When an object is launched from the Earth into high orbit, it gains angular momentum and the Earth loses it. The angular momentum of the earth is 0.4 M r^2 \omega or 0.4 × 5.9722e24 kg × 6378000m2 × 2π / 86164.0905s = 7e33 kg m2/s . Launching a kilogram from eastbound from the Earth's surface to escape velocity removes 1kg × 11km/s × 6378000m or 7e10 kg m2/s from the earth's rotation. So the day grows longer by a factor of 1e-23 for every kilogram launched, or 8.6e-19 seconds/day .
Launching a billion tons will lengthen the day by 8.6e-7 seconds, or 860 nanoseconds.