B How does Earth's rotation affect our movement?

[Clair de Lune]

TL;DR Summary

Even though Earth's linear and constant motion, shouldn't it affect our movement? I've never been able to understand why it takes the same amount of hours to reach the same distances by plane, regardless of the direction of travel.

How is it possible that Earth's rotation doesn't affect our relative velocity? In other words, if I walk in the opposite direction of Earth's rotation, shouldn't I reach destinations faster than if I walk in the same direction?

Sorry if the terms are not that accurate, I’m an architect!

 

[Baluncore]

Welcome to PF.

In other words, if I walk in the opposite direction of Earth's rotation, shouldn't I reach destinations faster than if I walk in the same direction?

All things are relative.

If you walk towards the west, you weigh more than when you walk towards the east. That slows you down when walking on soft ground. It happens because Earth's rotation reduces your weight by about 0.3%.

The time also depends on how many time zones you cross, and if you cross the dateline.

If your destination is 1 km east of your current position, you will not get there quicker if you walk west.

 

[Ibix]

How is it possible that Earth's rotation doesn't affect our relative velocity?

The answer depends a bit on how you choose to frame the question. Perhaps the most straightforward way is to imagine being in a spaceship hovering above the Earth watching the world turn. You could watch a person sitting in a chair on the equator. They are moving at 1000mph in a circle.

Then they get up and walk towards a house due east of them. People can typically walk at 4mph, so from our spaceship vantage point we see the person accelerate from 1,000mph to 1,004mph. But their destination is attached to the Earth, so it's moving in the same direction at 1,000mph and the person is only closing the gap at 1,004 - 1,000 = 4mph.

Once the person reaches the house they turn round and come back. Since they're now walking west, their speed is reduced from 1,000mph to 996mph. So from this perspective they are still going east - just not quite as fast as their chair which is still doing 1,000mph. Again, the gap between them closes at 1,000 - 996 = 4mph.

In summary, then, the rotation makes no difference to travel times because it's the difference in speed between the person and their destination that matters.

As @Baluncore points out, there are a number of ways in which this isn't quite true because the fact that the surface of the Earth is moving in a circle does matter. However, the effects are tiny on a human scale. Unless you are into detailed mathematical modelling of the weather, or are a gunnery officer on a battleship, you'll never notice them.

 

[PeroK]

TL;DR Summary: Even though Earth's linear and constant motion, shouldn't it affect our movement? I've never been able to understand why it takes the same amount of hours to reach the same distances by plane, regardless of the direction of travel.

How is it possible that Earth's rotation doesn't affect our relative velocity? In other words, if I walk in the opposite direction of Earth's rotation, shouldn't I reach destinations faster than if I walk in the same direction?

Sorry if the terms are not that accurate, I’m an architect!

The Earth rotates at about $400 \ m/s$ at the equator. If you can jump into the air for $1s$, then you would expect to land $400 \ m$ west of where you started? Assuming there are no buildings in the way.

 

[Baluncore]

In other words, if I walk in the opposite direction of Earth's rotation, shouldn't I reach destinations faster than if I walk in the same direction?

When you walk on an escalator or a travelator, you get there faster if you walk in the direction of travel, rather than against the direction of travel.

“It's not the destination, it's the journey”. Ralph Waldo Emerson.
If you walk against an escalator, you will meet more interesting people during your journey, than if you walk with it. If you stand still, you will be alone.

 

[A.T.]

if I walk in the opposite direction of Earth's rotation, shouldn't I reach destinations faster than if I walk in the same direction?

When you walk in a train that moves at constant speed, do you get faster from the front to the back, than in the opposite direction? Does the answer change, if the train moves in a large circle?

 

[Clair de Lune]

Yes, that's true. But if I'm located at point A and points B and C are both 500 meters away from me, B is moving towards me and C is moving in the same direction… which one do I reach first?!

 

[Bandersnatch]

Nothing on Earth is moving towards you as a result of its rotation, though. You and all of it rotate together.

 

[A.T.]

Yes, that's true.

What is true? Please use the quote function.

 

[jbriggs444]

[...] if I'm located at point A and points B and C are both 500 meters away from me, B is moving towards me and C is moving in the same direction… which one do I reach first?!

This seems to have little to do with the situation you first asked about.

