What would it take to eliminate leap years?

[some bloke]

TL;DR Summary

When 3-gorges dam was built in china, it changed the length of a day by 0.06 microseconds. What would it take to adjust the length of a year from 365.242189 days to exactly 365?

I am curious as to how exactly to calculate this!

The concept is that when they raised all the water up in the 3-gorges dam, it adjusted the length of a day by a very small amount.

Using this principle, what would it take for us to slow the Earth's rotation down sufficiently that it rotates exactly 365 times per year instead of 365.242189? How can I calculate it?

Obviously there will be two variables - the mass raised and the distance raised. The momentum of the mass will remain the same, so I suppose the logical approach is to work out the exact impact of raising 1kg by 1m, and then solve from there to get the amount of work done required to slow the Earth by the desired amount?

 

[Vanadium 50]

If you want to change the day by 21,000 seconds, and one dam changes the day by 60 nanoseconds, how many trillion dams do you need?

 

[jbriggs444]

Obviously there will be two variables - the mass raised and the distance raised. The momentum of the mass will remain the same.

If you are working from first principles, you should probably be thinking in terms of angular momentum, moment of inertia and angular velocity.

 

[sophiecentaur]

An alternative could be to tinker with the Moon. Drop its orbit a bit and start it spinning, perhaps. Still a ridiculous amount of Energy involved. How long would we be prepared to take over the project?

 

[jbriggs444]

Or we could just wait.

The tidal acceleration of the Moon slows the rotation rate of the Earth and increases the Earth-Moon distance. Friction effects—between the core and mantle and between the atmosphere and surface—can dissipate the Earth's rotational energy. These combined effects are expected to increase the length of the day by more than 1.5 hours over the next 250 million years

Hold your breath if you like. I'm going back to my game of Pinochle.

 

[sophiecentaur]

Or we could just wait.
Hold your breath if you like. I'm going back to my game of Pinochle.

Your link shows what will happen when left to itself. By starting the Moon spinning a bit faster and dropping its orbit you can speed up the Earth by reverse the natural tidal effect. I was just wondering if the energy required to do it this way would be greater or less than re-arranging the Earth's mass. It could use some of the Moon's orbital energy 'for free', as with slingshot orbits. @jbriggs444 might not have to wait so long.

 

[jbriggs444]

Your link shows what will happen when left to itself. By starting the Moon spinning a bit faster and dropping its orbit you can speed up the Earth by reverse the natural tidal effect. I was just wondering if the energy required to do it this way would be greater or less than re-arranging the Earth's mass. It could use some of the Moon's orbital energy 'for free', as with slingshot orbits. @jbriggs444 might not have to wait so long.

To make sure I have it straight. You are going to spin up the moon and lower its orbit, thereby conserving angular momentum. But you want to go far enough to actually reverse the tidal effect. That is, you want to lower the moon far enough so that its orbital period is less than a sidereal day. So that it acts to spin the Earth up rather than spinning it down.

I think you'll disintegrate the moon if you try, either at the Roche limit or due to centrifugal force. At a guess, the moon spin rate will be the problematic factor by a huge margin.

There is also a positive feedback loop here. As the Earth spins up and the moon is retarded, its orbital period [counter-intuitively] decreases even further and the Earth spins even faster. If no other failure mode intrudes first, you wind up with an Earth-moon impact.

 

[Vanadium 50]

Which is easier? Moving the moon or building a trillion dams?

 

[jbriggs444]

Which is easier? Moving the moon or building a trillion dams?

Moon, I think. You'll run out of real estate for the dams.

[Good, fast, cheap. If we want cheap, I think we're going to need to compromise on fast]

 

[sophiecentaur]

That is, you want to lower the moon far enough its orbital period is less than a sidereal day.

No. Just significantly less than one month - I am being 'reasonable' my demands. Also make its spin a bit slower (or faster - I'm not sure yet) than the new month. The effect should be to increase Earth's spin speed.

Which is easier? Moving the moon or building a trillion dams?

I would have thought that the environmental effect would be a lot less and I was hoping there could be some energy advantage too.

 

[jbriggs444]

No. Just significantly less than one month - I am being 'reasonable' my demands. Also make its spin a bit slower (or faster - I'm not sure yet) than the new month. The effect should be to increase Earth's spin speed.

It does not work that way. If the month is longer than the day, the tidal bulges on the Earth lead the moon and the effect is to slow the Earth down. Making the month shorter does not help until you hit the one month = one day threshold.

