Question

Let's assume that there was some mechanism by which we could remain suspended in air. By this I mean that our feet is not in contact with the ground. One possible way of doing this would be by means of a jetpack. If we could remain suspended in air for a while in this manner, will we be in a different place when we come down, due to the Earth's rotation? When I thought of this problem in the micro scale using a ball (which rotates), it appears like I'll be in a different place when I come down from my suspended state. Am I overlooking something here?

Answer 1

If you're standing on the equator then you're moving, along with the earth's surface, at about 1,000 miles per hour. So if you fly up e.g. 100 meters with your jet pack you're still moving sideways at the same speed so the spot you took off from remains below you.

Well, not quite. Because you're 100m above the surface you're moving in a circle that has a 100m greater radius than the Earth, so it has a bigger circumference than the earth's surface. That means that the earth will rotate slightly faster than you will, so you'll see your takeoff spot gradually move away to the East. If you're a distance d meters above the surface your orbit is 2?d meters larger than the Earth's surface, so in the example above your take off spot will move away at about 630m a day or about 26m per hour. The chances are that the winds or random movements of your jetpack would be more than this so you probably wouldn't notice.