# Rotation question

1. Aug 18, 2004

### Sidewalk

Hello there -

You may remember me from such lackluster questions as what happens to light when it fades? Thanks to everyone for clear responses on that one, I get it now.

Anyhow, my new confusion surrounds the rotation of the planet.

OK - The earth rotates once on it's axis in 24 hours in what for the purposes of simplicity I'll say is in an easterly direction, or counter clockwise if we were looking down on the planet from above the north pole.

My question involves flight times, say from Tokyo to a city somewhere in the eastern hemisphere located directly on the opposite side of the planet, for the sake of argument let's say Kansas City. Let's say that the flight itself takes roughly 12 hours travelling in an easterly direction. It stands to reason that if there were limited or no wind that the travelling time would be the same for the trip heading westward.

Now, here comes the stupid element of my question: Since the earth is spinning at a rate of one rotation per 24 hours, it's rotates halfway around in 12 hours. It seems fair to me (although I know logically it's wrong) to imagine that one could leave Tokyo, float directly up off the earth's surface in a helicopter for example for 12 hours, then go straight down again, and land somewhere on the other side of the planet. I know this is wrong, I'm just not sure why.

I assume that the reason is that our atmosphere is rotating at the same speed as the earth, so although we think we're staying still we're actually rotating right along with it if we float straight up. If this is the case then wouldn't flying in one direction (along with the planet's spin) get us to our destination at a different time than if we were travelling against the grain so to speak?

Sorry for a long winded simple question, but I'm interested in finding out...

Thanks again -
Sidewalk

2. Aug 18, 2004

### BobG

If the airport were located on the equator, the plane would be travelling a little over 1000 mph while sitting on the ground at the end of the runway.

If the plane travels 300 mph in an easterly direction after take-off, you have to take into consideration that the '300 mph' is only a relative speed. In actuality, the plane is travelling a little over 1300 mph (forunately, the atmosphere is travelling a little over 1000 mph to the east, as well, or wind resistance would be a huge problem).

If the destination airport were also located on the equator, about 12,500 miles away, the destination airport is also moving a little over 1000 mph to the east. Since the plane is travelling 300 mph faster than the destination airport, it will eventually catch up (in about 42 hours).

If the plane travels to the west at 300 mph (relative speed), it is really travelling east at about 700 mph. Since the destination airport is travelling to the east at about 1000 mph, the airport eventually catches up to the plane (in about 42 hours).

For travel time, it's easier just to consider relative speed, which is why we do just list relative speed for things like the speedometer on our car.

Plus, if people driving west thought about how they were really travelling east at a 1000 mph, they might be tempted to drive with their heads pointed towards the rear window. :tongue2:

3. Aug 18, 2004

### Cyrus

Heres somthing to think about, if you were in that helicopter, you would naturally want to stay over some fixed point because your brain would want to 'think' its just hovering. So you would naturally inch your way forward as the earth rotates with you so that in your mind, you are stationary. In actuality, you would be canceling out the effect of the earth rotating below you. If there was absolutely no air currents causing you to drift, I do think you are correct, you would end up somewhere else in the world, however, you have to realize how slow the earth rotates. To you, it would feel like you went no where in a hurry. Watch the sun in the sky, it goes up and down in 12 hours (more or less), but for after one hour of staring, it seems to just stand in place the whole time. I think the reason you might think this does not seem right is becauase of the large time scale involved that it would take to stay up there for 12 hours. A typical flight from the east coast to europe is around 6 hours, but here you are fighting wind, drag, weight etc. I think this would be an example of the coriolis effect, the earth spinning about its axis. I have read that trains experience effects of the earth rotating as they travel longs distances north-south. This is because the earth rotates in one constant direction. The result is that it wears one side of the tracks more than the other. This is an example of what your talking about. The train is just going north south, but the earth is trying to make it rotate east-west, thus wearing out the track, just like the earth would rotate below you, and you could land at some other location. I would think that the main difference is where on earth you are. If you were near the poles, you could take off and land back where you started in a shorter distance, whereas near the equator, you would travel the greatest distance. This would mean you traveled fastest along the equator, since you did one revolution in the same amount of time as up at the pole, but you went a greater distance. Im not sure if I am right, but it may provide some insight into the problem. If not, im sorry i steared you in the worng direction.

Good luck,

Cyrus