[Script Info]
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[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:07.74,0:00:11.88,Default,,0000,0000,0000,,In 2009, two researchers ran \Na simple experiment.
Dialogue: 0,0:00:11.88,0:00:15.06,Default,,0000,0000,0000,,They took everything we know \Nabout our solar system
Dialogue: 0,0:00:15.06,0:00:21.11,Default,,0000,0000,0000,,and calculated where every planet would be\Nup to 5 billion years in the future.
Dialogue: 0,0:00:21.11,0:00:25.11,Default,,0000,0000,0000,,To do so they ran over 2,000 \Nnumerical simulations
Dialogue: 0,0:00:25.11,0:00:29.83,Default,,0000,0000,0000,,with the same exact initial conditions\Nexcept for one difference:
Dialogue: 0,0:00:29.83,0:00:35.14,Default,,0000,0000,0000,,the distance between Mercury and the Sun,\Nmodified by less than a millimeter
Dialogue: 0,0:00:35.14,0:00:37.80,Default,,0000,0000,0000,,from one simulation to the next.
Dialogue: 0,0:00:37.80,0:00:41.07,Default,,0000,0000,0000,,Shockingly, in about 1 percent \Nof their simulations,
Dialogue: 0,0:00:41.07,0:00:46.42,Default,,0000,0000,0000,,Mercury’s orbit changed so drastically \Nthat it could plunge into the Sun
Dialogue: 0,0:00:46.42,0:00:48.78,Default,,0000,0000,0000,,or collide with Venus.
Dialogue: 0,0:00:48.78,0:00:49.50,Default,,0000,0000,0000,,Worse yet,
Dialogue: 0,0:00:49.50,0:00:54.98,Default,,0000,0000,0000,,in one simulation it destabilized\Nthe entire inner solar system.
Dialogue: 0,0:00:54.98,0:00:58.98,Default,,0000,0000,0000,,This was no error; \Nthe astonishing variety in results
Dialogue: 0,0:00:58.98,0:01:05.06,Default,,0000,0000,0000,,reveals the truth that our solar system \Nmay be much less stable than it seems.
Dialogue: 0,0:01:05.06,0:01:10.24,Default,,0000,0000,0000,,Astrophysicists refer to this astonishing\Nproperty of gravitational systems
Dialogue: 0,0:01:10.24,0:01:12.42,Default,,0000,0000,0000,,as the n-body problem.
Dialogue: 0,0:01:12.42,0:01:15.24,Default,,0000,0000,0000,,While we have equations \Nthat can completely predict
Dialogue: 0,0:01:15.24,0:01:17.95,Default,,0000,0000,0000,,the motions of two gravitating masses,
Dialogue: 0,0:01:17.95,0:01:23.60,Default,,0000,0000,0000,,our analytical tools fall short \Nwhen faced with more populated systems.
Dialogue: 0,0:01:23.60,0:01:28.86,Default,,0000,0000,0000,,It’s actually impossible to write down\Nall the terms of a general formula
Dialogue: 0,0:01:28.86,0:01:34.77,Default,,0000,0000,0000,,that can exactly describe the motion\Nof three or more gravitating objects.
Dialogue: 0,0:01:34.77,0:01:41.88,Default,,0000,0000,0000,,Why? The issue lies in how many unknown\Nvariables an n-body system contains.
Dialogue: 0,0:01:41.88,0:01:45.19,Default,,0000,0000,0000,,Thanks to Isaac Newton, \Nwe can write a set of equations
Dialogue: 0,0:01:45.19,0:01:49.19,Default,,0000,0000,0000,,to describe the gravitational force \Nacting between bodies.
Dialogue: 0,0:01:49.19,0:01:53.86,Default,,0000,0000,0000,,However, when trying to find a general \Nsolution for the unknown variables
Dialogue: 0,0:01:53.86,0:01:55.15,Default,,0000,0000,0000,,in these equations,
Dialogue: 0,0:01:55.15,0:01:58.00,Default,,0000,0000,0000,,we’re faced with \Na mathematical constraint:
Dialogue: 0,0:01:58.00,0:02:01.83,Default,,0000,0000,0000,,for each unknown, \Nthere must be at least one equation
Dialogue: 0,0:02:01.83,0:02:04.04,Default,,0000,0000,0000,,that independently describes it.
Dialogue: 0,0:02:04.04,0:02:08.93,Default,,0000,0000,0000,,Initially, a two-body system appears \Nto have more unknown variables
Dialogue: 0,0:02:08.93,0:02:12.72,Default,,0000,0000,0000,,for position and velocity \Nthan equations of motion.
Dialogue: 0,0:02:12.72,0:02:14.68,Default,,0000,0000,0000,,However, there’s a trick:
Dialogue: 0,0:02:14.68,0:02:18.92,Default,,0000,0000,0000,,consider the relative position \Nand velocity of the two bodies
Dialogue: 0,0:02:18.92,0:02:22.62,Default,,0000,0000,0000,,with respect to the center \Nof gravity of the system.
Dialogue: 0,0:02:22.62,0:02:27.35,Default,,0000,0000,0000,,This reduces the number of unknowns\Nand leaves us with a solvable system.
Dialogue: 0,0:02:27.35,0:02:33.08,Default,,0000,0000,0000,,With three or more orbiting objects \Nin the picture, everything gets messier.
Dialogue: 0,0:02:33.08,0:02:37.46,Default,,0000,0000,0000,,Even with the same mathematical trick \Nof considering relative motions,
Dialogue: 0,0:02:37.46,0:02:42.09,Default,,0000,0000,0000,,we’re left with more unknowns \Nthan equations describing them.
