So, if my maths is right that’s about 1 second extra slower every 500 days, which means a day will take 48 hours in about 43 million years
That seems very very fast on galactic time scales - we would get tidally locked (rotate at speed of orbit?) in about 150x43 million … oh about 3 billion years … yeah never mind
Edit
A slightly different way of looking at it is we add a leap second every 2 or so years on average (27 in past 53 years). This seems about right with the above maths - it just amazes me
No, it's 2.3ms per day slower every 100 years. After 100 years the cumulative "loss" would be 100365.25(2.3/2), or about 11 hours, but each day would be about the same length as it is today.
If rotation was 86400 seconds per day today, then in 100 years time it will be 86,400.0023 seconds.
In 1,000 years time it will be 23ms slower
In 10,000 years time 230ms slower
In 100,000 years time 2.3 seconds slower.
In 1 million years 23 seconds, a 86400s day will take 86423 seconds
In 43 million years at that speed of 2.3ms per 100 years, a day will take 86,989 seconds, or 24 hours 16 minutes.
(there are other factors effecting earth's rotation)
Not 2.3 seconds per day, 2.3 seconds in total over that 1000 days, not 2.3 seconds per day which would be crazy.
On average each day over the last 100 years is only about 1.2ms longer, so total extra length after 100 years is 100365.251.15. A cumulative 42 seconds has been added in 100 years.
>Currently the secular change in the rotation rate increases the length of day by some 2.3 milliseconds per day per century. [emphasis added]
>suppose the rotating earth is our clock and it's been 100 years [...] Then after 1000 days our earth clock loses about 2.3 seconds,
I think the math here is very wrong, or else I haven't had enough coffee yet.
>it's been about 100 years so now each day is 2.3 milliseconds longer
>after 1000 days 1000 * 2.3 milliseconds = 2.3 seconds
I don't think the example helps at all to explain the concept, but I think the math is right
So, if my maths is right that’s about 1 second extra slower every 500 days, which means a day will take 48 hours in about 43 million years
That seems very very fast on galactic time scales - we would get tidally locked (rotate at speed of orbit?) in about 150x43 million … oh about 3 billion years … yeah never mind
Edit A slightly different way of looking at it is we add a leap second every 2 or so years on average (27 in past 53 years). This seems about right with the above maths - it just amazes me
What amazes me more is they are going to stop using leap seconds https://en.m.wikipedia.org/wiki/Leap_second by 2035
No, it's 2.3ms per day slower every 100 years. After 100 years the cumulative "loss" would be 100365.25(2.3/2), or about 11 hours, but each day would be about the same length as it is today.
If rotation was 86400 seconds per day today, then in 100 years time it will be 86,400.0023 seconds.
In 1,000 years time it will be 23ms slower
In 10,000 years time 230ms slower
In 100,000 years time 2.3 seconds slower.
In 1 million years 23 seconds, a 86400s day will take 86423 seconds
In 43 million years at that speed of 2.3ms per 100 years, a day will take 86,989 seconds, or 24 hours 16 minutes.
(there are other factors effecting earth's rotation)
An interesting similar thought is to work out the length of a day during the Jurassic period
Not 2.3 seconds per day, 2.3 seconds in total over that 1000 days, not 2.3 seconds per day which would be crazy.
On average each day over the last 100 years is only about 1.2ms longer, so total extra length after 100 years is 100365.251.15. A cumulative 42 seconds has been added in 100 years.
If you are interested in math, computers and tides, check out:
Charles Petzold - "Computer of the Tides" (2014)
https://www.youtube.com/watch?v=O-N5DuEUap8
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