Q: Is it possible to say if the Earth is moving or sitting still without going into space?

Physicist: Relativity (both Galileo‘s and Einstein‘s) states that the laws of physics will work the same no matter how fast or slow you’re moving, so long as that movement is at a constant speed and in a constant direction.  Galileo talked about boats, and Einstein talked about trains, but it’s all the same stuff.  A point on the Earth, rather than moving in a nice straight line, is being swung around on 3 circles at the same time.  As a result, physics doesn’t work quite the way it should.

One of these circles is the wobble induced by the Moon’s pull.  Rather than thinking that “the Moon orbits the Earth” it helps to think that “the Moon and the Earth orbit their common center of mass”.  The Earth is about 80 times more massive than the Moon, and as such, the center of the Earth-Moon system is about 1,500 km beneath the surface of the Earth (not in space between them), which is why I’m describing the effect as a “wobble”.  This wobble is made apparent by the tides, which would otherwise be very mysterious (where does the force come from?).

The Earth (blue) and the point around which the Earth wobbles (red).

Another circle is the Earth’s orbit around the Sun.  Although they originally didn’t know why, sailors have always been aware that in addition to lunar tides there is a smaller “solar tide” that occurs every day at noon and midnight.  This tide is a symptom of the Earth moving around the Sun, and it’s about 46% as strong as the lunar tide.
Finally, the most dramatic, fastest circle is the Earth’s rotation.  You can tell the difference between the Sun and Moon moving around the Earth, and the Earth spinning because a stationary Earth doesn’t experience “coriolis forces”

Coriolis forces are responsible for large scale weather phenomena like hurricanes, as well as a host of much smaller, more boring effects, like Foucault pendulums.

The direction in which a Foucault Pendulum swings back and forth slowly rotates. In reality, the pendulum is trying to remain swinging in the same direction, but the Earth is turning under it.

So even before knowing the cause, it’s possible to deduce that the Earth is not stationary, because the laws of physics here are not the same as the laws we would observe on a completely stationary object.