Dialogue: 0,0:02:42.09,0:02:46.34,Default,,0000,0000,0000,,There are simply too many variables\Nfor this system of equations
Dialogue: 0,0:02:46.34,0:02:49.61,Default,,0000,0000,0000,,to be untangled into a general solution.
Dialogue: 0,0:02:49.61,0:02:53.52,Default,,0000,0000,0000,,But what does it actually look like \Nfor objects in our universe
Dialogue: 0,0:02:53.52,0:02:58.63,Default,,0000,0000,0000,,to move according to analytically \Nunsolvable equations of motion?
Dialogue: 0,0:02:58.63,0:03:01.88,Default,,0000,0000,0000,,A system of three stars—\Nlike Alpha Centauri—
Dialogue: 0,0:03:01.88,0:03:05.36,Default,,0000,0000,0000,,could come crashing\Ninto one another or, more likely,
Dialogue: 0,0:03:05.36,0:03:10.47,Default,,0000,0000,0000,,some might get flung out of orbit \Nafter a long time of apparent stability.
Dialogue: 0,0:03:10.47,0:03:14.47,Default,,0000,0000,0000,,Other than a few highly improbable \Nstable configurations,
Dialogue: 0,0:03:14.47,0:03:20.57,Default,,0000,0000,0000,,almost every possible case \Nis unpredictable on long timescales.
Dialogue: 0,0:03:20.57,0:03:24.77,Default,,0000,0000,0000,,Each has an astronomically large range\Nof potential outcomes,
Dialogue: 0,0:03:24.77,0:03:29.58,Default,,0000,0000,0000,,dependent on the tiniest of differences\Nin position and velocity.
Dialogue: 0,0:03:29.58,0:03:33.74,Default,,0000,0000,0000,,This behaviour is known \Nas chaotic by physicists,
Dialogue: 0,0:03:33.74,0:03:37.47,Default,,0000,0000,0000,,and is an important characteristic \Nof n-body systems.
Dialogue: 0,0:03:37.47,0:03:42.20,Default,,0000,0000,0000,,Such a system is still deterministic—\Nmeaning there’s nothing random about it.
Dialogue: 0,0:03:42.20,0:03:45.79,Default,,0000,0000,0000,,If multiple systems start \Nfrom the exact same conditions,
Dialogue: 0,0:03:45.79,0:03:48.24,Default,,0000,0000,0000,,they’ll always reach the same result.
Dialogue: 0,0:03:48.24,0:03:53.98,Default,,0000,0000,0000,,But give one a little shove at the start,\Nand all bets are off.
Dialogue: 0,0:03:53.98,0:03:57.24,Default,,0000,0000,0000,,That’s clearly relevant \Nfor human space missions,
Dialogue: 0,0:03:57.24,0:04:02.49,Default,,0000,0000,0000,,when complicated orbits need \Nto be calculated with great precision.
Dialogue: 0,0:04:02.49,0:04:06.49,Default,,0000,0000,0000,,Thankfully, continuous advancements\Nin computer simulations
Dialogue: 0,0:04:06.49,0:04:09.38,Default,,0000,0000,0000,,offer a number of ways\Nto avoid catastrophe.
Dialogue: 0,0:04:09.38,0:04:13.70,Default,,0000,0000,0000,,By approximating the solutions \Nwith increasingly powerful processors,
Dialogue: 0,0:04:13.70,0:04:19.56,Default,,0000,0000,0000,,we can more confidently predict the motion\Nof n-body systems on long time-scales.
Dialogue: 0,0:04:19.56,0:04:22.76,Default,,0000,0000,0000,,And if one body in a group \Nof three is so light
Dialogue: 0,0:04:22.76,0:04:25.88,Default,,0000,0000,0000,,it exerts no significant force \Non the other two,
Dialogue: 0,0:04:25.88,0:04:30.73,Default,,0000,0000,0000,,the system behaves, with very good \Napproximation, as a two-body system.
Dialogue: 0,0:04:30.73,0:04:34.73,Default,,0000,0000,0000,,This approach is known \Nas the “restricted three-body problem.”
Dialogue: 0,0:04:34.73,0:04:38.10,Default,,0000,0000,0000,,It proves extremely useful \Nin describing, for example,
Dialogue: 0,0:04:38.10,0:04:41.61,Default,,0000,0000,0000,,an asteroid in the Earth-Sun \Ngravitational field,
Dialogue: 0,0:04:41.61,0:04:46.70,Default,,0000,0000,0000,,or a small planet in the field \Nof a black hole and a star.
Dialogue: 0,0:04:46.70,0:04:49.48,Default,,0000,0000,0000,,As for our solar system, \Nyou’ll be happy to hear
Dialogue: 0,0:04:49.48,0:04:52.65,Default,,0000,0000,0000,,that we can have reasonable confidence\Nin its stability
Dialogue: 0,0:04:52.65,0:04:56.33,Default,,0000,0000,0000,,for at least the next \Nseveral hundred million years.
Dialogue: 0,0:04:56.33,0:04:58.02,Default,,0000,0000,0000,,Though if another star,
Dialogue: 0,0:04:58.02,0:05:02.00,Default,,0000,0000,0000,,launched from across the galaxy, \Nis on its way to us,
Dialogue: 0,0:05:02.00,0:05:03.85,Default,,0000,0000,0000,,all bets are off.