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How fast are you moving right now?

How fast are you moving right now? The answer, of course, depends on a lot of factors. However, the most important factor is the point of reference. That is, how fast are you moving compared to what?

Speed is completely relative; you cannot report the speed of something without saying what point of reference you are using. This seemingly simple fact is what forced Albert Einstein to revise the whole of physics.

Let me use myself as an example. As I am writing this, I am sitting on a chair in my apartment. Relative to the chair, the floor, and the ground beneath, I am not moving.

However, relative to the center of the Earth, I am moving quite fast. That is because the Earth is spinning so that it completes one rotation in approximately 24 hours.

How fast am I moving compared to the center of the Earth? Let us come up with an estimate of my speed by making some simplifying assumptions. Making such estimates is common practice in physics, especially a physicist just wants to know “around how much” a quantity is. Such estimates are called “Fermi estimates,” after the physicist Enrico Fermi who was great at making such quick and rough estimates of physical quantities.

To get an estimate for my speed, let us assume that the Earth is a perfect sphere. This assumption is, of course, not true because the Earth is slightly oblong, bulging around the equator. (More accurately, the Earth is an oblate spheroid.)

However, the difference is quite small compared to the size of the Earth. The distance from the center of the Earth to the equator is 6,378 kilometers, while the distance from the center to the poles is 6,356 kilometers, a difference of 0.3 percent.

Given the small difference, it is safe to neglect this difference and assume the Earth is a perfect sphere with radius 6,371 kilometers.

So back to the question: How fast am I moving with respect to the Earth’s center?

Before we can proceed, we have to know one other thing: Where on Earth am I? Even if the Earth were a perfect sphere, the speed at which I move will still depend on my location.

Imagine looking down on a spinning basketball (you are looking at it from above). Now imagine ants on the surface of the ball. You will see that an ant sitting on the ball’s “north pole” is not moving at all compared to the ball’s center. Meanwhile, an ant on the ball’s “equator” is moving quite fast. A third ant halfway between the pole and equator is moving slower than the ant on the equator.

In other words, how fast I am moving with respect to Earth’s center depends on how far north or south I am of the equator. In other words, it depends on my latitude.

After a quick Google search, I find that my latitude is approximately 14.5 degrees north, which is the approximate latitude of most of Metro Manila (North Caloocan is at 14.75 degrees while Muntinlupa is at 14.4 degrees).

Using the fact the the Earth spins once every 24 hours and a bit of trigonometry, I find that I move at the speed of approximately 1,600 kilometers per hour with respect to the Earth’s center. And so does the rest of the Metro Manila.

If we choose a different frame of reference, we are traveling even faster. For example, if we use the Sun as the point of reference, then the Earth’s center is moving at 107,000 kph.

As I am typing this, it is close to noontime, where I am on Earth is spinning in the opposite direction that the Earth is moving (the Earth is both spinning and moving around the Sun in a counterclockwise direction), so I am moving at a speed of 107,000 kph minus 1,600 kph with respect to the Sun. For people on the opposite side of the Earth, the minus becomes a plus, because they are on the side of Earth spinning in the same direction as the Earth’s motion in space. (The plus and minus are not exact, but again, we’re only making Fermi estimates.)

Still we can go on. The Sun is around the center of our galaxy at 720,000 km/h. Meanwhile, our galaxy is on a collision course with the neighboring Andromeda Galaxy, moving towards it at 402,000 km/h. (The collision will not happen in 4 billion years.)

So even while sitting still relative to the ground, we, all of us, are hurtling at astronomical speeds relative to the rest of the universe. Sometimes it is nice to remember that.

Topics: Speed , Science , Earth , Enrico Fermi , Andromeda Galaxy , Physics
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