Conservation of momentum
When people jump, Earth recoils with equal and opposite momentum, but its mass makes the motion vanishingly small. The equation is simple; the scale is the surprise.
Earth & Space
This question has a precise, calculated answer. It is very, very anticlimactic. All eight billion humans jumping together sounds planetary. Conservation of momentum gives the deflating answer: humanity's combined mass is tiny compared with Earth's. The jump does almost nothing to Earth. Getting everyone home afterward is the actual disaster.
Quick answer
Earth would recoil by far less than a hydrogen atom's width, with a tiny local seismic signal and no meaningful change to orbit or rotation. The mass ratio makes direct human physical force irrelevant at planetary scale. Humans do measurably affect Earth's rotation through climate-driven ice redistribution, groundwater extraction, and reservoirs, just not by jumping.

The short answer
Earth would recoil by far less than a hydrogen atom's width, with a tiny local seismic signal and no meaningful change to orbit or rotation.
Conservation of momentum
When people jump, Earth recoils with equal and opposite momentum, but its mass makes the motion vanishingly small.
Curiosity twist
Humans do measurably affect Earth's rotation through climate-driven ice redistribution, groundwater extraction, and reservoirs, just not by jumping.
Common mistake
If enough people coordinate, humanity can physically shift Earth by force.
Next tiny mystery

Earth & Space
Another big-question explanation in the same collection.

Earth & Space
Another big-question explanation in the same collection.

Earth & Space
Another big-question explanation in the same collection.