## What-If 0026: "Leap Seconds"

What if there was a forum for discussing these?

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ysth
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### Re: What-If 0026: Leap Seconds

Yupa wrote:After we finish fine tuning the rotation of the Earth, I'd like to work on adjusting the curvature of the universe, or at least our local patch of it, to make PI exactly 3.14175

Or make an inch exactly 2.54 centimeters. Oh, wait, we did that.
A math joke: r = | |csc(θ)|+|sec(θ)| |-| |csc(θ)|-|sec(θ)| |

MacFreek
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### Re: What-If 0026: Leap Seconds

[Leap seconds] leads to all kinds of little headaches, particularly for programmers.

I recently came accross this article by Geoff Huston, which details what sort of problems occur. It is more fascinating than I anticipated:
http://www.ipjforum.org/?p=792

Spoe
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### Re: What-If 0026: Leap Seconds

Klear wrote:
webgrunt wrote:The solution is clear. We must move the moon into a geostationary orbit.

...or push it away from orbit altogether, possibly using some kind of laser.

...or find some moon clones and set up an appropriate Klemperer rosette with them to cancel out the effects of the any tidal bulges? Of course, there'd be the station-keeping problems since these rosettes aren't dynamically stable.

danix
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### Re: What-If 0026: Leap Seconds

I was surprised that Randall didn't go and propose "nuke the moon". That's what supposedly happens in the Time Machine 2002 movie, I do wonder if the effects shown in that movie would be real though.

gmalivuk
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### Re: What-If 0026: Leap Seconds

Davidy wrote:Eventually, the moon's affect on the earth's rotation and the necessity of leap seconds will dissappear entirely.
The moon will stop affecting Earth's rotation when either Earth becomes tidally locked with it or the Moon disappears entirely. The first won't happen naturally before the Sun explodes, and the second has already been suggested as a solution, but would require substantially more energy than simply speeding up Earth's rotation a bit.
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jgh
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### Re: What-If 0026: Leap Seconds

Why not just go back in time to the 1960s and define the second as 9,192,631,780 periods of cesium instead of 9,192,631,770.

chretienorthodox
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### Re: What-If 0026: Leap Seconds

jgh wrote:Why not just go back in time to the 1960s and define the second as 9,192,631,780 periods of cesium instead of 9,192,631,770.

Because earth decelerates (in mean values), after several years new increment to secSI will be needed.

elasto
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### Re: What-If 0026: Leap Seconds

chretienorthodox wrote:
jgh wrote:Why not just go back in time to the 1960s and define the second as 9,192,631,780 periods of cesium instead of 9,192,631,770.

Because earth decelerates (in mean values), after several years new increment to secSI will be needed.

That's no problem. When the definition drifts too far out of sync you merely travel back to the 1960s to define it as the new correct value again.

So long as all the headache is on past-self and not present-self it's all good!

rmsgrey
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### Re: What-If 0026: Leap Seconds

elasto wrote:
chretienorthodox wrote:
jgh wrote:Why not just go back in time to the 1960s and define the second as 9,192,631,780 periods of cesium instead of 9,192,631,770.

Because earth decelerates (in mean values), after several years new increment to secSI will be needed.

That's no problem. When the definition drifts too far out of sync you merely travel back to the 1960s to define it as the new correct value again.

So long as all the headache is on past-self and not present-self it's all good!

The trouble lies in getting your (inaccurate) value accepted in the past...

Wnderer
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### Re: What-If 0026: Leap Seconds

Why use UTC to define anything except time of day? Everything in the background of the computer should be running on atomic time and only translated into UTC when you need to know the time of day. It should work like this.

