If the earth rotates around the sun at the speed of 108,000 km an hour, why does the air in earth's atmosphere not disperse and become lost to the vast vacuum that is space?
An orbit is considered to be free fall toward a larger mass, where the transverse velocity of the smaller mass is enough to keep the two from colliding. Newton showed that the acceleration of the smaller body was only dependent on the mass of the larger.
In other words, the Earth and its atmosphere are both accelerating toward the sun at the same rate. Since there is no difference in acceleration caused by the sun, the Earth's gravity is enough to dominate the atmosphere.
The sun's solar wind, however, would be able to strip away the Earth's atmosphere if we did not have a strong magnetosphere to protect us. Astronomers believe that this is what happened to Mars's atmosphere.