## Change in Earth's Axis and Rotational Speed

Having read with interest the submissions made with regard to the above subject. A number of theories were put forward to account for the fluctuation of Earth's rotational speed, it was though, surprising that no mention was made of the influence 'leaf-fall' has by the physical movement of millions of tons of vegetation closer to the center of gravity in either of the two hemispheres!
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 Admin Not the same mass, and the fall is only 100 ft or so, and less at temperate latitudes. The two hemispheres are 6-mo out of phase. And the leaves grow back in the spring. The shift in earth mass is more or less permanent, or changes slowly over a much longer time scale.
 I have a question. Does the amount of pounds of thrust against the earth necessary to project vehicles into space have any possible bearing on change in earth's axis and rotation?

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## Change in Earth's Axis and Rotational Speed

 Quote by K.R.C. I have a question. Does the amount of pounds of thrust against the earth necessary to project vehicles into space have any possible bearing on change in earth's axis and rotation?
Theoretically, yes. Angular momentum is a conserved quantity.

Practically speaking, no. I calculate that the Earth's rotation rate slows by about 10-17 seconds for every kilogram put into geostationary orbit. Having a million metric tons of stuff in geostationary orbit would increase the length of day by 12 nanoseconds.

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 Quote by D H Theoretically, yes. Angular momentum is a conserved quantity. Practically speaking, no. I calculate that the Earth's rotation rate slows by about 10-17 seconds for every kilogram put into geostationary orbit. Having a million metric tons of stuff in geostationary orbit would increase the length of day by 12 nanoseconds.
Great news! I get a longer shower in the morning.
 not sure if your on about the link between weather and changes in atmospheric pressure was what you meant in your original question but it is not proven yet but there is strong evidence for it i am led to believe. it is according to NASA "atmospheric pressure fluctuations may affect how our planet rotates on its axis". http://www.nasa.gov/centers/goddard/...0rotation.html

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 Quote by misnderstudge not sure if your on about the link between weather and changes in atmospheric pressure was what you meant in your original question but it is not proven yet but there is strong evidence for it i am led to believe. it is according to NASA "atmospheric pressure fluctuations may affect how our planet rotates on its axis". http://www.nasa.gov/centers/goddard/...0rotation.html
misnderstudge, you appear to be addressing the original post here. Gundytech hasn't visited this site for quite some time.

That said, the seasonal effect of deciduous foliage on the Earth's rotation rate is very small.

Being a physics site, let's estimate. The temperate deciduous forests are shown in dark green on this map.

Note that the Eastern Asia, Western Europe, Eastern US, and far Western US & Canada account for the vast bulk of the landmass covered by such forests. I'll assume, very generously, that these forests account for 10% of the Earth's land mass. I'll also assume that the average latitude of these forests is 45 degrees. I also need an estimate of the foliage biomass and the average height of the foliage. I'll use one kilogram per square meter (an intentionally high estimate) and 30 meters (another intentionally high estimate).

The portion of the Earth's surface covered by land is about 150 million km2, so about 15 million km^2 for temperate deciduous forests. At 1 kg/m2, this results in a foliage mass of 15 billion metric tonnes. Imagine this mass as a ring around the Earth at 45 degrees latitude that springs up by 30 meters in the Northern Hemisphere spring, only to fall back down in Northern Hemisphere fall. That corresponds to a seasonal change of 4×1021 kg·m2 in the Earth's inertia tensor. Since the Earth's moment of inertia is about 8×1037 kg·m2, this season change represents a 1 part in 2×1016 change in the Earth's inertia tensor, or a 4 picosecond change in the length of a day.

Needless to say, this is immeasurably small.
 I understand that, but I was unsure how or were he/she was going with the question. My point is the surface of the planet and the atmospheric condition can change the Axis a very Small amount but not really anything measurable that is correct. but i was on about the entire earth mountains buildings trees etc, which is ever so slightly but still is measurable during large storms winds and it has been noted to be off by a fraction of a millisecond "not much but still". would i be correct in getting to this point i was trying to get across badly but still attempting
 DH - congratulation on all the work you put into the question re. earth's inertia and the very biblical 'fall of a leaf' .... Needless to say, this is immeasurably small. indeed. Off onto another topic, perhaps you can direct me to a site for explanation or in a few quick illustration clear up my understanding..... Black holes - some with masses measured in multiples of the mass of the sun, will eventually disappear from losses due to Hawking's radiation. Yet as far as I can see Hawking's radiation must be rather tiny - half the mass of a particle/anti-particle. This, it seems to me, would qualify under your rubric of 'immeasurably small'. In this context, will the earth stop rotation before one of these super massive black holes fades away?

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 Quote by misnderstudge I understand that, but I was unsure how or were he/she was going with the question. My point is the surface of the planet and the atmospheric condition can change the Axis a very Small amount but not really anything measurable that is correct.
The Earth's rotation axis undergoes measurable changes in direction and magnitude. Over the long term these changes result from the precession of the Earth's axis and transfer of angular momentum from the Earth to the Moon. Some short term variations in the rotation axis and the length of day can only be observed after-the-fact. These observed but currently unmodeled variations include are called polar motion (change in axis orientation) and variation in length of day / delta UT1 (change in rotation rate).

