A point on the Earth, rather than moving in a nice straight line, is being swung around on 3 circles at the same time. 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”. This wobble is made apparent by the tides, which would otherwise be very mysterious (where does the force come from?). This tide is a symptom of the Earth moving around the Sun, and it’s about 46% as strong as the lunar tide. 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.