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  "events": [ {
    "tStartMs": 7745,
    "dDurationMs": 4135,
    "segs": [ {
      "utf8": "In 2009, two researchers ran \na simple experiment."
    } ]
  }, {
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    "dDurationMs": 3175,
    "segs": [ {
      "utf8": "They took everything we know \nabout our solar system"
    } ]
  }, {
    "tStartMs": 15055,
    "dDurationMs": 6052,
    "segs": [ {
      "utf8": "and calculated where every planet would be\nup to 5 billion years in the future."
    } ]
  }, {
    "tStartMs": 21107,
    "dDurationMs": 4000,
    "segs": [ {
      "utf8": "To do so they ran over 2,000 \nnumerical simulations"
    } ]
  }, {
    "tStartMs": 25107,
    "dDurationMs": 4722,
    "segs": [ {
      "utf8": "with the same exact initial conditions\nexcept for one difference:"
    } ]
  }, {
    "tStartMs": 29829,
    "dDurationMs": 5307,
    "segs": [ {
      "utf8": "the distance between Mercury and the Sun,\nmodified by less than a millimeter"
    } ]
  }, {
    "tStartMs": 35136,
    "dDurationMs": 2660,
    "segs": [ {
      "utf8": "from one simulation to the next."
    } ]
  }, {
    "tStartMs": 37796,
    "dDurationMs": 3278,
    "segs": [ {
      "utf8": "Shockingly, in about 1 percent \nof their simulations,"
    } ]
  }, {
    "tStartMs": 41074,
    "dDurationMs": 5346,
    "segs": [ {
      "utf8": "Mercury’s orbit changed so drastically \nthat it could plunge into the Sun"
    } ]
  }, {
    "tStartMs": 46420,
    "dDurationMs": 2360,
    "segs": [ {
      "utf8": "or collide with Venus."
    } ]
  }, {
    "tStartMs": 48780,
    "dDurationMs": 720,
    "segs": [ {
      "utf8": "Worse yet,"
    } ]
  }, {
    "tStartMs": 49500,
    "dDurationMs": 5483,
    "segs": [ {
      "utf8": "in one simulation it destabilized\nthe entire inner solar system."
    } ]
  }, {
    "tStartMs": 54983,
    "dDurationMs": 4000,
    "segs": [ {
      "utf8": "This was no error; \nthe astonishing variety in results"
    } ]
  }, {
    "tStartMs": 58983,
    "dDurationMs": 6075,
    "segs": [ {
      "utf8": "reveals the truth that our solar system \nmay be much less stable than it seems."
    } ]
  }, {
    "tStartMs": 65058,
    "dDurationMs": 5181,
    "segs": [ {
      "utf8": "Astrophysicists refer to this astonishing\nproperty of gravitational systems"
    } ]
  }, {
    "tStartMs": 70239,
    "dDurationMs": 2180,
    "segs": [ {
      "utf8": "as the n-body problem."
    } ]
  }, {
    "tStartMs": 72419,
    "dDurationMs": 2820,
    "segs": [ {
      "utf8": "While we have equations \nthat can completely predict"
    } ]
  }, {
    "tStartMs": 75239,
    "dDurationMs": 2710,
    "segs": [ {
      "utf8": "the motions of two gravitating masses,"
    } ]
  }, {
    "tStartMs": 77949,
    "dDurationMs": 5651,
    "segs": [ {
      "utf8": "our analytical tools fall short \nwhen faced with more populated systems."
    } ]
  }, {
    "tStartMs": 83600,
    "dDurationMs": 5261,
    "segs": [ {
      "utf8": "It’s actually impossible to write down\nall the terms of a general formula"
    } ]
  }, {
    "tStartMs": 88861,
    "dDurationMs": 5910,
    "segs": [ {
      "utf8": "that can exactly describe the motion\nof three or more gravitating objects."
    } ]
  }, {
    "tStartMs": 94771,
    "dDurationMs": 7105,
    "segs": [ {
      "utf8": "Why? The issue lies in how many unknown\nvariables an n-body system contains."
    } ]
  }, {
    "tStartMs": 101876,
    "dDurationMs": 3310,
    "segs": [ {
      "utf8": "Thanks to Isaac Newton, \nwe can write a set of equations"
    } ]
  }, {
    "tStartMs": 105186,
    "dDurationMs": 4000,
    "segs": [ {
      "utf8": "to describe the gravitational force \nacting between bodies."
