[TETENAL]

You probably all know this effect in figure skating where when the figure skater makes a pirouette and has her arms stretched out she is spinning slowly and when she moves her arms together she will spin faster.

Now I had the following thought process: At day we are all standing or walking around, so we have a center of gravity at 100 cm above the ground maybe. However, at night when we all lay down to sleep the center of gravity is only a little bit higher than the height of the bed, let's say at 45 cm. For the earth this would by like pulling her arms together. And of course most animals lay down to sleep as well at night, so the effect is even higher.

Now you might say, that when it is night at one half of the earth, it is day at the other, so the effect balances out (like a figure skater alternately stretching out only one arm and then only the other). I thought of this too. But with the Pacific being so large, there are more people living on one side of the earth with more of the contents than on the other side with the Pacific.

So the question is: Does the earth rotate faster at night, if ever so slightly? Did anybody try to measure this?

[Spook E]

doubt it cos all the people are moving about in different directions.

More importantly how come i can look at the window at 2pm and see the moon when its supposed to be over america (somewhere) and the it mysteriously rises from the east when i already saw it around lunch time.

Freak-o!

[greenamp]

If we were all 10 miles tall and weighed several thousand tons it might make a difference. But we are so small compared to the size of the earth it doesn't effect anything. It would be like a figure skater with arms 1/10 of a mm long.

[black bear theory]

Originally Posted by TETENAL

You probably all know this effect in figure skating where when the figure skater makes a pirouette and has her arms stretched out she is spinning slowly and when she moves her arms together she will spin faster.

Now I had the following thought process: At day we are all standing or walking around, so we have a center of gravity at 100 cm above the ground maybe. However, at night when we all lay down to sleep the center of gravity is only a little bit higher than the height of the bed, let's say at 45 cm. For the earth this would by like pulling her arms together. And of course most animals lay down to sleep as well at night, so the effect is even higher.

Now you might say, that when it is night at one half of the earth, it is day at the other, so the effect balances out (like a figure skater alternately stretching out only one arm and then only the other). I thought of this too. But with the Pacific being so large, there are more people living on one side of the earth with more of the contents than on the other side with the Pacific.

So the question is: Does the earth rotate faster at night, if ever so slightly? Did anybody try to measure this?

no. it's probably not anything that we could measure leastways.

the mass of humans on earth is infinitely miniscule compared to a figure-skaters arms and her body. the mass of tidal water is by far much more substantial.

weren't the chinese threatening to throw us out of orbit by all jumping at the same time?

[Mister Elf]

Uh...it's always day somewhere on Earth, and, likewise, always night somewhere on Earth. The terminator line doesn't move enough, if at all, for this to be possible.

[TETENAL]

Originally Posted by black bear theory

the mass of humans on earth is infinitely miniscule compared to a figure-skaters arms and her body.

I know the effect would be miniscule. But even though it is interesting to think about there is an effect on rotation speed, even if not yet measurable. And you are forgetting animals which also are adding to the effect.

[meelk]

hahahahahahaahahahahahahahahahahaha

[wallinbl]

Height of man: 1.6 m
Diameter of earth: 25,512,540 m

Mass of man: 100 kg
Mass of Earth: 5,973,600,000,000,000,000,000,000 kg

Aside from that, there are people on all sides of the planet, so it's not like you could have the combined effect of 3 billion people, since the people on the other side are in the opposite state.

[f1000]

Originally Posted by TETENAL

So the question is: Does the earth rotate faster at night, if ever so slightly? Did anybody try to measure this?

It might rotate slower or faster depending on how living organisms redistributed their net masses at night. You assume that most organisms lower their centers of mass during sleep, but many birds roost in treetops. Also, humans in first world countries often sleep in beds that elevate their supine centers of gravity from off the floor.

I propose that geophysical effects, such as the rapid cooling of continental landmasses at night, have more of an effect on rotational speed than the movement of living organisms.

[demibob]

Originally Posted by wallinbl

Height of man: 1.6 m
Diameter of earth: 25,512,540 m

Mass of man: 100 kg
Mass of Earth: 5,973,600,000,000,000,000,000,000 kg

Aside from that, there are people on all sides of the planet, so it's not like you could have the combined effect of 3 billion people, since the people on the other side are in the opposite state.

