Of Particular Significance

# Chapter 2, Endnote 8

Keeping track of time zones and the motion of planes can be confusing. It would be easier if the Earth weren’t spinning and if the atmosphere were rigid — that is, there were no wind.

I’ve already explained the difference between ground speed and airspeed by focusing on the effect of the wind, that is, the motion of air relative to the ground. But now, to keep things simpler and set our focus on the effect of the Earth’s spin, let’s imagine that the Earth had no wind. If that were the case, then the Earth’s air would rotate in the same way as does the Earth’s rock, as though it were icing on a spherical cake, making ground speed and airspeed the same.

With that simplification, let’s take consider two very simple plane journeys. The animation below shows two planes, one (green) flying west and one (red) flying east along the equator, having taken off from an airport shown in yellow. The Earth rotates west to east, carrying the airport along with it on a 24 hour journey, half of which is spent in sunlight and half of which is spent in darkness. From the point of view of someone standing on the Earth, the two planes are flying in opposite directions at exactly the same ground speed (remember we’ve set the wind to zero, so airspeed and ground speed are equal); notice that the distance between the green and yellow dots grows at the same rate as the distance between the red and yellow dots.)

However, from our perspective, at rest relative to the Sun and watching the Earth rotate, both planes move east to west! The plane trying to fly east is carried rapidly to the east by the combination of its flight through the air and the Earth’s rotation. The plane trying to fly west makes progress relative to the ground, but the spinning ground overwhelms its westward motion and carries it to the east after all.

Correspondingly, from the point of view of the eastward-flying plane, the day is very short — the Sun crosses its sky much more rapidly than it does if you’re standing on the ground. Meanwhile, those on the westward-flying plane do see the Sun rise in the east, as usual, and set in the west, but its motion is far slower than for someone on the ground, and the day lasts much longer than it usually does.

More concretely, if you look at my animation carefully, you’ll see that it lasts 24 hours (the yellow dot starts and ends at the far left) and in that time,

• from the perspective of someone on and rotating with the Earth, the red plane travels halfway around the globe to the east, while the green plane travels halfway around the globe to the west
• from the perspective of someone near the Sun, or otherwise stationary relative to the Sun, the red plane travels one and a half times around the globe to the east, while the green plane travels halfway around the globe to the east

and so the motion of the red plane is three times as fast relative to the Sun as it is relative to the ground, while the green plane moves equally fast relative to the Sun as it does to the ground, but in the opposite direction! Notice that this means that, along the lines pointed out in the original endnote,

• The pilots on the red plane see two sunsets and one sunrise in that 24 hours
• The pilots on the green plane see only a single sunset, with no sunrise, in that 24 hours

The more general lesson, once we consider more complicated plane flights and account for wind, is that motion relative to the ground, the air, and the Sun are all different, and all of them have consequences that pilots and airlines need to account for!

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A decay of a Higgs boson, as reconstructed by the CMS experiment at the LHC