Newton's Third Law in space

[LloydGarmadon]

Newton's Third Law states that forces occur in pairs of equal magnitude acting in opposite directions on opposing bodies. When we push against a wall, the wall pushes back with a force of equal magnitude and we move as a result of not being inert enough. What would the force pair be if an astronaut pushes against nothingness in space? Is the reaction pair within the body, and the fist accelerates orders of magnitude more noticeable than the body due to difference in inertia?

 

[Nugatory]

Is the reaction pair within the body, and the fist accelerates orders of magnitude more noticeable than the body due to difference in inertia?

yes, so the body moves a little bit in one direction, the fist moves a lot more in the other direction, and the center of mass of the astronaut doesn’t move at all. If they’re floating stranded ten meters from the hatch of their spaceship they’re as helpless as if it were ten thousand kilometers - no way of moving themself through space.

 

[LloydGarmadon]

@Nugatory Thanks for the kind help. If we apply this understanding on earth, say punching a wall, your centre of mass remains stationary until the punch reaches the wall and the reaction force pushes you backwards... and a net force is only created when you apply some of that force/momentum of the wall to have it back at you.. If thats the case, can it be qualitatively understood by: say we have numbers representing "units" of forces. before you touch the wall, its -10 vs 10, centre of mass no movement, but when you hit the wall, some of that action goes to the wall and the wall pushes you, which results is -10 + -5 vs 5, hence generating a net force?

 

[berkeman]

No, you are overthinking this. At every instant of time, if you are in a frictionless environment, your center of mass position is constant. So if you are on a frictionless sheet of ice and move your body or push a heavy dumbbell to the side, the center of mass of you and <whatever> stays in the same position.

 

[Nugatory]

and a net force is only created when you apply some of that force/momentum of the wall to have it back at you

It’s easier to think about these problems if we consider the wall to have infinite mass; no matter what force we apply to it its acceleration is zero so it never moves. (This is a really good approximation when the wall is rigidly attached to the planet earth…. a worthwhile exercise would be to calculate just how good the approximation is for reasonable assumptions about your weight and strength).

With that assumption, when you are pushing on the wall we have three things each subject to their own forces:
- the wall, which is subject to a force from the hand pushing on it.
- the hand, which is subject to the third-law equal and opposite force from the wall and also to the force from your body pushing on it.
- your body, which is subject to the third-law equal and opposite force from the hand.

The wall doesn’t move, by assumption.
The hand doesn’t move because the net force on it is zero - the forces on it cancel.
Your body is subject to the non-zero force from the hand, so it moves,

It’s often best to think of these problems by drawing what’s called a “free body diagram”, Google will find some good descriptions.

If thats the case, can it be qualitatively understood by: say we have numbers representing "units" of forces. before you touch the wall, its -10 vs 10, centre of mass no movement, but when you hit the wall, some of that action goes to the wall and the wall pushes you, which results is -10 + -5 vs 5, hence generating a net force?

Much better to think in terms of $F=ma$. When the wall is not there to provide an opposing force your hand will accelerate away from you, you won’t be able to keep applying that force unless your arm can keep up and there’s only so fast that it can move. So there’s only so much acceleration possible and hence a limit on how much force you can apply to the hand.

 

[A.T.]

If we apply this understanding on earth, say punching a wall, your centre of mass remains stationary until the punch reaches the wall ...

Only if you are standing on a frictionless surface.

 

[sophiecentaur]

Is the reaction pair within the body

There is nothin to push against so the "pair" of forces would both be zero. There are plenty of forces going on inside the body as the muscles accelerate limbs etc but they are hard to identify in detail. With a hanging chain, each link - link pair will have a N3 pair and the pairs will have increasing magnitude as you look higher up the chain and smaller as you go down. The 'N3 pair' at the very bottom surface of the bottom link will be zero-zero (Newton works over the whole chain).