So you are walking along a sidewalk which you consider to be at rest. 500 meters in front of you, you see the two objects rolling along the sidewalk. One rolling toward you and one rolling away from you.

You reach the one that is rolling toward you first, of course.

The situation on the rotating Earth is not very similar. You are sitting on the sidewalk. You consider the sidewalk to be at rest. [Someone else claims that both you and the sidewalk are moving eastward]. You look westward and see an object at rest on the sidewalk. [Someone else claims that the object is moving eastward toward you as you recede eastward from it]. You look eastward and see another object at rest on the sidewalk. [Someone else claims that the object is moving eastward as you chase eastward toward it].

You can clearly see that both objects are 500 meters away. At 1 meter per second, it will take you 500 seconds to reach either one.

The someone else also sees that both objects are 500 meters away from you and sees the sidewalk moving at nearly 500 meters per second eastward as a result of the Earth's rotation. He sees you swept away from the westward object at 499 meters per second eastward as the object moves at 500 meters per second toward you. Net closing rate: 1 m/s. Elapsed time until you meet: 500 seconds.

Similarly, that someone selse sees you approaching the eastward object at 501 meters per second as it flies away at 500 meters per second. Net closing rate: 1 m/s. Elapsed time until you meet: 500 seconds.

 

[Herman Trivilino]

Note that spacecraft are launched eastward to take advantage of Earth's rotation.

 

[Clair de Lune]

@jbriggs444 --
Thank you very much for this comprehensive explanation. This question particularly disturbs me when it comes to flights. In my mind, Earth's rotation should have a much greater impact on flight durations.

 

[PeroK]

Thank you very much for this comprehensive explanation. This question particularly disturbs me when it comes to flights. In my mind, Earth's rotation should have a much greater impact on flight durations.

The atmosphere is rotating with the Earth, so if you want to fly faster westwards, you still need the greater airspeed. If the atmosphere didn't rotate with the Earth, then there would be permanently strong easterly winds at the surface. Why does the atmosphere rotate?

https://physics.stackexchange.com/questions/1193/why-does-the-atmosphere-rotate-along-with-the-earth

 

[Clair de Lune]

The atmosphere is rotating with the Earth, so if you want to fly faster westwards, you still need the greater airspeed. If the atmosphere didn't rotate with the Earth, then there would be permanently strong easterly winds at the surface. Why does the atmosphere rotate?

https://physics.stackexchange.com/questions/1193/why-does-the-atmosphere-rotate-along-with-the-earth

Thank you so much! This is so mind blowing!!

 

[hutchphd]

Of course the direction of pravailing wind currents in the atmosphere are in fact caused mostly by the rotation of the earth, but not in a simple way. So when flying in the jet stream thank (or blame) the rotation, solar heating, and Coriolis Force.

 

[Herman Trivilino]

Get on a jet plane in Boston at noon, headed for San Fransisco. You cross three time zones and the flight takes 3 hours. So it's noon in San Fransisco when you land. What happened? While you were flying the Earth rotated under you. You didn't move far, but the Earth did.

 

[jbriggs444]

Get on a jet plane in Boston at noon, headed for San Fransisco. You cross three time zones and the flight takes 3 hours. So it's noon in San Fransisco when you land. What happened? While you were flying the Earth rotated under you. You didn't move far, but the Earth did.

That jet is about twice as fast as an ordinary commercial airliner. The first direct flight I found was just a bit under six hours. So if you start at 12:00 Eastern, it'll be 3:00 pm Pacific when you land.

 

[PeroK]

Get on a jet plane in Boston at noon, headed for San Fransisco. You cross three time zones and the flight takes 3 hours. So it's noon in San Fransisco when you land. What happened? While you were flying the Earth rotated under you. You didn't move far, but the Earth did.

You have to specify the reference frame in which "you didn't move far". I guess you mean in a reference frame that is not rotating with the Earth. That is no more an absolute frame of reference than the surface of the Earth. While you were flying, you and the Earth moved about 300,000 km in the orbit round the Sun. And the Sun moved in its orbit about the galactic centre and so on.

 

[Herman Trivilino]

I guess you mean in a reference frame that is not rotating with the Earth.

Correct. I thought that was implied but you're right, I should have specified it.

 

[Herman Trivilino]

That jet is about twice as fast as an ordinary commercial airliner.

Yes, I know. It would have to be something like the old Concorde.