UTC = TI at some TI = 0 point.
UTC = TI +f(TI)

where f(TI) is some function that attempts to predict UTC. The function could be some multi-point calibrated polynomial. Lets say 5 points, so;

f(TI) = A*(TI)^4 + B*(TI)^3 + C*(TI)^2 +D*(TI) + E

Some standards committee releases the coefficients. The function deals with the increasing need for leap seconds over time but because the need for leap seconds is not completely predictable, new coefficients could be released periodically that keep the curve continuous and smear the growing leap seconds. Why care if a UTC second doesn't equal a TI second? Don't use them for anything. Always convert back to TI when calculating or measuring lengths of time.

CityZen
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### Re: What-If 0026: Leap Seconds

Seems to me that part of the problem can be solved more simply. For the measure of time that needs to be constant (GPS, etc), it should use different units so that people don't confuse them with the measure of time that needs to be earth-based. The new units should follow nice decimal metrics. Perhaps something like microns, centons, etc.

Of course, there is one little problem with this: xkcd com/927 [actual link triggers spam filter]

sla29970
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### Re: What-If 0026: Leap Seconds

Wnderer wrote:Why use UTC to define anything except time of day? ...
Some standards committee releases the coefficients.

This is already possible to the current level of precision. See http://www.ucolick.org/~sla/leapsecs/right+gps.html but note that implementing it requires significant effort that violates existing practices and that there is no indication that the Powers That Be will decide on anything like this.

cdxf6465
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### Re: What-If 0026: Leap Seconds

a123dv wrote:I think blowing up the moon would be more efficient.

KA-ME-HA-ME-HAAAAAAAAAA!!!!

chretienorthodox
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### Re: What-If 0026: Leap Seconds

Leap second is problem for Network Time Protocols. US Administration is demanding not only leap second be discontinued but also atomic time to become Civil Time. Later demand is opposite by UK, Canada and China. My proposal to ITU-R, SG7 is that leapsecond to be discontinued but Civil Time to acquire its own second stepping changing in order that Civil Time follows Mean Solar Time. Second SI to remain unit for scientific purposes. Scientific unit of time must be constant for other units are depending on it.
News is that in April ITU-R, WP7A is gonig to make decision on the matter and submit to SG7.
I make note am Greek citizen living in France.
Last edited by chretienorthodox on Tue Jan 08, 2013 11:14 am UTC, edited 1 time in total.

ijuin
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### Re: What-If 0026: Leap Seconds

CityZen wrote:Seems to me that part of the problem can be solved more simply. For the measure of time that needs to be constant (GPS, etc), it should use different units so that people don't confuse them with the measure of time that needs to be earth-based. The new units should follow nice decimal metrics. Perhaps something like microns, centons, etc.

I propose that for scientific purposes we use lightspeed measurements for time. Instead of speaking of seconds, minutes, etc., we would speak of the time that it would take for light to go a certain distance. (for convenience of example I will pretend that c = exactly 300 million m/s.) Such a system would make the time measurements fixed to the local spacetime rather than linked to variable things like planetary motion.

So,that would give us something like:
a "mega" (light-megameter) would be about 3 1/3 milliseconds
a "giga" would be about 3 1/3 seconds
a "tera" would be about 0.926 hours
a "peta" would be about 38.6 days
an "exa" would be about 106 years
a "zetta" would be about 106 thousand years
a "yotta" would be about 106 million years

The age of the universe at present would be only about 130 yottas, so we are probably safe with going to exponential notation for larger amounts than that.

gmalivuk
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### Re: What-If 0026: Leap Seconds

That would be nice, if not for the fact that the meter is already defined in terms of our unit of time. Defining our unit of time in terms of the meter, therefore, wouldn't actually be a terribly good idea.
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Socks
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### Re: What-If 0026: Leap Seconds

Worth it.

Wnderer
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### Re: What-If 0026: Leap Seconds

If we want to define new standards of time, we should define the plank minute.

1 plank minute = 1 milli-yotta-yotta plank time ~= 54 seconds.
1 plank second = plank minute/60
1 plank hour = plank minute * 60

How can you go wrong with something defined as milli-yotta-yotta plank time. It's like a character out of Seinfeld. "Here comes Milly 'Yada Yada' Planktime. She always leaves out the details."