    } ]
  }, {
    "tStartMs": 109186,
    "dDurationMs": 4677,
    "segs": [ {
      "utf8": "However, when trying to find a general \nsolution for the unknown variables"
    } ]
  }, {
    "tStartMs": 113863,
    "dDurationMs": 1290,
    "segs": [ {
      "utf8": "in these equations,"
    } ]
  }, {
    "tStartMs": 115153,
    "dDurationMs": 2849,
    "segs": [ {
      "utf8": "we’re faced with \na mathematical constraint:"
    } ]
  }, {
    "tStartMs": 118002,
    "dDurationMs": 3831,
    "segs": [ {
      "utf8": "for each unknown, \nthere must be at least one equation"
    } ]
  }, {
    "tStartMs": 121833,
    "dDurationMs": 2210,
    "segs": [ {
      "utf8": "that independently describes it."
    } ]
  }, {
    "tStartMs": 124043,
    "dDurationMs": 4891,
    "segs": [ {
      "utf8": "Initially, a two-body system appears \nto have more unknown variables"
    } ]
  }, {
    "tStartMs": 128934,
    "dDurationMs": 3790,
    "segs": [ {
      "utf8": "for position and velocity \nthan equations of motion."
    } ]
  }, {
    "tStartMs": 132724,
    "dDurationMs": 1956,
    "segs": [ {
      "utf8": "However, there’s a trick:"
    } ]
  }, {
    "tStartMs": 134680,
    "dDurationMs": 4235,
    "segs": [ {
      "utf8": "consider the relative position \nand velocity of the two bodies"
    } ]
  }, {
    "tStartMs": 138915,
    "dDurationMs": 3710,
    "segs": [ {
      "utf8": "with respect to the center \nof gravity of the system."
    } ]
  }, {
    "tStartMs": 142625,
    "dDurationMs": 4728,
    "segs": [ {
      "utf8": "This reduces the number of unknowns\nand leaves us with a solvable system."
    } ]
  }, {
    "tStartMs": 147353,
    "dDurationMs": 5726,
    "segs": [ {
      "utf8": "With three or more orbiting objects \nin the picture, everything gets messier."
    } ]
  }, {
    "tStartMs": 153079,
    "dDurationMs": 4382,
    "segs": [ {
      "utf8": "Even with the same mathematical trick \nof considering relative motions,"
    } ]
  }, {
    "tStartMs": 157461,
    "dDurationMs": 4627,
    "segs": [ {
      "utf8": "we’re left with more unknowns \nthan equations describing them."
    } ]
  }, {
    "tStartMs": 162088,
    "dDurationMs": 4252,
    "segs": [ {
      "utf8": "There are simply too many variables\nfor this system of equations"
    } ]
  }, {
    "tStartMs": 166340,
    "dDurationMs": 3270,
    "segs": [ {
      "utf8": "to be untangled into a general solution."
    } ]
  }, {
    "tStartMs": 169610,
    "dDurationMs": 3910,
    "segs": [ {
      "utf8": "But what does it actually look like \nfor objects in our universe"
    } ]
  }, {
    "tStartMs": 173520,
    "dDurationMs": 5111,
    "segs": [ {
      "utf8": "to move according to analytically \nunsolvable equations of motion?"
    } ]
  }, {
    "tStartMs": 178631,
    "dDurationMs": 3250,
    "segs": [ {
      "utf8": "A system of three stars—\nlike Alpha Centauri—"
    } ]
  }, {
    "tStartMs": 181881,
    "dDurationMs": 3478,
    "segs": [ {
      "utf8": "could come crashing\ninto one another or, more likely,"
    } ]
  }, {
    "tStartMs": 185359,
    "dDurationMs": 5112,
    "segs": [ {
      "utf8": "some might get flung out of orbit \nafter a long time of apparent stability."
    } ]
  }, {
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    "segs": [ {
      "utf8": "Other than a few highly improbable \nstable configurations,"
    } ]
  }, {
    "tStartMs": 194471,
    "dDurationMs": 6100,
    "segs": [ {
      "utf8": "almost every possible case \nis unpredictable on long timescales."
    } ]
  }, {
    "tStartMs": 200571,
    "dDurationMs": 4197,
    "segs": [ {
      "utf8": "Each has an astronomically large range\nof potential outcomes,"
    } ]
  }, {
    "tStartMs": 204768,
    "dDurationMs": 4808,
    "segs": [ {
      "utf8": "dependent on the tiniest of differences\nin position and velocity."
