I've always wondered, that since the Earth is moving at a very fast velocity around the Sun, why is it that when astronauts leave the Earth, the Earth doesn't immediately move away from them at extremely large speeds?
[Physics] Why doesn’t the Earth release you as soon as you escape it
astrophysicsearthgravityrotation
Related Solutions
Velocity does indeed have to be measured relative to something. We can measure our radial velocity relative to any other astronomical object we care to, by measuring Doppler shifts. But if you want to know our velocity "relative to the Universe as a whole" rather than relative to any one object, we have to be a bit careful to define our terms.
Because the Universe appears to be approximately homogeneous and isotropic, it makes sense to define a "rest frame" at any given point. (The rest frames at different points are moving with respect to each other -- that's what it means to say that the Universe is expanding.) This "rest frame" is essentially the frame in which the stuff surrounding that point appears to be moving isotropically (the same in all directions). In practice, the best way to define that rest frame is to find the frame in which the cosmic microwave background appears the same in all directions (has no dipole moment, to be precise). Relative to this frame, the local group of galaxies is moving at about 600 km/s (Wikipedia gives precise numbers and probably citations that I'm too lazy to look up).
People sometimes worry about whether the existence of a preferred "rest frame" of this sort is in conflict with the principle of relativity. The answer is that it isn't. There are a couple of ways to see why. One is to note that the principle of relativity says that the laws of physics have no preferred frames, but particular solutions to the laws can have preferred frames. Another way of putting it, which I prefer, is that the "rest frame" we use in cosmology is simply the center-of-momentum frame of a bunch of particles (namely the CMB photons in our neighborhood). In other contexts, we're not surprised or worried by the fact that a bunch of particles have a rest frame, so why should we worry about it here?
Because the rotation of the earth is very smooth and doesn't change, the centripetal acceleration we feel is very nearly constant. This means that the (small) centrifugal force from the rotation gets added to gravity to make up the "background force" we don't notice.
Earthquakes are not at all smooth and the accelerations involved are large and change direction a lot. This makes it easy to feel them.
Best Answer
Because you were also in orbit around the sun with the Earth and still have that velocity.
You may be imagining this in terms of stepping off of a slow moving vehicle on the Earth: you jump off, you come to a stop relative the ground and watch the trolley car go it's merry way. But that is a feature of friction between you and the ground. There is no such thing as a absolute reference frame in the universe and when you "leave the Earth" you don't come to stop relative anything so that you can watch the Earth fly away.
Newton's laws apply here: "a body in motion (that's the you or the planet) will continue in motion unless acted on by an external force". You just keep going except for changed induced by your drive.