Crosshair
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### Re: What-If 0026: Leap Seconds

Chad Cloman wrote:I'm thinking a much easier way would be to get rid of the Moon. Maybe we could put some really big rockets on it and send it far, far away. We might have to make some minor adjustments to the Earth's spin rate afterwards, but tidal forces would no longer be a factor.

Except then we destroy civilization. Without the moon stabilizing Earth's orbital axis we create an awful lot of problems in regards to the climate.

So I guess it all depends on what you consider more important, getting rid of leap seconds or having a life permitting climate.

CityZen wrote:Seems to me that part of the problem can be solved more simply. For the measure of time that needs to be constant (GPS, etc), it should use different units so that people don't confuse them with the measure of time that needs to be earth-based. The new units should follow nice decimal metrics. Perhaps something like microns, centons, etc.

frogthroat
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### Re: What-If 0026: Leap Seconds

1. Sails on the moon to move it to the correct distance that tidal waves are no longer an issue, but close enough so it cancels out continental drift changes in rotation.
2. Sails on the orbit, tethered to the equator to adjust to the correct speed.

Of course with the possibility to close the sails and reopen them as needed.

The size of the sails would probably be something astronomical, but could it work, at least in theory?
[insert nerdy witticism here]

ijuin
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### Re: What-If 0026: Leap Seconds

gmalivuk wrote:That would be nice, if not for the fact that the meter is already defined in terms of our unit of time. Defining our unit of time in terms of the meter, therefore, wouldn't actually be a terribly good idea.

Oh, good point. Perhaps then we need a "quantum time" unit that is defined in terms of atomic time.

Pfhorrest
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### Re: What-If 0026: Leap Seconds

ijuin wrote:
gmalivuk wrote:That would be nice, if not for the fact that the meter is already defined in terms of our unit of time. Defining our unit of time in terms of the meter, therefore, wouldn't actually be a terribly good idea.

Oh, good point. Perhaps then we need a "quantum time" unit that is defined in terms of atomic time.

I think what you really want is Planck time, which has already been mentioned here before. The Planck time is the amount of time it takes something moving as fast as theoretically possible to to cross the shortest theoretically measurable distance, both of which are experimentally quantifiable values not dependent on measurements of any particular physical objects.
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Novgorod
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### Re: What-If 0026: Leap Seconds

I'm surprised nobody pointed out that bombarding earth with a constant shower of asteroids would not exactly compensate for the tidal forces, at least not on the long term... In fact, you would not only add momentum by the collisions (which is desired), but also add mass to the surface near the equator - thus increasing the moment of inertia and decreasing the rotational speed again.

At a rate of a "billion liters of rock per second" which are deposited in a "perfect" ring around the equator (let's ignore the width and height dimensions and distributions of that ring), the gain in moment of inertia would slow down the earth by ~0.01ms per day! If this asteroid rate delivers exactly enough momentum transfer to compensate for the average slow-down of 0.8ms per day, then the accelerating effect will be cancelled within less than 3 months and the earth will slow down at an even higher rate from that on (not that it would matter much, since the crust should be turned into glowing lava at that time)...
In this calculation I assumed a rock density of 3kg/liter and the earth as a perfect homogeneous spere with mass/density/radius values from wikipedia - so give or take an order of magnitude for inaccuracy, the bombardment method will never keep the earth from slowing down - I would rather prefer the already mentioned slingshot method...

keithl
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### Re: What-If 0026: Leap Seconds

Ooopsie. The first thing to do is to check Randall's calculations, which he did not show, nor did he share most of the assumptions and numbers he started with.