    } ]
  }, {
    "tStartMs": 209576,
    "dDurationMs": 4166,
    "segs": [ {
      "utf8": "This behaviour is known \nas chaotic by physicists,"
    } ]
  }, {
    "tStartMs": 213742,
    "dDurationMs": 3730,
    "segs": [ {
      "utf8": "and is an important characteristic \nof n-body systems."
    } ]
  }, {
    "tStartMs": 217472,
    "dDurationMs": 4729,
    "segs": [ {
      "utf8": "Such a system is still deterministic—\nmeaning there’s nothing random about it."
    } ]
  }, {
    "tStartMs": 222201,
    "dDurationMs": 3590,
    "segs": [ {
      "utf8": "If multiple systems start \nfrom the exact same conditions,"
    } ]
  }, {
    "tStartMs": 225791,
    "dDurationMs": 2450,
    "segs": [ {
      "utf8": "they’ll always reach the same result."
    } ]
  }, {
    "tStartMs": 228241,
    "dDurationMs": 5739,
    "segs": [ {
      "utf8": "But give one a little shove at the start,\nand all bets are off."
    } ]
  }, {
    "tStartMs": 233980,
    "dDurationMs": 3260,
    "segs": [ {
      "utf8": "That’s clearly relevant \nfor human space missions,"
    } ]
  }, {
    "tStartMs": 237240,
    "dDurationMs": 5249,
    "segs": [ {
      "utf8": "when complicated orbits need \nto be calculated with great precision."
    } ]
  }, {
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    "segs": [ {
      "utf8": "Thankfully, continuous advancements\nin computer simulations"
    } ]
  }, {
    "tStartMs": 246489,
    "dDurationMs": 2890,
    "segs": [ {
      "utf8": "offer a number of ways\nto avoid catastrophe."
    } ]
  }, {
    "tStartMs": 249379,
    "dDurationMs": 4316,
    "segs": [ {
      "utf8": "By approximating the solutions \nwith increasingly powerful processors,"
    } ]
  }, {
    "tStartMs": 253695,
    "dDurationMs": 5870,
    "segs": [ {
      "utf8": "we can more confidently predict the motion\nof n-body systems on long time-scales."
    } ]
  }, {
    "tStartMs": 259565,
    "dDurationMs": 3190,
    "segs": [ {
      "utf8": "And if one body in a group \nof three is so light"
    } ]
  }, {
    "tStartMs": 262755,
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    "segs": [ {
      "utf8": "it exerts no significant force \non the other two,"
    } ]
  }, {
    "tStartMs": 265885,
    "dDurationMs": 4842,
    "segs": [ {
      "utf8": "the system behaves, with very good \napproximation, as a two-body system."
    } ]
  }, {
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    "dDurationMs": 4000,
    "segs": [ {
      "utf8": "This approach is known \nas the “restricted three-body problem.”"
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  }, {
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    "segs": [ {
      "utf8": "It proves extremely useful \nin describing, for example,"
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  }, {
    "tStartMs": 278097,
    "dDurationMs": 3510,
    "segs": [ {
      "utf8": "an asteroid in the Earth-Sun \ngravitational field,"
    } ]
  }, {
    "tStartMs": 281607,
    "dDurationMs": 5093,
    "segs": [ {
      "utf8": "or a small planet in the field \nof a black hole and a star."
    } ]
  }, {
    "tStartMs": 286700,
    "dDurationMs": 2780,
    "segs": [ {
      "utf8": "As for our solar system, \nyou’ll be happy to hear"
    } ]
  }, {
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    "dDurationMs": 3170,
    "segs": [ {
      "utf8": "that we can have reasonable confidence\nin its stability"
    } ]
  }, {
    "tStartMs": 292650,
    "dDurationMs": 3680,
    "segs": [ {
      "utf8": "for at least the next \nseveral hundred million years."
    } ]
  }, {
    "tStartMs": 296330,
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    "segs": [ {
      "utf8": "Though if another star,"
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  }, {
    "tStartMs": 298020,
    "dDurationMs": 3980,
    "segs": [ {
      "utf8": "launched from across the galaxy, \nis on its way to us,"
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  }, {
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    "dDurationMs": 1850,
    "segs": [ {
      "utf8": "all bets are off."
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