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

How to make sustainable choices in everyday life

Identifying ways to reduce waste and conserve resources

Understanding the impact of human actions on the environment

Discover 99 similar ideas in

It takes just

## The three-body problem

Mathematical equations can predict the motions of two gravitating masses. But when a third or more are introduced, our analytical tools fall short.

It is impossible to write down all the terms of a general formula that can accurately describe the motion of three or more gravitating objects. The problem is in knowing how many unknown variables an n-body system contains.

11

## The mathematical constraint

Thanks to Isaac Newton, we can write a set of equations to describe the gravitational force that acts between bodies.

But, when we try to find a general solution for the unknown variables in these equations, we are faced with a mathematical limitation.

For every unknown, there must be one equation that describes it. A two-body system is solvable because its gravitational attraction influences the paths they take in such a way that a simple mathematical formula can describe it. But three or more orbiting objects leaves us with more variables than equations that can describe them.

11

## Objects that move according to analytically unsolvable equations of motion

A system of three stars could come crashing or flung out of orbit after a long time of apparent stability.

Almost every possible configuration is unpredictable on long timescales. A slight difference in position and velocity could have a large range of potential outcomes. Physicists describe this behaviour as chaotic - an important characteristic of n-body systems. But it is still deterministic; it’s not random.

11

## The restricted three-body system

Advancements in computer simulations help to avoid disaster. By approximating solutions with powerful processors, we can better predict the motion of n-body systems on long time scales.

When one body in a group of three is so light it has no significant force on the other two, the system behaves as a two-body system. This is known as the “restricted three-body problem.”

The restricted three-body system is useful to describe an asteroid in the Earth-Sun gravitational field or a small planet in the field of a black hole and a star.

11

# CURATED BY

My math book needs to commit suicide. It has way to many problems.

# CURATOR'S NOTE

For space missions to avoid catastrophe, complicated orbits must be calculated with great precision.

## Explore the World’sBest Ideas

### 200,000+ ideas on pretty much any topic. Created by the smartest people around & well-organized so you can explore at will.

#### An Idea for Everything

Explore the biggest library of insights. And we've infused it with powerful filtering tools so you can easily find what you need.

Knowledge Library

#### Powerful Saving & Organizational Tools

Save ideas for later reading, for personalized stashes, or for remembering it later.

# Personal Growth

### Organize your ideas & listen on the go. And with Pro, there are no limits.

#### Listen on the go

Just press play and we take care of the words.

#### Never worry about spotty connections

No Internet access? No problem. Within the mobile app, all your ideas are available, even when offline.

#### Get Organized with Stashes

Ideas for your next work project? Quotes that inspire you? Put them in the right place so you never lose them.

My Stashes

Join

2 Million Stashers

4.8

5,740 Reviews

App Store

4.7

72,690 Reviews

Ashley Anthony

This app is LOADED with RELEVANT, HELPFUL, AND EDUCATIONAL material. It is creatively intellectual, yet minimal enough to not overstimulate and create a learning block. I am exceptionally impressed with this app!

Best app ever! You heard it right. This app has helped me get back on my quest to get things done while equipping myself with knowledge everyday.

samz905

Don’t look further if you love learning new things. A refreshing concept that provides quick ideas for busy thought leaders.

Sean Green

Great interesting short snippets of informative articles. Highly recommended to anyone who loves information and lacks patience.

Ghazala Begum

Even five minutes a day will improve your thinking. I've come across new ideas and learnt to improve existing ways to become more motivated, confident and happier.

Giovanna Scalzone

Brilliant. It feels fresh and encouraging. So many interesting pieces of information that are just enough to absorb and apply. So happy I found this.

Laetitia Berton

I have only been using it for a few days now, but I have found answers to questions I had never consciously formulated, or to problems I face everyday at work or at home. I wish I had found this earlier, highly recommended!

Jamyson Haug

Great for quick bits of information and interesting ideas around whatever topics you are interested in. Visually, it looks great as well.

20x Faster

without
deepstash

with
deepstash

with

deepstash

Unlimited idea saving & library

Unlimited history

Unlimited listening to ideas