Randall claims he needs a billion liters of cometary rock, perhaps 3 million metric tonnes, per second, I assume to reduce day length by 800 microseconds over ten years. Wrong! It turns out you can do that with only 3.6 thousand tonnes per second, a factor of 800 error. After that, you can stabilize against an average rate of 14 microseconds per day per year with about 100 tonnes per second, a factor of 30,000 error. The big burst of energy will heat the earth by 2.3 degrees, the latter by .13 degrees, and you can use the heat energy to create all the world's electricity. You can use the initial 10 year burst of energy to separate all the excess CO2 from the atmosphere and sequester it at the bottom of an ocean trench.

Calculations on my wiki. I also touch on moving mass towards the poles, and lightsails (30% fewer calories than regular sails). Of course, as Wnderer pointed out, there is nothing steady about the change of rotation rate, sometimes you will be subtracting angular momentum rather than adding it.

rmsgrey
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### Re: What-If 0026: Leap Seconds

keithl wrote:Randall claims he needs a billion liters of cometary rock, perhaps 3 million metric tonnes, per second, I assume to reduce day length by 800 microseconds over ten years. Wrong! It turns out you can do that with only 3.6 thousand tonnes per second, a factor of 800 error. After that, you can stabilize against an average rate of 14 microseconds per day per year with about 100 tonnes per second, a factor of 30,000 error. The big burst of energy will heat the earth by 2.3 degrees, the latter by .13 degrees, and you can use the heat energy to create all the world's electricity. You can use the initial 10 year burst of energy to separate all the excess CO2 from the atmosphere and sequester it at the bottom of an ocean trench.

How are you planning to convert heat energy dumped more-or-less uniformly around the equator and spread by the usual mechanisms into useful energy for doing work with? It strikes me as a non-trivial detail, considering how little of the thermal energy transfer from equator to poles we normally intercept...

dash
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### Re: What-If 0026: Leap Seconds

AnticlimacticDervish wrote:How about moving vast amounts of mass from the equator to the poles, thereby changing earth's moment of inertia?

Yep I had the same idea and had to search around the forums to find where to suggest it. But it's old news...
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PM 2Ring
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### Re: What-If 0026: Leap Seconds

Pfhorrest wrote:I think what you really want is Planck time, which has already been mentioned here before. The Planck time is the amount of time it takes something moving as fast as theoretically possible to to cross the shortest theoretically measurable distance, both of which are experimentally quantifiable values not dependent on measurements of any particular physical objects.

The Planck units are theoretically interesting because they simplify many fundamental equations, but they are not so useful as the basis for practical systems of units because it isn't easy to determine their values to a high precision.

Note that we can't measure the Planck length and time units directly. Like all the Planck units, their values are derived by simple algebraic manipulation of fundamental constants (in this case, G, the gravitational constant, h-bar, the reduced Planck constant, and c, the speed of light), so the precision of the Planck units is dependent on the precision in our measurements of those constants. In particular, our current estimate of G is not very precise - we know what the first 4 digits are, but after that it gets a bit fuzzy.

From http://en.wikipedia.org/wiki/Gravitational_constant#Laws_and_constants
The gravitational constant is a physical constant that is difficult to measure with high accuracy.[3] In SI units, the 2010 CODATA-recommended value of the gravitational constant (with standard uncertainty in parentheses) is:
G = 6.67384(80) × 10-11 m3 kg-1 s-2
with relative standard uncertainty 1.2×10−4.

The Planck length isn't exactly the shortest theoretically measurable distance. If spacetime is quantised, then it's quite possible that it happens somewhere around the Planck scale, and if so, spatial distances smaller than the Planck length and temporal durations shorter than the Planck time may not even make theoretical sense, since the structure of spacetime could be a weird non-linear fractal at that scale. Of course, we need a working theory of quantum gravity to address such issues. Still, it's fairly safe to say that we may never be able to measure the Planck length directly.

However, there might be be some physical significance to the Planck length, since the Bekenstein-Hawking entropy of a black hole is kA / 4, where k is Boltzmann's constant and A is the surface area of the black hole's event horizon measured in square Planck lengths. OTOH, as mentioned above, many equations take on simple form when using Planck units, so maybe this is of no special significance.

