Ask a Physicist Answers
In his book "Understanding Physics," Isaac Asimov writes "As the earth rotates about its axis, the surface of the earth is continually undergoing an acceleration inward toward the center of the earth (just as the moon does in revolving around the earth." Does that mean that the acceleration on the surface (g = 9.8 m/s2) is directly related to the centripetal acceleration of an object traveling in a circle (a = v2/r)? - DW, Raleigh, NC
Though a gifted writer of science and a capable scientist, Asimov hasn't done you a favor in this case. He's not wrong, but he's misleading. He has drawn too close a connection between two objects that are traveling in circles for different reasons.
Any object that travels in a circle is experiencing an inward net force, a centripetal force, that is bending its normally straight inertial path into a circular one. Exactly what that centripetal force is depends on the situation. Sometimes its gravity, sometimes it's a string, and other times it's a combination of many individual forces working together.
The surface of the earth travels in a circle because each portion of it experiences a centripetal force that's just strong enough to bend its path into a circle the size of the earth. This inward force isn't a single force, but rather a composite consisting of gravity pulling downward and various supporting forces pushing upward. These opposing forces almost cancel completely, so each portion of the earth's surface experiences only a tiny inward force. It's just enough to bend that portion's path into an earth-sized circle that closes on itself once per day.
In contrast, the centripetal force that bends the moon's path into an enormous moon-orbit-sized circle is the earth's gravity. There is no supporting force to slow the moon's inward acceleration-it is falling freely toward the earth. Despite the enormity of the moon's orbital circumference and the moon's distance from the earth, this inward acceleration is fast enough to bend the moon's path into a moon-orbit-sized circle that closes on itself once per lunar month.
If the earth's surface were in free fall like the moon, it would accelerate inward much more quickly and would thus travel in a much smaller arc. To stretch its path back to an earth-sized circle, the surface would have to travel much faster. The earth's surface near the equator would have to travel at the speed of low earth orbit-the speed of the space shuttle-and would complete its circle about once every 84 minutes. The day would be over before you finished breakfast.Answered by Lou A. Bloomfield of the University of Virginia.