+ when your lying on a bed your raised above the ground so on average your body parts would be the same distance from the ground
this thread is a bit rediculous anyway

[f1000]

Originally Posted by wallinbl

Height of man: 1.6 m
Diameter of earth: 25,512,540 m

Mass of man: 100 kg
Mass of Earth: 5,973,600,000,000,000,000,000,000 kg

It doesn't matter how small a single man is versus the mass of the Earth: conservation of mass and energy dictate that the rotation of the Earth/man system must react to the movement of a single human or even bacterium on its surface.

Originally Posted by wallinbl

Aside from that, there are people on all sides of the planet, so it's not like you could have the combined effect of 3 billion people, since the people on the other side are in the opposite state.

People aren't anywhere near evenly distributed across the Earth's surface.

[MM-o4]

it is always day some where!

nice try

MM

[Kerrigan]

Did you know that when you are standing up, your head is moving faster than your feet? Only slightly, but it is still traveling about the centre of the earth at a faster speed. And according to Einstein, time would be passing at a slower rate in your head due to the effects of speed on the spacetime continuum.

[Chuckit]

The physics aren't exactly the same. The inertia change created by a figure skater holding his arms out in earth's gravity doesn't really have an analogue when you're talking about a planet floating in the vacuum of space. Even if so, though, I imagine it would be such a minuscule effect that it wouldn't really determine the planet's speed by even a tiny amount. The effect of tides, seismic activity and heat change is much greater than any friction our tiny mass could create, so we couldn't cause the earth to rotate slower at night.

I'm not any kind of physics expert or geologist, though. That's just what I think from what I know.

[Ghoser777]

Originally Posted by demibob

this thread is a bit rediculous anyway

Is there any other kind?

[Fyre4ce]

Originally Posted by f1000

It doesn't matter how small a single man is versus the mass of the Earth: conservation of mass and energy dictate that the rotation of the Earth/man system must react to the movement of a single human or even bacterium on its surface.


People aren't anywhere near evenly distributed across the Earth's surface.

This is the scientist's perspective. I'm an engineer. I say, if there is an effect, it's negligible for all practical purposes. End of story.

[euchomai]

Originally Posted by Fyre4ce

This is the scientist's perspective. I'm an engineer. I say, if there is an effect, it's negligible for all practical purposes. End of story.

What does driving trains have to do with this?


kidding (not funny, I know)

[f1000]

Originally Posted by Chuckit

The physics aren't exactly the same. The inertia change created by a figure skater holding his arms out in earth's gravity doesn't really have an analogue when you're talking about a planet floating in the vacuum of space.

This is wrong, period.

Originally Posted by Chuckit

Even if so, though, I imagine it would be such a minuscule effect that it wouldn't really determine the planet's speed by even a tiny amount. The effect of tides, seismic activity and heat change is much greater than any friction our tiny mass could create, so we couldn't cause the earth to rotate slower at night.

Again, this is wrong. You can't say that just because we're miniscule we have no effect on the physical system.

[f1000]

Originally Posted by Fyre4ce

This is the scientist's perspective. I'm an engineer. I say, if there is an effect, it's negligible for all practical purposes. End of story.

"No theories for you!"

[goMac]

The reason the ice skater can do that is because by folding in her arms she's no longer fighting air resistance.

There is no air in space, therefore the Earth isn't fighting air resistance, therefore things sticking out from the Earth don't matter.

In other words: no.

[wataru]

More important than lying down vs. standing up would be the average elevation of workplaces vs. beds. Even more important than that would be population densities weighted by elevation of land masses, and distribution of land masses across the face of the earth. For the sake of argument, let's assume that all of these work out to what you're hypothesizing--that waking people contribute more to the earth's moment of inertia than sleeping people do.

The next problem is that it's always night for one half of the earth. That means that an ice skater is not an appropriate model for the situation. The ice skater changes his or her moment of inertia by extending or contracting his or her arms, changing the distribution of mass by changing shape. For all intents and purposes, the earth is not changing its shape at all--it always has a "lump" of waking people facing the sun, and a lesser lump of sleeping people facing away from the sun. Since the distribution of mass is not changing here except for relative to the earth's geological features, there is no change in moment of inertia and so no change in rotational speed.