If the month were shorter than the day then the tidal bulges on the Earth would trail the moon. The Earth would spin up and the moon would be retarded in its orbit. Counter-intuitively, this would increase the moon's orbital velocity and reduce its orbital radius and period further.

In any case, if we want to go from 365.25 days per year to 365.00 days per year, we need to make the days longer, not shorter.

 

[vela]

Which is easier? Moving the moon or building a trillion dams?

I hear the National Forest Service and Bureau of Land Management are looking into moving the Moon.

 

[Richard R Richard]

The Earth is not spherical, it has more circumference through the equator than across the poles, but if the radius from the center to the surface at each pole is further reduced by approximately 3km according to my best calculation and at the same time that same material is placed by enlarging the radius of the equator another 3 km, then the Earth's moment of inertia would increase by the necessary amount, going from a sphere to an ellipsoid and would reduce the period of rotation to obtain 365 revolutions in 365 d 5h 48min 45.22s ...
You have to dig a lot, so don't tell me to push the shovel, my back hurts, so much work to run to avoid tearing one more page from the almanac every four years, I prefer the latter ...

Moving the earth-moon system about 148000km towards the sun also solves the problem, but who gets down to push

regards

 

[Baluncore]

The Gregorians want to change the Earth-Moon system to fit their solar Calendar. But what will that do to the lunar based Islamic calendar?

 

[TeethWhitener]

Or we could make every year a leap year. The 2011 Sendai earthquake decreased the length of a day by 1.8 $\mu s$, which is 300 times more than the Three Gorges Dam increased its length. So we only need to trigger a modest few billion 9.0 magnitude earthquakes to get to 366 days per year, as opposed to @Vanadium 50 ’s trillions of dams, which is clearly ludicrous.

 

[mfb]

but if the radius from the center to the surface at each pole is further reduced by approximately 3km according to my best calculation and at the same time that same material is placed by enlarging the radius of the equator another 3 km, then the Earth's moment of inertia would increase by the necessary amount

Material on Earth would move to counter that attempt - on a timescale far faster than we could move the material. It's not an accident that Earth is so close to being a perfect oblate spheroid. Some local topography is fine, but not a global 3 km bulge away from equilibrium.

Has someone mentioned a few quadrillion rocket launches?

 

[Baluncore]

It is unfortunate that isostatic movement of the crust would counter any mass transport across the face of the Earth.
But if we could dig a honeycomb of caves in equatorial regions, stacking the spoil on top of the cave system to maintain the mass per unit area, the moment of inertia could be raised to slow the Earth to 365 days per year.

The cave system would need to be built above sea level so it could be drained of water. The exact rotation rate could be adjusted by changing the rate of water outflow to the sea. Sumatra, Papua New Guinea, and Ecuador would be good candidates to become Swiss cheese.

Another local advantage would be the storm-free shipping canals that could be established where there were once only mountain chains separating the oceans.

 

[jbriggs444]

Perhaps a few quintillion equatorial hamster wheels with a continuing supply of alfalfa pellets?

 

[Ibix]

Perhaps a few quintillion equatorial hamster wheels with a continuing supply of alfalfa pellets?

The wheels being a stopgap measure until the buildup of hamster "byproducts" achieves the required mass redistribution?

 

[256bits]

The Earth is not spherical, it has more circumference through the equator than across the poles, but if the radius from the center to the surface at each pole is further reduced by approximately 3km according to my best calculation and at the same time that same material is placed by enlarging the radius of the equator another 3 km, then the Earth's moment of inertia would increase by the necessary amount, going from a sphere to an ellipsoid and would reduce the period of rotation to obtain 365 revolutions in 365 d 5h 48min 45.22s ...
You have to dig a lot, so don't tell me to push the shovel, my back hurts, so much work to run to avoid tearing one more page from the almanac every four years, I prefer the latter ...

Moving the earth-moon system about 148000km towards the sun also solves the problem, but who gets down to push

regards

Start investing in heavy Earth moving equipment.

Easier way, for free - heat the Earth so the polar ice caps melt.
Greenland alone adds 2ms.
For example, if the Greenland ice sheet were to completely melt and the meltwater were to completely flow into the oceans, then global sea level would rise by about seven meters (23 feet) and the Earth would rotate more slowly, with the length of the day becoming longer than it is today, by about two milliseconds.
https://climate.nasa.gov/faq/30/if-...an-what-would-happen-to-the-planets-rotation/

Well maybe not enough polar ice

 

[Helios]

The Gregorians want to change the Earth-Moon system to fit their solar Calendar.

