If people on the earth take off at the same time, will the earth deviate from its original orbit according to the principle of conservation of momentum?

First of all, people on the earth should jump in one direction, otherwise the effect of jumping on both sides of the earth will be offset because the earth is spherical.

In this case, your idea is right. There will be a little deviation on the earth, which is equal to the average jumping height of all people multiplied by the weight of all people multiplied by the weight of the earth. If everyone weighs 70 kilograms and everyone jumps 1 meter, the mass of the earth is 600 billion kilograms. 6 billion people together can make the maximum deviation of the earth reach 0.0000000000007 meters, needless to say 13 zeros.

From here, we can realize the smallness of human beings. Besides, don't forget that we have to fall after jumping up. In this way, due to the conservation of momentum in the process of falling, the earth moves 0.00000007 meters and then comes back.

In fact, the earth's orbit itself is unstable, and the change is generally in the order of centimeters. Compared with this, people's influence on the earth is really pitiful.