If I fire a harpoon at Earth from space would I be pulled back by earth's rotation?

So I was going to pass on this question, because many others have given much better answers than I would have.

But I thought of something that might make the entire situation impossible.

OK, so imagine this situation. 

There you are, floating in space, with your harpoon gun.

You’re ready to shoot Jaws, er, I mean Earth. You fire the gun. What happens? The harpoon flies forward, right?

• Well, kinda. What also happens is that you fly backwards.

Without friction, you move away from Earth while the harpoon moves forward. If you’ve got a relatively short rope (say just barely long enough to get to Earth), you and the harpoon eventually stretch that rope out, rebound, and come back together, right back to where you started. (not quite…the rope will warm up a bit, atmospheric friction, greater gravitational attraction on the harpoon, etc…but close enough).

OK, so what if we have a longer rope?

• Well, an additional problem is that as the rope gets pulled along, the speed of the harpoon will slow and slow until it’s barely moving. The harpoon doesn’t have that much kinetic energy, and as mass goes up (from all the added rope), velocity goes down…quickly. Pretty soon the harpoon is essentially still, and it never gets to Earth.

OK, so what if we use a much heavier harpoon and really thin string?

• Then you fly backward even faster, and the harpoon barely moves!

OK, so we get a REALLY powerful harpoon gun, a lightweight harpoon and super thin string.

• Even this won’t work. To get to the Earth, the harpoon will have to go REALLY fast. For that, you’ll need the world’s most impressive harpoon gun. There’s only one word for what this really is: a rocket.

Now that might work. Attach a rocket engine to your harpoon and you’ve got a shot at this. But you’re really just riding a really long rocket made of rope now…