Here is a physics question Emily and I were debating recently: Imagine you are floating in deep space, a few metres from your space ship. All you have are a space suit – from which nothing can be vented – and a bowling ball in your hands. The obvious way to shift yourself towards your ship is to throw the ball in the opposite direction. If you are very patient, you could also (a) wait for your ship’s gravitational field to draw you in or (b) release the bowling ball, letting it hit you and push you back.
Is there any way to generate movement towards the ship without releasing the ball? My contention is that any way you can move it without letting go will only put you in some kind of spin, it will not actually move you towards your ship. Basically, this is because Newton’s third law ensures that any collection of actions will be self-compensating. Am I right to believe so?
Note: One major reason for confusion about this is because we are used to situations in which it is possible to push off something. When you stand on the ground and hurl a ball on earth, both your mass and that of the earth absorb the equal and opposite force. Those floating helplessly in space have no such luxuries.
I thought about this for quite a while, and I realized the solution is deceptively simple. First, you will be able to rotate yourself. You can do this because the preservation of angular momentum is not a linear function – you can always spin by rotating the heavy ball father out from you, then pulling it towards yourself and rotating it back.
However, it is quite obvious that it is impossible to move forward or backward, and this is easy to show in a simple thought experiment. First, ever movement you make will have two components, a rotational component and a velocity. We can ignore the rotational component since I delt with it above. Now, if we consider purely the velocity modification of any action, it is quite clear in every case that every action has an equal and opposite reaction, and since there is nothing to react against, in every attempt at movement, even divided into miniscule fragments, your centre of mass will remain at the same velocity.
Another way to think of this is to say every change in velocity is a collision, and the best you can do on your own in space is a collision with yourself. And an object colliding with itself does not change velocity.
One deceptive image is that of moving an office chair without touching the ground. You can do so by swinging part of your body forward quickly, then retracting it slowly.
In the first case, you overcome friction and move. In the second, you stay still – not falling back.
Of course, there is no friction in deep space. There is also no planet to absorb forces that do not cause you to move. Remember that every time you push off against the earth in a vector that doesn’t radiate from its centre of mass you are very slightly altering the planet’s rotation.
The forces always need to balance out.