So, in other words, no.

If you could get all of the Western hemisphere to stand up and all of the Eastern hemisphere to sit down all at once for a length of time, then hypothetically there would be an effect. But even then it would be so minimal as to be undetectable.

Originally Posted by goMac

The reason the ice skater can do that is because by folding in her arms she's no longer fighting air resistance.

There is no air in space, therefore the Earth isn't fighting air resistance, therefore things sticking out from the Earth don't matter.

In other words: no.

Right conclusion, utterly wrong premises. This has very little to do with air resistance. It's all about moment of inertia, an object's resistance to rotation. The more of an object's mass is concentrated near the axis of rotation, the more easily it will rotate.

[f1000]

Originally Posted by Kerrigan

Did you know that when you are standing up, your head is moving faster than your feet? Only slightly, but it is still traveling about the centre of the earth at a faster speed. And according to Einstein, time would be passing at a slower rate in your head due to the effects of speed on the spacetime continuum.

1. SR: Your head and feet are in the same inertial frame of reference (i.e., they're not moving with respect to one another); hence, no time dilation between them.

2. GR: Your feet are closer to the center of the Earth than your head is, which means that they are in a slightly stronger gravitational potential; hence, the clock in your head runs faster than the one in your feet.

3. GR: As the Earth rotates, it drags spacetime around it. Someone else is going to have to explain how this might cause time dilation between the head and the feet.

[Chuckit]

Originally Posted by f1000

Again, this is wrong. You can't say that just because we're miniscule we have no effect on the physical system.

You just took what I said and turned it into a bizarre absolute.

Me: "There are more significant factors, so our position alone would not determine whether the earth spins faster or slower."
You: "This is wrong! You can't say we have no effect on the physical system!"

[Railroader]

Originally Posted by euchomai

What does driving trains have to do with this?

kidding (not funny, I know)

At work when things are extremely FUBAR I always ask my bosses for a train driver to get this thing back on track. I always get that "Did you jst say you kissed my sisiter" look.

SLIGHTLY ON TOPIC: what would happen if everyone on Earth ran in the same direction as fast as they could?

[black bear theory]

if you really wanted to study this you could do it on the moon!

no tectonic forces, no tides, and very few people have walked on the moon (and they all returned to the same spot) and it's the closest non-earth spot.

you'd also have to set up a sidereal frame of reference since you can't do it relative to any earthly reference point.

but i bet, all that work and you'd still not find anything!

[wataru]

Originally Posted by f1000

1. SR: Your head and feet are in the same inertial frame of reference (i.e., they're not moving with respect to one another); hence, no time dilation between them.

No, if we're bothering to consider the difference in gravity over the length scale of the human body, your feet and head are not in the same inertial frame. They're not in an inertial frame at all, since they're accelerating (with rotation). And they are moving relative to each other--over one revolution of the earth your head goes from above your feet to below them and back.

2. GR: Your feet are closer to the center of the Earth than your head is, which means that they are in a slightly stronger gravitational potential; hence, the clock in your head runs faster than the one in your feet.

But they're not accelerating due to gravity, except as it's gravity that attaches them to the earth and causes them to rotate. My relativity isn't so great, but I think time dilation is due to velocity only. Gravity comes in because in general it causes things to increase velocity, but not in this case because the earth's surface is preventing us from accelerating down any further.

3. GR: As the Earth rotates, it drags spacetime around it. Someone else is going to have to explain how this might cause time dilation between the head and the feet.

The earth distorts spacetime so that your feet and head follow the shortest paths in curved spacetime. That should lead us to the same conclusions as before.

To clarify this "are we accelerating" thing: Acceleration is a change in velocity. Velocity is not just speed; it has a direction. So we can be accelerating without changing speed--we'd then be changing direction only. Rotation is just such an acceleration.

[black bear theory]

Originally Posted by Railroader

SLIGHTLY ON TOPIC: what would happen if everyone on Earth ran in the same direction as fast as they could?

a big log-rolling contest?

