saturn        2.856E-04  
Saturn/Titan      2.374E-04  
Jupiter/Ganymede  7.789E-05  
Jupiter/Callisto  5.684E-05  
Sun/Neptune       5.153E-05  
Jupiter/Io        4.700E-05  
Sun/Uranus        4.366E-05  
Jupiter/Europa    2.526E-05  
Saturn/Rhea       4.046E-06  
Sun/Earth         3.039E-06  
Sun/Venus         2.448E-06  
Saturn/Dione      1.935E-06  
Saturn/Tethys     1.091E-06  
Sun/Mars          3.229E-07  
Saturn/Enceladus  1.935E-07  
Sun/Mercury       1.659E-07  
Saturn/Mimas      7.037E-08  
Mars/Phobos       1.682E-08  
Sun/Pluto&Charon  7.149E-09  
Mars/Deimos       2.803E-09  
Sun/Ceres         4.741E-10

Jupiter and Saturn have some big moons. You'll find a lot of the gas giant moons near the top of the list when arranged by µ.

For more on this see my mass parameter and ITN

If the orbiting body's mass is a significant fraction of the central body's mass, the weak stability boundaries can be more dramatic.

Call the mass of the central body + orbiting body 1. Call the orbiting body's mass µ. Then the central body would have mass 1-µ.

Here are pairs arranged in order of µ

Pluto/Charon 1.043E-01
Earth/Moon 1.216E-02
Sun/Jupiter 9.545E-04
Sun/Saturn 2.856E-04
Saturn/Titan 2.374E-04
Jupiter/Ganymede 7.789E-05
Jupiter/Callisto 5.684E-05
Sun/Neptune 5.153E-05
Jupiter/Io 4.700E-05
Sun/Uranus 4.366E-05
Jupiter/Europa 2.526E-05
Saturn/Rhea 4.046E-06
Sun/Earth 3.039E-06
Sun/Venus 2.448E-06
Saturn/Dione 1.935E-06
Saturn/Tethys 1.091E-06
Sun/Mars 3.229E-07
Saturn/Enceladus 1.935E-07
Sun/Mercury 1.659E-07
Saturn/Mimas 7.037E-08
Mars/Phobos 1.682E-08
Sun/Pluto& Charon 7.149E-09
Mars/Deimos 2.803E-09
Sun/Ceres 4.741E-10

Jupiter and Saturn have some big moons. You'll find a lot of the gas giant moons near the top of the list when arranged by µ.

For more on this see my mass parameter and ITN

If the orbiting body's mass is a significant fraction of the central body's mass, the weak stability boundaries can be more dramatic.

Call the mass of the central body + orbiting body 1. Call the orbiting body's mass µ. Then the central body would have mass 1-µ.

Here are pairs arranged in order of µ

Pluto/Charon      1.043E-01  
Earth/Moon        1.216E-02  
Sun/Jupiter       9.545E-04  
Sun/Saturn        2.856E-04  
Saturn/Titan      2.374E-04  
Jupiter/Ganymede  7.789E-05  
Jupiter/Callisto  5.684E-05  
Sun/Neptune       5.153E-05  
Jupiter/Io        4.700E-05  
Sun/Uranus        4.366E-05  
Jupiter/Europa    2.526E-05  
Saturn/Rhea       4.046E-06  
Sun/Earth         3.039E-06  
Sun/Venus         2.448E-06  
Saturn/Dione      1.935E-06  
Saturn/Tethys     1.091E-06  
Sun/Mars          3.229E-07  
Saturn/Enceladus  1.935E-07  
Sun/Mercury       1.659E-07  
Saturn/Mimas      7.037E-08  
Mars/Phobos       1.682E-08  
Sun/Pluto&Charon  7.149E-09  
Mars/Deimos       2.803E-09  
Sun/Ceres         4.741E-10

Jupiter and Saturn have some big moons. You'll find a lot of the gas giant moons near the top of the list when arranged by µ.

For more on this see my mass parameter and ITN

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HopDavid
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If the orbiting body's mass is a significant fraction of the central body's mass, the weak stability boundaries can be more dramatic.

Call the mass of the central body + orbiting body 1. Call the orbiting body's mass µ. Then the central body would have mass 1-µ.

Here are pairs arranged in order of µ

Pluto/Charon 1.043E-01
Earth/Moon 1.216E-02
Sun/Jupiter 9.545E-04
Sun/Saturn 2.856E-04
Saturn/Titan 2.374E-04
Jupiter/Ganymede 7.789E-05
Jupiter/Callisto 5.684E-05
Sun/Neptune 5.153E-05
Jupiter/Io 4.700E-05
Sun/Uranus 4.366E-05
Jupiter/Europa 2.526E-05
Saturn/Rhea 4.046E-06
Sun/Earth 3.039E-06
Sun/Venus 2.448E-06
Saturn/Dione 1.935E-06
Saturn/Tethys 1.091E-06
Sun/Mars 3.229E-07
Saturn/Enceladus 1.935E-07
Sun/Mercury 1.659E-07
Saturn/Mimas 7.037E-08
Mars/Phobos 1.682E-08
Sun/Pluto& Charon 7.149E-09
Mars/Deimos 2.803E-09
Sun/Ceres 4.741E-10

Jupiter and Saturn have some big moons. You'll find a lot of the gas giant moons near the top of the list when arranged by µ.

For more on this see my mass parameter and ITN