This puzzle has you look at how fast you are moving, in the big picture.

Right this minute. Sitting or standing in front of your computer monitor—or reading this on a printed sheet of paper—how fast are you moving?

Silly question, right? You're standing still!

Wrong!!!!

Even when you are sitting still in front of your computer, the Earth is rotating, so you are moving along with the Earth as it rotates on its axis. You are not aware of this motion because your chair, your desk, your home or school, even your entire city, country, and the air around you—all appear to be standing still. But all of them are moving with the rotation of the Earth.

The space and objects around you make up a frame of reference. You are not moving with respect to your frame of reference, so you think you are standing still. Your frame of reference however, is moving—with respect to the Sun's frame of reference—at the speed determined by the Earth's rotation.

But how fast is your frame of reference moving with respect to the Sun? To figure this out, you'll need a little geometry and a couple of facts you probably already know about the speed of the Earth's rotation and the Earth's diameter.

How can this help you determine how fast you're moving? Well, it's simple (it really is). Since you know that the Earth makes a complete rotation every 24 hours, you know that you travel along the circumference of a circle, and that it takes 24 hours. All you need to do now is find that circumference and divide by the total time, 24 hours, to get your speed.

The circumference of a circle C = 2 x π x R, where R is the radius of the circle and π (pi) is a mathematical ratio with an approximate value of 3.14. The radius of your circle depends on how far you are from the Equator.

How Fast Would You Be Moving at the Equator?

Find the approximate speed (km/h) you would be moving right now if you were at the Equator? You'll need to look up the radius of the Earth at the Equator. There are many Web sites where you can find this value. One good resource is Windows to the Universe [1], at the University Corporation for Atmospheric Research (UCAR).

What If You Are Not at the Equator?

If you were at the North Pole, you'd spin around but wouldn't go anywhere because the distance from the Earth's axis is zero. If you're somewhere between the Equator and one of the poles—and let's face it, most of us are—the distance from the Earth's axis, not the Earth's radius—determines how far you'll travel in 24 hours. Finding this distance takes a little bit of trigonometry and requires that you know your latitude. Your latitude can be measured as an angle between the center of the Earth and the Earth's radius at the Equator. It goes from 0 degrees at the Equator to 90 degrees north or south latitude, at one of the poles. Imagine you are at point P, somewhere north of the Equator.

To simplify the mathematics, assume that the Earth is a sphere. (It's really an "oblate spheroid," which means that it is a little bit thicker across at the Equator than it is from pole to pole, but the difference is small and we can ignore it for this problem.)

Instead of traveling around the circumference of the Earth at the equator, you are traveling along the circumference of a smaller circle at latitude L.

In the diagram (right), P is your point on the Earth along latitude line L. r represents the radius of the smaller circle you are traveling along. R stands for the radius of the Earth. L is the latitude angle. The radius, r, varies with your latitude. It goes from 0 at the North Pole to the Earth's radius at the Equator. r and R are related by the following equation:

r = R x cosine (L)

where cosine (L) is a ratio that is a function of the latitude angle, L.

If you know your latitude, you can look up the cosine of L. You should now be able to figure out your speed, just as you did in example 1.

You can find a chart of cosines and other trigonometric functions at Trigonometric Tables [2]

Just look down the cos column until you find your latitude. Use the value in the table to find r.

Then use the same method as before to figure out your speed using r instead of R.

How Fast is the Earth Moving Around the Sun?

Now that you've got the idea, here's another challenge.

Since you are sitting in the Earth's frame of reference, you won't feel the motion, any more than you feel the motion of the Earth revolving on its axis. In addition, the Earth's frame of reference is moving in an orbit around the Sun. You can work out that speed because you know that the Earth takes about 365 days to travel around the Sun. You can also figure out the average distance from the Sun to the Earth. For example, use the data at Windows to the Universe [1]. This Web site gives both the maximum and minimum distances. You can use an approximate average for your calculation. Although the Earth's orbit is an ellipse, it's actually very close to a circle, and you can assume it's a circle for this calculation.

See if you can find your approximate speed around the Sun in km/h.

Which Speed is Larger?

Which is larger, the speed caused by the revolution of the Earth about its axis or the speed of rotation of the Earth around the Sun? By how much is it larger?

How Fast is the Sun Moving?

You may not realize it, but the Sun's frame of reference is also moving (quite rapidly) in an orbit with respect to a frame of reference at the center of the Milky Way Galaxy. The Earth and all the planets in the solar system are moving right along with it. How fast is the Sun moving? You can consider the motion to be approximately circular and use the scienceworld [3] Web site (from Wolfram Research) to gather the necessary data.

Be careful. These are really big numbers.

How Fast Are You Moving Right Now?

When you are sitting still at your desk or your computer, your motion is the sum of all three motions: the Earth's rotation on its axis, the Earth's orbital motion around the Sun, and the Sun's orbital motion around the Milky Way's galactic center.

What are the largest and smallest possible speeds at which you are moving right now?