100 Essential Things You Didn't Know You Didn't Know Read Free Page B

similar mass is introduced into the system, then something quite dramatic generally 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 fantastic counter-intuitive property of Newton’s theory of gravity discovered by Jeff Xia in 1992. First, take four 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 five particles will expand to infinite size in a finite time!

    How does this happen? The little oscillating particle runs from one pair to the other, 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 separated 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 a finite time. Clearly, in a Newtonian world where there is no speed limit, it is. Unfortunately (or perhaps fortunately), this behaviour 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/c 2 , 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 three 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 basket ball or smooth-surfaced football) and a small ball (like a ping-pong or tennis ball). Hold the small ball just above the large ball at about chest height 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
nine
times higher than it would have gone if it had just been dropped on the ground from the same height. fn1 You might not want to do this indoors!
    fn1 The basket ball rebounds from the ground with speed V and hits the ping-pong ball when it is still falling at speed V. So, relative to the basket ball, the ping-pong ball rebounds upwards at speed 2V after its velocity gets reversed by the collision. Since the basket ball is moving at speed V relative to the ground this means that 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 V 2 this means that it will rise 3 2 = 9 times higher than in the absence of its collision with the basket ball. In practice, the loss of energy incurred at the bounces will ensure that it rises a little less than this.

10
    It’s a Small World After All
    It’s a small world but we all run in big circles.
    Sasha Azevedo
    How many people do you know? Let’s take a round number, like 100, as a good average guess. If your 100 acquaintances each know