According to this wiki page the earth farts around the sun at an average speed of 107218 km/h. But what about relative to the rest of the surroundings? Is it possible to estimate how fast the earth moves compared to the milky way compared to other galaxies compared to the universe expanding? Are we zooming through space at the same speed as the rest of its constituents?
Yes, but the song is all in miles, my metric brain does not compute… guru meditation…
I have no answers, but I have wondered about this, too. I was taught that our solar system is moving pretty fast in a circular pattern within our galaxy, relative to the galaxy’s center. Since the big bang, everything is moving fast away from everything else. 
If we can pick one reference point, and say our sun is moving at X rate from there, Earth and the other planets are not moving at a steady speed. Relative to our ref. pt., we’d move faster for half a year, then slower for the other half in our orbit around the sun. Earth’s path through the cosmos is not a straight one, and our moon’s path is crazier yet.
Is the solar system’s speed through space fast enough to make Earth’s path a wobble, or slow enough so the path is a series of loops? I feel like a little boy asking why the moon doesn’t fall out of the sky. I think my question is a wee bit less clueless, but not much. :smack:
Asking questions like this eventually led to disproving the old aether theory and to Relativity.
*** Ponder
The question is incorrect. The Universe expands uniformly, which means that any point in the Universe has an equal claim to being the “center”. So we’re not moving relative to the expansion of the Universe, and some galaxy we observe ten billion lightyears away which is receding from us at a fair fraction of the speed of light is also not moving relative to the expansion of the Universe.
If, on the other hand, you just want our velocity relative to the average of some very large chunk of the Universe, the best you can do there is to compare our velocity to the average frame of the cosmological microwave background. In this case, the answer is that our Solar System is moving at approximately 368 km/s relative to the CMB.
So the cosmological microwave background is the furthest out we can “see”, like our edge of the universe? So it is within these edges that we are moving in 368 km/s, but since what we see follows as the cosmological microwave background, were not really moving at all? I’m I in the wrong universe now?
Saying that we’re moving relative to the CMB is fundamentally no different than saying that a car is moving relative to the Earth. The Earth is a pretty big object, by human scales, so it’s often convenient to say how fast something is moving relative to it. The material which emitted the CMB is also a really big object, on astronomical scales, so it’s often convenient to say how fast something is moving relative to that. Neither has any fundamental significance, though, and you can’t say that something is moving relative to the Universe itself.
I appreciate your patience with my feeble grasp on this astronomical subject 
So one more question; do we know how fast the unverse is expanding? And is it slowing down?