Hello I'm new to these forums and I shall post many informative 'articles' for you fellow scientists to read. So without further ado, let us begin! [All credit goes to the author John D. Barrow- '100 essential things you didn't know you didn't know'. I couldn't find a particular website so...']

'Two's company, Three's a crowd'

Two people who get on well together can often find their relationship destabilised by the arrival of a third into their orbit. This is even more noticeable when gravity is the force of attraction involved. Newton taught us that 2 masses can remain in stable orbit around their centre of mass under their mutual gravitational forces- as do the Earth and the Moon. But if a third body of similar mass is introduced into the system, then something quite dramatic happens. One body finds itself kicked out of the system by the gravitational forces, while the two that remain are drawn into a more tightly bound stable orbit.

This simple 'slingshot' process is the source of a counter intuitive property of Newton's theory of gravity. First, take 4 particles of equal mass M and arrange them in two pairs orbiting within two planes that are parallel and with opposite directions of spin so there is no overall rotation. Now introduce a fifth much lighter particle m that oscillates back and forth along the perpendicular through the mass centres of the two pairs. The group of 5 particles will expand to infinite size in a finite time!

How does this happen? The little oscillating particle runs from one pair to another, and at the other it creates a little 3-body problem and gets ejected, and the pair recoils outwards to conserve momentum. The lightest particle then travels across to the other pair and the same scenario is repeated. This happens time and time again without end, and accelerates the two pairs so hard that they become infinitely seperated in a finite time, undergoing an infinite number of oscillations in the process.

This example actually solves an old problem posed by philosophers as to whether it is possible to perform an infinite number of actions in finite time. Clearly, in a Newtonian world where there is no speed limit, it is. Unfortunately (or perhaps fortunately), this behavior is not possible when Einstein's relativity is taken into account. No information can be transmitted faster than the speed of light and gravitational forces cannot become arbitrarily strong in Einstein's theory of motion and gravitation.

Nor can masses get arbitrarily close to each other and recoil. When two masses of mass M get closer than a distance 4GM/c², where G is Newton's gravitation constant and c is the speed of light, then a 'horizon' surface of no-return forms around them and they form a black hole from which they cannot escape.

The slingshot effect of gravity can be demonstrated in your back garden with a simple experiment. It shows how 3 bodies can combine to create big recoil as they try to conserve momentum when they pass close to each other (in the case of astronomical bodies) or collide (as it will be in our experiment).

The three bodies will be the Earth, a large ball (like a basketball or smooth surfaced football) and a small ball (like a ping pong or tennis ball). Hold the small ball at chest height just above the large ball and let them both fall to the ground together. The big ball will hit the ground first and rebound upwards, hitting the small ball while it is still falling. The result is rather dramatic. The small ball bounces up to a height about 9 times higher than it would've gone if it had just been dropped on the ground from the same height.*

*The basket ball rebounds from the ground with speed V and hits the ping pong ball while it is still falling at speed V. So, relative to the basket ball, the ping pong ball rebounds upwards at speed 2V after it's velocity gets reversed by the collision. Since the basket ball is moving at speed V relative to the ground this means the ping pong ball is moving upwards at 2V + V = 3V relative to the ground after the collision. Since the height reached is proportional to v² this means it will rise 3² = 9 times higher than in the absence of its collision, In practice, the loss of energy at the bounces will ensure that it rises to a little less than this.

Thanks for reading, sorry for the length...!

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