There are many completely impractical but at the same time extremely entertaining questions. The question in the title of this article is just one of them. Let us get it right.
Since all people are distributed more or less evenly across the Earth, nothing will happen in general, since the blows from landing people on different parts of the Earth mutually cancel each other out.
Yes, of course, if we consider the Earth as a ball, then it turns out that for almost all land areas, on the other side of the Earth, there is an ocean. Only Portugal crosses slightly with New Zealand. Also, in the northern hemisphere, there are many more people than in the southern hemisphere, but all the same, since the force will be spread over a large surface, a significant part of it will be mutually compensated and the resulting force will be negligible.
Let us imagine that in some magical way, all the people gathered in one place. For simplicity, we assume that all people jump to the same height, 30 centimeters.
A drop in the mass of 400 billion kilograms will cause a change in the speed of the Earth’s orbital motion by about 2.6 • 10⁻¹³ m/s. In other words, this is a 0.25 nanometers shift in the orbit of the earth by or about half the diameter of a hydrogen atom.
However, the Earth very quickly “bounces back” due to the gravitational connection with the Sun.
If we assume that all people will gather together in a relatively small territory, for example, on the territory of a city such as New York, and the entire jumping surface will be asphalted, then the joint landing of all people will cause a tremendous noise, an acoustic shock comparable in volume to an atomic bomb explosion.
It will also cause a very strong earthquake in this area. It is difficult to predict the exact strength of the earthquake, but most likely, it will be one of the strongest earthquakes in history.