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Geoffrey Irving
Geoffrey Irving
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Update: There's nothing obviously preventing (negative) energy from bleeding from a pair of close bodies to others, so this answer is wrong as stated.

At least for sufficiently large $N$, the case of equal masses reduces to the case of unequal masses to give a positive probability of bounded motion. This is because two bodies that are sufficiently close together relative to other masses can act as a body of twice the mass, since they will be energetically bound. Thus if one can build a solar system out of unequal masses, one can build a stable solar system out of equal masses.

Edit: Since two masses are stable, there is a positive probability of stability for any $N$ by iteratively replacing one mass by two.

At least for sufficiently large $N$, the case of equal masses reduces to the case of unequal masses to give a positive probability of bounded motion. This is because two bodies that are sufficiently close together relative to other masses can act as a body of twice the mass, since they will be energetically bound. Thus if one can build a solar system out of unequal masses, one can build a stable solar system out of equal masses.

Edit: Since two masses are stable, there is a positive probability of stability for any $N$ by iteratively replacing one mass by two.

Update: There's nothing obviously preventing (negative) energy from bleeding from a pair of close bodies to others, so this answer is wrong as stated.

At least for sufficiently large $N$, the case of equal masses reduces to the case of unequal masses to give a positive probability of bounded motion. This is because two bodies that are sufficiently close together relative to other masses can act as a body of twice the mass, since they will be energetically bound. Thus if one can build a solar system out of unequal masses, one can build a stable solar system out of equal masses.

Edit: Since two masses are stable, there is a positive probability of stability for any $N$ by iteratively replacing one mass by two.

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Geoffrey Irving
Geoffrey Irving
  • 1.8k
  • 11
  • 21

At least for sufficiently large $N$, the case of equal masses reduces to the case of unequal masses to give a positive probability of bounded motion. This is because two bodies that are sufficiently close together relative to other masses can act as a body of twice the mass, since they will be energetically bound. Thus if one can build a solar system out of unequal masses, one can build a stable solar system out of equal masses.

Edit: Since two masses are stable, there is a positive probability of stability for any $N$ by iteratively replacing one mass by two.

At least for sufficiently large $N$, the case of equal masses reduces to the case of unequal masses to give a positive probability of bounded motion. This is because two bodies that are sufficiently close together relative to other masses can act as a body of twice the mass, since they will be energetically bound. Thus if one can build a solar system out of unequal masses, one can build a stable solar system out of equal masses.

At least for sufficiently large $N$, the case of equal masses reduces to the case of unequal masses to give a positive probability of bounded motion. This is because two bodies that are sufficiently close together relative to other masses can act as a body of twice the mass, since they will be energetically bound. Thus if one can build a solar system out of unequal masses, one can build a stable solar system out of equal masses.

Edit: Since two masses are stable, there is a positive probability of stability for any $N$ by iteratively replacing one mass by two.

Source Link
Geoffrey Irving
Geoffrey Irving
  • 1.8k
  • 11
  • 21

At least for sufficiently large $N$, the case of equal masses reduces to the case of unequal masses to give a positive probability of bounded motion. This is because two bodies that are sufficiently close together relative to other masses can act as a body of twice the mass, since they will be energetically bound. Thus if one can build a solar system out of unequal masses, one can build a stable solar system out of equal masses.