If you’re like me — and who isn’t? — then you’ve often wondered how traveling around on the surface of our planet affects its rotation. If you haven’t ever wondered this, then I suggest you go in for a psychiatric evaluation, because no sane person should be able to go for a walk without worrying about the cosmic ramifications of every step he or she takes.
The Earth rotates toward the east; and when you’re standing still with respect to the ground, you’re actually moving along with its surface. If, however, you decide to start walking east, the initial steps you take to get moving will push westward against the Earth, slowing its rotation ever so slightly. You’ll be stealing a bit of the Earth’s angular momentum. If you go west, your feet will push eastward against the Earth, and you will actually speed up its rotation.
The question on my mind — and on yours too, I’m assuming — is how much the Earth’s rotation will be affected if you travel eastward all the way around the world and come to a stop right back where you started. During the trip, the Earth will be rotating at a slower-than-normal rate; and when you come to a stop, it will return to its normal rate of rotation. As a result of this period of slowed rotation, each point on the Earth’s surface will now lag behind where it would have been otherwise. Sunrise will happen a little bit later for everyone.
Well . . . how much later?
This question burns, doesn’t it? Well, relax, because we’re going to answer it right here. We just need to find expressions for the total angular momentum of the system (which consists of you and the Earth) for when you’re standing still and when you’re traveling. By conservation of angular momentum, we can set these two expressions equal to each other and solve for the Earth’s reduced angular velocity during the trip. From this, we can then determine how much lag the Earth will accumulate. Piece of cake!
For the curious, I’ve written out the full solution here, in PDF form. Below, I’ll spare you the calculations and just present the results.
For a 60-kg person making the trip, the amount of time by which sunrise will be delayed is 2.17 attoseconds. In case you’re wondering what the heck an attosecond is, it’s 1/1,000,000,000,000,000,000 of a second, which is roughly how long it takes a beam of light to travel the length of three hydrogen atoms lined up against each other. In other words, it’s a very short time.
One interesting thing about this answer is that it is completely independent of how fast you make the trip. Whether you zip all the way around in less than a second or crawl along over a period of several years, the net effect will still be a delay in the Earth’s rotation of 2.17 attoseconds. It’s your mass, not your speed, that determines how big the resulting delay will be.
If you gained a bit of weight, you would have a bigger impact. We might ask, for example, what your mass would have to be in order to delay the Earth’s rotation by a full second. It turns out you would have to weigh a hefty 27.6 quintillion kilograms, which would require a large number of trips to McDonald’s and is not something you should aim for.
So now we know how the Earth’s rotation is affected each time a person circumnavigates the globe. It’s a small effect; but just to be safe, whenever you take an intercontinental trip, you should probably return the way you came rather than going all the way around the world. Keeping track of time is difficult enough with Daylight Saving Time.