As for leap seconds, I've never been very happy with them because they are messy and insufficiently predictable. The notion of saving them up for a leap hour seems ludicrous to me, but a leap minute would be OK, IMHO.

keithl
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### Re: What-If 0026: Leap Seconds

keithl wrote:The big burst of energy will heat the earth by 2.3 degrees, the latter by .13 degrees, and you can use the heat energy to create all the world's electricity. You can use the initial 10 year burst of energy to separate all the excess CO2 from the atmosphere and sequester it at the bottom of an ocean trench.

rmsgrey wrote:How are you planning to convert heat energy dumped more-or-less uniformly around the equator and spread by the usual mechanisms into useful energy for doing work with? It strikes me as a non-trivial detail, considering how little of the thermal energy transfer from equator to poles we normally intercept...

The energy is not "more-or-less uniformly spread" - it is arriving as big chunks of rock at perhaps 50km/sec, hopefully very precisely aimed. I will leave the pesky details of turning a rock's kinetic energy into a large boiler full of 1000C steam to the asteroid steam power plant engineers. However, if you are making 50,000 GW of electricity, that will be a BUNCH of power plants; if there are 40,000 around the equator, in line (no good reason for that) they will be about a kilometer apart. Pretty close to "more or less uniformly", though you will actually want to stagger them north and south into a band, or the rocks for boiler entrance N+1 will graze too close to the top of boiler entrance N.

I assume that like most thermal power plants, we can achieve Carnot efficiencies of 40% - there wouldn't be combustion air and flue gas, but there would be lots of losses from nonuniform heating of the working fluid. And like all thermal power plants, 60% of the heat is dissipated near the plant, and the rest in power lines and the load elsewhere. In truth, it is probably silly to assume some average heating of around 0.1 Celsius, when most of the heat makes a thermal column just above the power plants, making the top of the troposphere near the plants quite hot, while distant regions get much less heating than that.

If these were iron meteoroids, you could perhaps slow them down in an electromagnetic coil gun run backwards as a generator. However, after their trip through the atmosphere they will probably not meet the tight mechanical tolerances of a coil gun, they will be pushing too much incandescent air in front, and coil guns are harder than they seem.

Nitpicker
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### Re: What-If 0026: Leap Seconds

So a question:

All we are trying to change is the rotational speed of the planet, right? So why all this attempt to add mass from outside when we only need to decrease the radius of the planet a little? For such a percentage change in the rotational speed it should require a similar change in the square of the radius, so

r/r0 = sqrt(86400/86400.0000008)

We should easily be able to do this by cooling the whole planet a tiny fraction of a degree (what's the thermal coefficient of expansion for the Earth?). On that note, wouldn't bombarding the earth with asteroids raise the overall temperature enough to negate any increase in angular momentum?

Novgorod
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### Re: What-If 0026: Leap Seconds

Nitpicker wrote:We should easily be able to do this by cooling the whole planet a tiny fraction of a degree (what's the thermal coefficient of expansion for the Earth?). On that note, wouldn't bombarding the earth with asteroids raise the overall temperature enough to negate any increase in angular momentum?

As mentioned before, I think the introduced mass will be more of a problem (i.e. reversing the effect).. I doubt that the heat energy will have any effect on the earth's diameter (in terms of thermal expansion), since it's generated at the surface and would merely penetrate through the earth's crust. Also, some part of the heat will be radiated back into space. Eventually the whole planet will boil away, of course, since we are talking about a continuous (i.e. endless) stream of asteroids - but I'm quite sure the effect on the earth's rotation will be compensated by the introduced mass (adding moment of inertia) first.. Maybe it's worth calculating...

If you want to cool down the planet instead, you'll have to cool down the entire planet, not just the crust! The earth is already losing heat from the inner part quite efficiently, so you'll just need to wait some millions of years or so.. Any possibility to significantly speed up the cooling process would involve science fiction and the destruction of the planet..

rossd
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### Re: What-If 0026: Leap Seconds

You can speed up the earth simply by hitting it with sunlight in the right way.

