Inertia for a large mass (in outer space)

Question

I understand that an object doesn't need a force to keep moving; that it will keep moving indefinitely in that direction at that speed. My question though is: if you were in outer space, where friction is not an issue like on earth, could you move an object with the same mass as a house just by lightly tapping it? My understanding, which probably isn't 100% correct, is that inertia means how much an object resists a change in motion. So is it even possible that an object floating in outer space, with mass the size of a house, could stay still from just a small push? Or would it move, just slowly, because force always causes some degree of acceleration?

Answer 1

You are correct that it will move, but also remember that conservation of momentum still holds, so, if you start out at rest, and push a large massed object, you have:

$$\begin{align}\Sigma p_{0} &= \Sigma p_{f}\\ 0 &= mv + MV \\ v &= - (M/m)V \end{align}$$

So, if your mass is small relative to the house, you will recoil from the house at a much larger velocity than the house will move with. In the limit that the house is infinitely larger than you, it will not move at all, and it will be like you are pushing off of a stationary object.