# When will the day be exactly 24:00:00.000 hours?

sonhouse
Posers and Puzzles 12 Mar '11 15:10
1. sonhouse
Fast and Curious
12 Mar '11 15:10
Right now the day is 23 hours 56 minutes and 4.1 seconds give or take.

around 100 million years ago the year was about 370 days long, so days are becoming longer now about 1.3 percent longer than back in the day of the dino's.
I calculated the day to be about 1100 seconds shorter back then, 20 odd minutes
so when is the day due to become 24 hours long exactly?

Also, why is the day becoming longer?
2. joe shmo
Strange Egg
12 Mar '11 16:16
Originally posted by sonhouse
Right now the day is 23 hours 56 minutes and 4.1 seconds give or take.

around 100 million years ago the year was about 370 days long, so days are becoming longer now about 1.3 percent longer than back in the day of the dino's.
I calculated the day to be about 1100 seconds shorter back then, 20 odd minutes
so when is the day due to become 24 hours long exactly?

Also, why is the day becoming longer?
Assuming a linear model, that is to say that the change in earths angular velocity per unit time remains constant ( which we cannot definitively say), the equation becomes in the format "VARIABLE_unit"

DAY_hrs = 6.289E-9_hrs/yrs*TIME_yrs + 23.9345_hrs

let day equal 24_hrs
solve for TIME_yrs

and I arrive at

TIME_yrs = 10,415,000

As to why it is slowing down, the simple answer is friction
3. sonhouse
Fast and Curious
12 Mar '11 17:223 edits
Originally posted by joe shmo
Assuming a linear model, that is to say that the change in earths angular velocity per unit time remains constant ( which we cannot definitively say), the equation becomes in the format "VARIABLE_unit"

DAY_hrs = 6.289E-9_hrs/yrs*TIME_yrs + 23.9345_hrs

let day equal 24_hrs
solve for TIME_yrs

and I arrive at

TIME_yrs = 10,415,000

As to why it is slowing down, the simple answer is friction
I got a couple of answers, 8.5 million years and 17 million, which may be due to a mistake, since 8.5 X2 =17.

But friction from what?

Also, using the change in time, couldn't you theoretically figure out what year it was, like if you had a time machine, by very accurate timing of the length of the day?\
Using your figures of 10 million years to change by around 4 minutes, or 185 seconds, then the change per year would be one second every 50,000 years give or take, so 1/50,000 of a second per year roughly. About 6 E-13 seconds per second. I think modern atomic and photonic clocks and get that kind of accuracy.

I don't think you could do it in one second though, you would have to have an extremely accurate telescope and a clear sky to see that little change in whatever angular change that would represent. Like a 1 meter movement around a 1 parsec circle?

There is also the problem of events like yesterday's gigantic earthquake which slightly changes the length of the day all by itself by sending mass deeper and speeding up the rotation rate of the Earth.

We already add a leap second every 18 months or so as it is, that would really swamp out a 1/50000 ths of a second change in one year, being by definition about 75000 times larger an effect for an 18 month time frame.

I guess it would be easier to just use the telescope to chart the movement of constellations in the sky but that would not work for a 10 million year time frame since the night sky would be unrecognizable either 10 mil in the past OR future.
4. 12 Mar '11 20:22
Careful here, I think you're getting a couple of closely related concepts confused.

If a day were only 23 hours and 56 minutes, that would result in your watch being off by almost an hour every 2 weeks.

We have days - the time it take for the earth to rotate on its axis.
And years - the time it takes for the earth to complete a revolution around the sun.

Both of these measures are likely to vary over time; hence, any attempt to calculate the relationships between "370 days per year 100 mil. years ago" and the modern equivalents has shall we say - a few challenges.

Finally, one should bear in mind, that the formal definitions of various units of measure are very important in these kinds of discussions. For example there was a time that 1 metre was formally defined as: the length of a particular bar of specific metallic composition at a specific temperature (to eliminate expansion and contraction effects).
- As it so happens, "day" is formally defined as 20*60*60 seconds - or exactly 24 hours.
- A "solar day" on the other hand, can apparently be a little shorter or longer depending on the time of the year. No doubt, in a few million years this will have changed.
5. 12 Mar '11 21:012 edits
As our world spins a "wave" of sea (which is the most obvious flexible bit of earth) moves to keep its high points in line with the moon, this is commonly known as the tide. As the tide moves it uses up energy moving things up and down and this slows the earth's spin down.

