For those of you wondering about the effect on the rotation of the Earth, here are some numbers.
The mass of the Earth is around 5,974,200,000,000,000,000,000 metric tons. To result in the loss of one second per year, you'd need to add .000003% of the mass of the Earth.
That's about 190 trillion metric tons of material, or roughly equal to the 100 tallest mountains on Earth combined (or Mount Everest thirty times over), and that's just to change the length of a day by 0.0027 seconds. To lose an hour each day we'd need 248,925,000,000,000,000,000 metric tons, or 50 million Mount Everests.
There is absolutely no risk of screwing up our orbit or day/night length by mining asteroids.