[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,In 2009, two researchers ran a simple \Nexperiment.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,They took everything we know about our\Nsolar system and calculated
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,where every planet would be up to 5 \Nbillion years in the future.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,To do so they ran over 2000 numerical \Nsimulations
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,with the same exact initial conditions\Nexcept for one difference:
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,the distance between Mercury and the Sun,\Nmodified by less than a millimeter
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,from one simulation to the next.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Shockingly, in about 1 percent of their \Nsimulations,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Mercury’s orbit changed so drastically \Nthat it could plunge into the Sun
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,or collide with Venus.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Worse yet,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,in one simulation it destabilized\Nthe entire inner solar system.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This was no error; the astonishing variety\Nin results
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,reveals the truth that our solar system \Nmay be much less stable than it seems.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Astrophysicists refer to this astonishing\Nproperty of gravitational systems
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,as the n-body problem.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,While we have equations that can \Ncompletely predict the motions
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,of two gravitating masses,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,our analytical tools fall short when \Nfaced with more populated systems.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,It’s actually impossible to write down\Nall the terms of a general formula
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,that can exactly describe the motion\Nof three or more gravitating objects.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Why? The issue lies in how many unknown\Nvariables an n-body system contains.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Thanks to Isaac Newton, we can write \Na set of equations
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,to describe the gravitational force \Nacting between bodies.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,However, when trying to find a general \Nsolution for the unknown variables
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,in these equations,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,we’re faced with a mathematical \Nconstraint: for each unknown,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,there must be at least one equation \Nthat independently describes it.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Initially, a two-body system appears to\Nhave more unknown variables
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,for position and velocity than \Nequations of motion.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,However, there’s a trick:
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,consider the relative position and \Nvelocity of the two bodies
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,with respect to the center of \Ngravity of the system.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This reduces the number of unknowns\Nand leaves us with a solvable system.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,With three or more orbiting objects in the\Npicture, everything gets messier.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Even with the same mathematical trick \Nof considering relative motions,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,we’re left with more unknowns than \Nequations describing them.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,There are simply too many variables\Nfor this system of equations
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,to be untangled into a general solution.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,But what does it actually look like for \Nobjects in our universe
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,to move according to analytically \Nunsolvable equations of motion?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,A system of three stars––
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,like Alpha Centauri could come crashing\Ninto one another or, more likely,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,some might get flung out of orbit \Nafter a long time of apparent stability.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Other than a few highly improbable \Nstable configurations,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,almost every possible case is \Nunpredictable on long timescales.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Each has an astronomically large range\Nof potential outcomes,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,dependent on the tiniest of differences\Nin position and velocity.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This behaviour is known as chaotic \Nby physicists,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,and is an important characteristic \Nof n-body systems.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Such a system is still deterministic—\Nmeaning there’s nothing random about it.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,If multiple systems start from the exact\Nsame conditions,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,they’ll always reach the same result.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,But give one a little shove at the start,\Nand all bets are off.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,That’s clearly relevant for human space\Nmissions,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,when complicated orbits need to \Nbe calculated with great precision.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Thankfully, continuous advancements\Nin computer simulations
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,offer a number of ways\Nto avoid catastrophe.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,By approximating the solutions with \Nincreasingly powerful processors,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,we can more confidently predict the motion\Nof n-body systems on long time-scales.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And if one body in a group of three is so\Nlight it exerts no significant force on the other two,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,the system behaves, with very good \Napproximation, as a two-body system.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This approach is known as the “restricted \Nthree-body problem.”
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,It proves extremely useful in describing,\Nfor example,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,an asteroid in the Earth-Sun \Ngravitational field,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,or a small planet in the field of a \Nblack hole and a star.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,As for our solar system, you’ll \Nbe happy to hear
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,that we can have reasonable confidence\Nin its stability
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,for at least the next several \Nhundred million years.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Though if another star, launched from \Nacross the galaxy, is on its way to us,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,all bets are off.