Well, first of all, remember that the Earth is a sphere (ball-shaped).
So chances are that some of the people will jump in exactly the opposite
direction compared to some of the others, and they'll all cancel each other.
But I understand what you're getting at. So let's assume that the Earth
is a big cube, and all the jumpers stand on the same face of the cube and
all jump in the same direction.
Momentum = (mass) x (speed) .
The combined momentum of your flash mob is
(2 billion) x (60kg) x (7 m/s) = 8.4 x 10¹¹ kg-m/s .
In order for linear momentum to be conserved, the Earth must move
in the opposite direction with the same momentum.
Earth's momentum = ( Earth's mass) x (Earth's speed)
Divide each side by (Earth's mass):
Earth's speed = (Earth's momentum) / (Earth's mass) =
(8.4 x 10¹¹ kg-m/s) / (5.98 × 10²⁴ kg) =
1.4 x 10⁻¹³ m/s .
As the crowd jumps upward, transferring their combined momentum
to the Earth, the Earth moves downward, at the speed of
0.000 000 000 14 millimeter per second .