Different parts of the year have different year lengths. I think there's two places in the year where the Gregorian is accurate, no change needed.

 

[jbriggs444]

Different parts of the year have different year lengths. I think there's two places in the year where the Gregorian is accurate, no change needed.

You are suggesting that, because the Earth has an elliptical orbit, the current rate of passage of the year as measured by the angular velocity of the Earth on a 360 degree track around the sun will vary over the course of the year? [The tropical year is about .01 of a degree off from 360 degrees, but we can ignore that].

Yes, there would be two places where the momentary progress rate would match the mean progress rate. And two slightly different places where it would match the average rate per the Gregorian calendar.

That doesn't make the year match its nominal length per the Gregorian or Julian calendars. Or a hypothetical no leap-year calendar.

It does suggest that a correctly timed (series of) circularizing burn(s) could normalize the year to fit the Gregorian calendar. It's not like we really need the oceans and the atmosphere, right?

Edit: Drat. Electrolyzing the oceans and using chemical thrusters won't do the trick. We need something more like ion thrusters to achieve exhaust velocities in excess of 7 miles per second.

 

[Helios]

That doesn't make the year match its nominal length per the Gregorian or Julian calendars.

The "mean tropical year" is based on the mean sun, and is not exactly equal to any of the times taken to go from an equinox to the next or from a solstice to the next.
Between two Southern solstices ( year 2000 ) equals 365.242740 days
So I guess two times around winter, the Gregorian would be accurate.

 

[jbriggs444]

The "mean tropical year" is based on the mean sun, and is not exactly equal to any of the times taken to go from an equinox to the next or from a solstice to the next.
Between two Southern solstices ( year 2000 ) equals 365.242740 days
So I guess two times around winter, the Gregorian would be accurate.

Yes, I understand that a half-year measured from summer solstice to winter solstice (for instance) will not, in general, match the length of the other half-year measured from winter solstice to summer solstice.

Yes, if we somehow computed a "year progress rate" based on the progress of the Earth in its orbit (or, more usefully, based on the measured angle between the polar axis and the Earth-sun direction) there would be two times during the year when this would match the nominal rate called for by the Gregorian calendar.

I fail to see the significance. We do not measure the accuracy of the Gregorian calendar day by day. We measure it long term.

 

[Baluncore]

Between two Southern solstices ( year 2000 ) equals 365.242740 days

The time it takes the Earth to orbit the Sun is not an exact multiple of the time it takes the Earth to rotate on it's axis. The 0.242740 is primarily corrected by one extra day every 4 years = 0.25, and secondly corrected by the 1 in 400 years exception.

The leap year is fundamentally an artefact of the calendar, not the Earth, it is used to keep the calendar synchronous with the seasons. It keeps the solstices and equinoxes on about the same Gregorian calendar date each year.

 

[Helios]

and secondly corrected by the 1 in 400 years exception.

The Gregorian reforms have THREE exceptions in 400 years, to the Julian, not one.

 

[jbriggs444]

The 0.242740 is primarily corrected by one extra day every 4 years = 0.25, and secondly corrected by the 1 in 400 years exception.

The once in 4 years exception to a nominal 365 day calendar gets you to 365.25. That's the Julian Calendar
The once in 100 years exception to that gets you down to 365.24. That's the first exception.
The once in 400 years exception to that gets you up to 365.2425. That's the Gregorian Calendar.

Counted that way, it's two exception rules from Julian to Gregorian.

The Gregorian reforms have THREE exceptions in 400 years, to the Julian, not one.

Or three exception days per 400 years.

 

[Baluncore]

The Gregorian reforms have THREE exceptions in 400 years, to the Julian, not one.

I believe the exception to an exception becomes a confusion of inversion.
You are free to object to the way I expressed it, or change the reference calendar if you wish.
I will ignore you and follow the standard numerical algorithm.

 

[cmb]

Summary:: When 3-gorges dam was built in china, it changed the length of a day by 0.06 microseconds. What would it take to adjust the length of a year from 365.242189 days to exactly 365?

I am curious as to how exactly to calculate this!

The concept is that when they raised all the water up in the 3-gorges dam, it adjusted the length of a day by a very small amount.

Using this principle, what would it take for us to slow the Earth's rotation down sufficiently that it rotates exactly 365 times per year instead of 365.242189? How can I calculate it?

