What would happen if the moon instantly disappeared? (Tidal waves, earthquakes,…?)
The moon’s gravity affects both the earth’s path through space and the earth’s shape. If the moon were to disappear, the earth’s path would change but probably not enough to cause a noticeable difference. The earth and the moon normally orbit one another but the moon, which has much less mass than the earth, does most of the moving. Without the moon, the earth would just orbit smoothly around the sun. As for the earth’s shape, the only part of the earth that responds noticeably to the moon’s gravity is the water on its surface. The tides are caused mostly by the moon’s gravity. Without the moon, the tides would be much smaller and caused only by the sun’s gravity. Thus, in the long run, you would probably have trouble telling that the moon was gone without looking overhead—the earth’s path wouldn’t change much and you would have to look carefully to see the effect on the earth’s oceans.
However, in the moments following the moon’s disappearance, there might be some dramatic waves and a few stress-related earthquakes. The oceans and the earth’s crust do experience substantial stresses due to the unevenness of the moon’s gravity (it’s stronger on the side of the earth nearest the moon than it is on the side of the earth farthest from the moon). But I doubt that the sudden change in stress caused by having the moon disappear would do more than temporarily flood a few coastal cities. One last effect worth noting is that the precession of the equinoxes, a 26,000 year process that shifts the earth’s rotational axis in space and causes the stars that are overhead at night during a particular season to change gradually, is driven by the moon’s gravity and would disappear if the moon were to disappear.