For example, if you cover the moon in mirrors and aim them so they reflect sunlight onto the receding part of the earth's equator, you get 2-3x the torque needed to counter the tidal slowing.

If you want to remove leap seconds, though, this method will take a long time (about 17000 years). You could speed it up by about a factor of 14x if you use a vast array of mirrors in orbit, even more if you allow more sunlight to hit the earth than currently hits it (probably a bad idea).

Fire Brns
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### Re: What-If 0026: Leap Seconds

I'm surprised no one suggested we get everyone in the word to get together in Road Island to focus the rotational momentum of their spinning.

Crosshair wrote:
Chad Cloman wrote:I'm thinking a much easier way would be to get rid of the Moon. Maybe we could put some really big rockets on it and send it far, far away. We might have to make some minor adjustments to the Earth's spin rate afterwards, but tidal forces would no longer be a factor.

Except then we destroy civilization. Without the moon stabilizing Earth's orbital axis we create an awful lot of problems in regards to the climate.

So I guess it all depends on what you consider more important, getting rid of leap seconds or having a life permitting climate.

A lot of people don't know this. A major reason, aside from the ice age ending, that North Africa went from rich forest to uninhabitable desert in recent geological history was a 2 degree shift in the Earth's tilt due to the moon drifting away from the Earth. Yay, climate change!
I've read analysis of solar models which suggest that a single large moon like that of Luna to Earth is necessary for (or at the least incredibly helpful to) the development of life on a planet.
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mathmannix
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### Re: What-If 0026: Leap Seconds

Fire Brns wrote:I've read analysis of solar models which suggest that a single large moon like that of Luna to Earth is necessary for (or at the least incredibly helpful to) the development of life on a planet.

My take from this is that, if we ever decided to completely ditch the earth and move to another planet far far away, we need to take the moon with us.
I hear velociraptor tastes like chicken.

Pfhorrest
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### Re: What-If 0026: Leap Seconds

mathmannix wrote:My take from this is that, if we ever decided to completely ditch the earth and move to another planet far far away, we need to take the moon with us.

Nah, much easier to just pick up a random rock of the appropriate size when we get there and install it in orbit. Needlessly costly to haul our own big dead rock all the way.
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Fire Brns
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### Re: What-If 0026: Leap Seconds

mathmannix wrote:
Fire Brns wrote:I've read analysis of solar models which suggest that a single large moon like that of Luna to Earth is necessary for (or at the least incredibly helpful to) the development of life on a planet.

My take from this is that, if we ever decided to completely ditch the earth and move to another planet far far away, we need to take the moon with us.

If we can colonize another planet we most likely no longer need a stable planet as we can supply our own needs with technology. If we wanted a planet on which we could establish a "natural" biosphere we would look for one with a single large moon.

Also the making our own moon suggestion works as well.
Pfhorrest wrote:As someone who is not easily offended, I don't really mind anything in this conversation.
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chretienorthodox
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### Re: What-If 0026: Leap Seconds

For those not familiar with leap second problem I have to say root of problem is the random (irregular, residual oscilation, anyway non predictable) component in earth rotational speed (omega, ω).

chretienorthodox
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### Re: What-If 0026: "Leap Seconds"

ITU-R WP7A in their session September 11-17 again failed in making decision.

chretienorthodox
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### Re: What-If 0026: "Leap Seconds"

ITU created blog for discussion about leap second at http://itu4u.wordpress.com/2013/10/11/t ... ds-behind/

zenten
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### Re: What-If 0026: "Leap Seconds"

What about really big rail guns to hurl rocks into space and out of orbit, pointed in the right direction to speed up the Earth's rotation appropriately?

pixeldigger
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### Re: What-If 0026: Leap Seconds

Fire Brns wrote:Also the making our own moon suggestion works as well.

Thats No Moon!