Obviously there will be two variables - the mass raised and the distance raised. The momentum of the mass will remain the same, so I suppose the logical approach is to work out the exact impact of raising 1kg by 1m, and then solve from there to get the amount of work done required to slow the Earth by the desired amount?

I'm laughing at this, on one side that humans would actually consider doing this (cf Tower of Babel, Gen 11:5) and on the other that they could actually do it ("If as one people speaking the same language they have begun to do this, then nothing they plan to do will be impossible for them.").

Yep, we have now defined measurement itself to the fundamental units of nature, that we have 'conquered' by intellect, and now we might seek to model the rotation of our home planet to our new found wisdom.

I don't have an answer for you, OP, but carry on thinking about it! ;)

 

[Helios]

The 0.242740 is primarily corrected by one extra day every 4 years = 0.25, and secondly corrected by the 1 in 400 years exception.

How else can this be construed that isn't an erroneous statement? The "1" is literally taken to mean "one extra day" and this would even be worse than the Julian calendar. Even if you said "1 less", that would still be wrong. Neither case matches what the Gregorian reforms prescribe.

You are free to object to the way I expressed it,

I am also free to correct a statement with an obvious implication that's false.

or change the reference calendar if you wish.

and what does this even mean? What is a "reference calendar" and why am I "wishing" to change it? I have said nothing about "changing the reference calendar".

I will ignore you and follow the standard numerical algorithm.

except that the standard numerical algorithm does not match your incorrect description, unless you can explain otherwise.

 

[Richard R Richard]

Start investing in heavy Earth moving equipment.

So that there are no leap years, we need
• Make the period of rotation of the Earth about its own axis proportional to the period of translation around the sun, how? Well there will be a thousand more or less funny occurrences, or some physically feasible formulation, and of them there will be only a few that achieve it without destroying the terrestrial ecosystem.
• On the other hand, we must make these two periods proportional to our definition of the second, to measure time.
So everything would be expressed in whole numbers .. We put a new number on the starting day, at the start time, and from there onwards, a masterpiece of precision and human intelligence ... but ... to what end? would be the utility?

 

[Baluncore]

except that the standard numerical algorithm does not match your incorrect description, unless you can explain otherwise.

If (y Mod 4 ) ≠ 0 Then Return 'common' Exit.
If (y Mod 100 ) ≠ 0 Then Return 'leap' Exit.
If (y Mod 400 ) ≠ 0 Then Return 'common' Exit.
Return 'leap' Exit. This is the one exception every 400 years.

 

[Helios]

"This is the one exception every 400 years."
I still count 3 exceptions to the Julian calendar every 400 years. Count them.
You haven't explained the "reference calendar" and why I would be wishing to change it. What did that mean?

 

[mfb]

I propose to stop the discussion whether it's one, two or three exceptions in the calendar. It's entirely subjective and further discussion won't help anyone.

@Richard R Richard: We already have leap seconds once in a while because the length of the day is not exactly 86400 seconds. Making days longer to have 365 days in a year would need ~15 leap seconds every day.
To avoid leap seconds we would need to speed up the rotation of Earth a bit. To avoid leap years at the same time we would need to get Earth closer to the Sun. Or maybe farther away is a better idea (366 or more days per year), looking at recent climate developments.

 

[Richard R Richard]

@Richard R Richard: We already have leap seconds once in a while because the length of the day is not exactly 86400 seconds. Making days longer to have 365 days in a year would need ~15 leap seconds every day.
To avoid leap seconds we would need to speed up the rotation of Earth a bit. To avoid leap years at the same time we would need to get Earth closer to the Sun. Or maybe farther away is a better idea (366 or more days per year), looking at recent climate developments.

I agree with what you say, but matching the angular velocities of rotation and translation at the same point year after year does not guarantee that it will be a whole number of seconds.
This can be achieved with many pairs of speeds, but there will only be a few pairs where the number of seconds is proportional to the current definition of a second.
But there will only be two pairs that have either 365 or 366 days, the periods must be those numbers multiplied exactly by 86400 if we want the hour system to remain unchanged.
The eccentricity of the orbit with respect to the sun will give us shorter or longer days during the year, and there will be no solution unless we also put that in our work, that is, we achieve at the same time that the orbit around the sun is circular and that the orbit of the moon with respect to the Earth is circular with a period also proportional to the definition of the year, only then will the moon, which moves us ahead and behind us in the solar orbit, will allow us to have an exact definition of the time of the day. just looking at distant stars.