[wataru]

Originally Posted by Railroader

SLIGHTLY ON TOPIC: what would happen if everyone on Earth ran in the same direction as fast as they could?

Well I assume you mean what if everyone ran in the same direction parallel to the equator.

As everyone accelerated the earth would accelerate the other way. So if everyone ran West, rotation would accelerate so that the day would be shorter. If everyone ran East, the day would be shortened.

But due to conservation of momentum as soon as everyone stops running and presumably slows themselves down with friction to match the earth's speed, everything will go back to exactly the way it was.

If everyone ran North or South it wouldn't affect the rotation at all except by minutely changing the moment of inertia. If everyone ran until they converged on one of the poles, then I suppose that would decrease the moment of inertia and the earth would spin faster.

[Chuckit]

Originally Posted by wataru

As everyone accelerated the earth would accelerate the other way. So if everyone ran East, rotation would accelerate so that the day would be shorter. If everyone ran West, the day would be shortened.

I think you mean running east would decelerate it and lengthen the day.

[wataru]

Yes, I had that reversed. Thanks.

[11011001]

This sounds like the plot of some super villain: make everyone sleep, all over the world, thus causing it to spin to such speeds so as to shed the atmosphere and exterminate all life as we know it.

[f1000]

Originally Posted by wataru

No, if we're bothering to consider the difference in gravity over the length scale of the human body, your feet and head are not in the same inertial frame. They're not in an inertial frame at all, since they're accelerating (with rotation). And they are moving relative to each other--over one revolution of the earth your head goes from above your feet to below them and back.

Yes, you're right, I shouldn't have said that they were in an "inertial" frame of reference.

What I was trying to do was use the equivalence principle to break the system into two parts: one that considered the relative motion between the head and the feet and one that considered the relative forces (accelerations) on the head and the feet.

As I pointed out before, there's no relative velocity between the head and the feet; hence, no time dilation due to relative velocities alone. There is a relative acceleration between the head and the feet, though, caused by both centrifugal forces and gravitation.

The following formula shows the difference in time:

<Placeholder>

It should be apparent that gravity is the far greater contributor to time dilation than centrifugal forces; hence, why I neglected to mention the latter in statement 2.

[f1000]

Originally Posted by Chuckit

You just took what I said and turned it into a bizarre absolute.

Me: "There are more significant factors, so our position alone would not determine whether the earth spins faster or slower."
You: "This is wrong! You can't say we have no effect on the physical system!"

Sorry, Chuckit, I can sound condescending when I'm just being lazy. In any case, if I misunderstood your original statement, then pardon moi.

[Spook E]

but what about the flippin moon!!??!!

[Railroader]

Originally Posted by Spook E

but what about the flippin moon!!??!!

I just saw a show on the Science channel called "If We Had No Moon" (or something like that) and I was amazed at how important the moon is to life on Earth. And that the moon is drifting farther away every year.

Basically, if we had no moon, life would never have been able to form because the moon keeps Earth in a steady rotation on it's axis.

[andreas_g4]

Yes, the earth does move faster. And - what gives me sleepless nights - if all chinese people synchronously jump from a table, the earth would be catapulted out of its orbit around the sun! Seriously.

[Rolling Bones]

Does the world rotate faster at night?

Only when the bar closes.

[wataru]

Originally Posted by f1000

As I pointed out before, there's no relative velocity between the head and the feet

But there is. If they change relative position, there is a relative velocity. It just doesn't happen to be in what we would normally consider the up-down direction (radially away from the earth). They basically orbit each other.

[OreoCookie]

Sure there is an effect. Here's another one:

Take a spoon and lift if 10 cm from the surface of the table. Now drop it. I can assure you (as a physicist) that you have influenced the orbit of the moon around the earth. Scary isn't it?

[Cubeoid]

Ba Ba Ba ba bloom bloom!

[analogika]

Originally Posted by goMac

The reason the ice skater can do that is because by folding in her arms she's no longer fighting air resistance.

There is no air in space, therefore the Earth isn't fighting air resistance, therefore things sticking out from the Earth don't matter.

In other words: no.