The atmosphere has tides too, but is not so easy to see, and so does the earth's crust, but that is so stiff it doesn't move much.

If the sun, earth and moon were inflexible spheres spinning in a vacuum thay would not slow down very much at all, perhaps quantum mechanics might give some ghost particles for the earth to bang into on it's way around, which might slow it down very gradually, or gravity waves could slow them down maybe.
6. 12 Mar '11 21:22
23 hours, 56 minutes and 4 seconds is a sidereal day, the "day" measured against the positions of stars.

http://www.universetoday.com/14700/how-long-is-a-day-on-earth/

Thinking about that rotation, we can see that in one sidereal day the earth will not have moved exactly once round "with respect to the sun", in fact it will still have about 1/365th of a rotation to go (the fraction of the angle round the sun it goes in one day)

So a solar day is about 366/365 * (23 hours, 56 minutes and 4 seconds), that gives 86400.7 seconds as an approximate solar day.

Apparently when accurate calculations are done a day turns out to be 86,400.002 seconds
(http://en.wikipedia.org/wiki/Day) since this is still a bit longer than 24 hours and the earth is slowing down, the answer to this question is NEVER.
7. sonhouse
Fast and Curious
13 Mar '11 01:142 edits
Originally posted by iamatiger
23 hours, 56 minutes and 4 seconds is a sidereal day, the "day" measured against the positions of stars.

http://www.universetoday.com/14700/how-long-is-a-day-on-earth/

Thinking about that rotation, we can see that in one sidereal day the earth will not have moved exactly once round "with respect to the sun", in fact it will still have about 1/365th o ...[text shortened]... it longer than 24 hours and the earth is slowing down, the answer to this question is NEVER.
Well, the sidereal day is still changing so it is right to say at some point in the future the sidereal day will be exactly 24 hours.

So the difference is the fact the earth moves around the sun and in 24 hours the exact same spot will not line up with the stars? It would be pointing at a space about 1 degree different than it did the day before, sounds like.

Still an interesting post, thanks for pointing that out.

So the real day length would be the time it takes for a fixed spot on earth, like on the equator, to pass the exact center to center line of the Earth and Sun.

I guess that would not even be totally accurate since the axis of the Earth is 23 odd degrees off the ecliptic. Dang.
8. sonhouse
Fast and Curious
13 Mar '11 06:02
Originally posted by sonhouse
Well, the sidereal day is still changing so it is right to say at some point in the future the sidereal day will be exactly 24 hours.

So the difference is the fact the earth moves around the sun and in 24 hours the exact same spot will not line up with the stars? It would be pointing at a space about 1 degree different than it did the day before, sounds ...[text shortened]... t even be totally accurate since the axis of the Earth is 23 odd degrees off the ecliptic. Dang.
So maybe we extend the line between the centers of the sun and Earth and make it a plane extending out into space, which of course is rotating around the sun by the daily movement of the Earth in its orbit.

Wouldn't that be a good reference point to measure the rotational day, since revolving on its axis, even 23 degrees off, an imaginary line extended into space would pass through the plane twice a day at exactly the same time, assuming the rotation rate to be constant.

That way it wouldn't matter what angle the rotation is compared to the ecliptic, even if Earths poles were pointed directly at the sun, the time would be the same for a line stretching into space to intersect the center-center plane.
9. 15 Mar '11 09:40
Originally posted by sonhouse
Right now the day is 23 hours 56 minutes and 4.1 seconds give or take.
Was that original value based on the changing time of sunrise or something like that? Your original value differs to 24 hours by approximately 1/365.24th of 24 hours, being 3 minutes 56.5 seconds - give or take....
10. 28 Mar '11 21:15
Originally posted by sonhouse
so when is the day due to become 24 hours long exactly?

[/b]
The average day is 24 hours long, its longer at some times of the year and shorter at others. Its exactly 24 hours on 16 April, 15 June, 1 September and 25 December each year. Look up 'The equation of time' for an explaination.