Below are a series of graphs that depict length of day variations.

The top plot shows the variation in length of day, with known high frequency variations removed to give a better picture of what is happening. The known high frequency component is the fourth plot in the set. Failing to remove this would result in a thick black blob that hides everything but the overall trend.

The overall trend is removed in the second plot, leaving a definite seasonal effect as the key characteristic. This seasonal effect can only be caused by transfer of angular momentum amongst the various parts of the Earth, including the atmosphere and the oceans. The International Earth Rotation and Reference Systems Service, the source of the above plot, has groups that attribute the total momentum of the Earth to the solid Earth, the oceans, the atmosphere, and the Earth's core.

 Quote by D H The portion of the Earth's surface covered by land is about 150 million km2, so about 15 million km^2 for temperate deciduous forests. At 1 kg/m2, this results in a foliage mass of 15 billion metric tonnes. Imagine this mass as a ring around the Earth at 45 degrees latitude that springs up by 30 meters in the Northern Hemisphere spring, only to fall back down in Northern Hemisphere fall. That corresponds to a seasonal change of 4×1021 kg·m2 in the Earth's inertia tensor. Since the Earth's moment of inertia is about 8×1037 kg·m2, this season change represents a 1 part in 2×1016 change in the Earth's inertia tensor, or a 4 picosecond change in the length of a day. Needless to say, this is immeasurably small.
This would be valid if all the material of the leaves stays below the trees during the winter, but most of the mass is probably water and Co2, wich will probably end up hundreds of kilometers south on average, and thus further away from the earth's axis.

 Quote by K.R.C. I have a question. Does the amount of pounds of thrust against the earth necessary to project vehicles into space have any possible bearing on change in earth's axis and rotation?
I doubt so, because most of the rocket's thrust is dissipated into turbulence of the atmosphere and lost. A different case would be if the vehicle was launched with rail-gun, like the one Navy is currently developing. In that case most of the momentum will go back into the rail and through the rail's foundation into the Earth. Now, green smoke reviews there would be some cumulative effect, because all the rockets are launched eastwards.

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 Quote by willem2 This would be valid if all the material of the leaves stays below the trees during the winter, but most of the mass is probably water and Co2, wich will probably end up hundreds of kilometers south on average, and thus further away from the earth's axis.
There also is a small amount of volatile organics lost from the leaves, but it is a small amount. Most of what is lost is water.

Leaves, when they are alive, need to be constantly supplied with water to compensate for evaporation from the leaves. Deciduous trees cut off that water supply to leaves in the fall and pull most of the degraded chlorophyll out of the leaves. Since water vapor is less dense than air, this water loss at the onset of fall will exaggerate the problem rather than ameliorate it. Less dense material moving away from the center of the Earth is equivalent to more dense material moving toward the center of the Earth.

So, double my estimate. Multiply it by a factor of ten or even one hundred. It doesn't really matter, though. My calculations would have to be many orders of magnitude low for the seasonal migration of mass from deciduous tree leaf loss to have a measurable affect on the Earth's rotation rate. I tried to make my estimates high, and the affect is still immeasurably small.

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 Quote by DROBNJAK I doubt so, because most of the rocket's thrust is dissipated into turbulence of the atmosphere and lost.
That most of the exhaust comes back to Earth means we can treat a launch of a vehicle into Earth orbit as a problem in a more-or-less isolated system. The vehicle in orbit has a good deal more angular momentum than it had when it was at rest with respect to the rotating Earth. Treating this is as a problem in an isolated system means that this gain in the vehicle's angular momentum comes at a loss in the Earth's rotational angular momentum.

The effect is of course extremely tiny.
 Stumbled across this thread while taking a googol on earthquakes and the Earth's question. Hopefully, it's ok to bump the thread back to life. Since the redistribution of mass in the Earth's surface can be caused by earthquakes, sometimes the Earth's rotation is increased or decreased by a small amount. Recent series of quakes seem to be related. To me, this makes sense, since if plate "A" should move, then plate "B" would also move. Somehow a portion of that stress would be felt by all the plates, but wouldn't necessarily result in distant quakes. But if an individual quake is big enough, could it cause some sort of chain reaction thru a large number of other tectonic plates resulting in, say, a week of global, huge quakes? After some time, a new tectonic homeostasis would be reached, but it would be a rough week for everyone on Earth. So that's one question. Then I ask, if this global shaking and quaking were to happen, could the tectonic balance around the Earth's axis be changed so much that the inclination might also change? Say, perhaps from 23.5 degrees to 24 degrees? And my third question would be regarding the Earth's core? Is it thought to be totally liquid, or does it have rotating solid chunks in it? What would be the relationship between tectonic activity on the surface, and the rotational stability of the core?
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