Wrong.

[OreoCookie]

Originally Posted by goMac

The reason the ice skater can do that is because by folding in her arms she's no longer fighting air resistance.

There is no air in space, therefore the Earth isn't fighting air resistance, therefore things sticking out from the Earth don't matter.

In other words: no.

Maybe you should brush up on your physics
The answer is energy conservation plus a change in the rotational inertia of the skater and has nothing to do with air resistance.

[TETENAL]

Originally Posted by MM-o4

it is always day some where!

It's always day somewhere, but there aren't people everywhere!



Obviously when it's night in Hawaii there are fewer people lying down than when it's night in India and China. That causes an uneven distribution of living beings lowering their body over the day depending where on earth it is night at the moment. So the earth might slightly speed up when it's night over a certain place, unless there are other effects that cause it to slow down. Someone mentioned the temperature of water/continents at night, but I don't see how that could have an effect. The temperature doesn't change the mass.

[turtle777]

Obly if ALL men went to bed at the same time, in the same bed. Uhm, not, wait ?

[JHromadka]

What if all the people on one side of the world were to lay down next to their toilets and flush them at the same time? Not only would the center of gravity be lower, but the water going down the toilet would cause the Earth to rotate even faster!

[turtle777]

And what if all people would turn on their hair dryers at the same time ?
No, wait, been there, done that, got that T-Shirt.

[SVass]

During a time out in the Super Bowl, many toilets ARE flushed simultaneously. Has there been a noticeable effect? sam

[turtle777]

Originally Posted by SVass

During a time out in the Super Bowl, many toilets ARE flushed simultaneously. Has there been a noticeable effect? sam

Floodings downstream ?

-t

[f1000]

<Continued from the placeholder above>

From Turcotte & Schubert, g can be calculated for any point above the Earth's surface (neglecting centripetal acceleration) as follows:



h = height above sea level
M = mass of the Earth
r = equatorial radius of the Earth
J = ellipticity
φ = latitude

To calculate g at the equator, set φ equal to zero,



Using the binomial expansion, we can approximate this g for small values of h,





The energy lost by a photon moving from sea level to a height, h, can now be calculated as follows,*



From this result, we can calculate the percent change in frequency of the photon,



Thus, neglecting the contribution of centripetal acceleration, a person of height h=1.8m standing at the equator would observe a clock at his feet to run 1 part in 5,070 trillion slower than one at eye level due to gravitational time dilation.

-----

The time dilation due to centripetal acceleration between sea level and a height, h, above it is,



c = speed of light
ω = rotational angular velocity of the Earth

From this, we can calculate the percent time dilation,



Using the binomial expansion,



Thus, a person of height h=1.8m standing at the equator would observe a clock at his feet to run 1 part in 1,472 quadrillion faster than one at eye level due to centripetal acceleration alone.

-----

Further points:

Originally Posted by f1000

1. SR: Your head and feet are in the same inertial frame of reference (i.e., they're not moving with respect to one another); hence, no time dilation between them.

I want to emphasize that the head and feet are not in an inertial frame of reference, but I'm pretending that they are to show that time dilation between them is mainly due to differences gravitational potential.

Originally Posted by f1000

2. GR: Your feet are closer to the center of the Earth than your head is, which means that they are in a slightly stronger gravitational potential; hence, the clock in your head runs faster than the one in your feet.

I should have said that your feet are at a slightly lower gravitational potential. The force of gravity is indeed stronger closer to the Earth's surface, but that's not the primary reason for gravitational time dilation.

*For some reason I can't type h-hat.

[olePigeon]

Here's a theory my dad came up on how to blow up the Earth:

The planet Earth, as you may know, oscilates at a certain frequency. As with glass you can have it resonate and eventually become unstable and break.

So what you can do is build a giant platform 20 feet high in China and have the entire population of China get onto the platform.

At the exact moment when the oscilation is at its peak in China, EVERYONE jumps off the platform at the same time.

Then the Earth will explode ...






























... from the sound of 4 billion Chinese people crying out in horror when their legs are broken.

( He told this to us when we were in a Chinese resturant of all places. Thankfully, it was after we ate. )