 ## Subtitles section Play video

• In 2009, two researchers ran a simple experiment.

• They took everything we know about our solar system

• and calculated where every planet would be up to 5 billion years in the future.

• To do so they ran over 2,000 numerical simulations

• with the same exact initial conditions except for one difference:

• the distance between Mercury and the Sun, modified by less than a millimeter

• from one simulation to the next.

• Shockingly, in about 1 percent of their simulations,

• Mercury's orbit changed so drastically that it could plunge into the Sun

• or collide with Venus.

• Worse yet,

• in one simulation it destabilized the entire inner solar system.

• This was no error; the astonishing variety in results

• reveals the truth that our solar system may be much less stable than it seems.

• Astrophysicists refer to this astonishing property of gravitational systems

• as the n-body problem.

• While we have equations that can completely predict

• the motions of two gravitating masses,

• our analytical tools fall short when faced with more populated systems.

• It's actually impossible to write down all the terms of a general formula

• that can exactly describe the motion of three or more gravitating objects.

• Why? The issue lies in how many unknown variables an n-body system contains.

• Thanks to Isaac Newton, we can write a set of equations

• to describe the gravitational force acting between bodies.

• However, when trying to find a general solution for the unknown variables

• in these equations,

• we're faced with a mathematical constraint:

• for each unknown, there must be at least one equation

• that independently describes it.

• Initially, a two-body system appears to have more unknown variables

• for position and velocity than equations of motion.

• However, there's a trick:

• consider the relative position and velocity of the two bodies

• with respect to the center of gravity of the system.

• This reduces the number of unknowns and leaves us with a solvable system.

• With three or more orbiting objects in the picture, everything gets messier.

• Even with the same mathematical trick of considering relative motions,

• we're left with more unknowns than equations describing them.

• There are simply too many variables for this system of equations

• to be untangled into a general solution.

• But what does it actually look like for objects in our universe

• to move according to analytically unsolvable equations of motion?

• A system of three starslike Alpha Centauri

• could come crashing into one another or, more likely,

• some might get flung out of orbit after a long time of apparent stability.

• Other than a few highly improbable stable configurations,

• almost every possible case is unpredictable on long timescales.

• Each has an astronomically large range of potential outcomes,

• dependent on the tiniest of differences in position and velocity.

• This behaviour is known as chaotic by physicists,

• and is an important characteristic of n-body systems.

• Such a system is still deterministicmeaning there's nothing random about it.

• If multiple systems start from the exact same conditions,

• they'll always reach the same result.

• But give one a little shove at the start, and all bets are off.

• That's clearly relevant for human space missions,

• when complicated orbits need to be calculated with great precision.

• Thankfully, continuous advancements in computer simulations

• offer a number of ways to avoid catastrophe.

• By approximating the solutions with increasingly powerful processors,

• we can more confidently predict the motion of n-body systems on long time-scales.

• And if one body in a group of three is so light

• it exerts no significant force on the other two,

• the system behaves, with very good approximation, as a two-body system.

• This approach is known as therestricted three-body problem.”

• It proves extremely useful in describing, for example,

• an asteroid in the Earth-Sun gravitational field,

• or a small planet in the field of a black hole and a star.

• As for our solar system, you'll be happy to hear

• that we can have reasonable confidence in its stability

• for at least the next several hundred million years.

• Though if another star,

• launched from across the galaxy, is on its way to us,

• all bets are off.

In 2009, two researchers ran a simple experiment.

Subtitles and vocabulary

Operation of videos Adjust the video here to display the subtitles

B1 system body solar system solar gravitational motion

# Newton’s three-body problem explained - Fabio Pacucci

• 0 0
林宜悉 posted on 2020/10/24
Video vocabulary