# What was the length of the solar day 73 million years ago?

How could this be estimated, or how accurately could it be extrapolated from a present-day measurement of the Earth's spin-down rate?

• Hint: Calculate the number of centuries in 73 million years (73E6/100 = 73E4), multiply by -0.0016 s/century, and add that value to the current length of day. The answer will be meaningless since the value of dP may change with time and has only been measured for the last 2000 years. That is not long enough to extrapolate back 73 million years. – JohnHoltz Oct 11 '18 at 2:48
• @RobJeffries Right, but look at the following answer. Such questions might have some significant historical or details matters. – Nosrati Oct 11 '18 at 6:32
• @Nosrati the question needs to change then. Or actually, just remove all the text and leave the question title! – ProfRob Oct 11 '18 at 6:45
• I have edited the question to make it on-topic. – ProfRob Oct 11 '18 at 16:57
• @RobJeffries which enables me to retract my close vote :) – Chappo Hasn't Forgotten Monica Oct 12 '18 at 0:29

There is evidence from Silurian coral fossils that, 430 My ago, there were 420 daily rotations in each annual season, compared to 365 days per year now. If we assume that the year (fixed by mean Earth-Sun distance and Kepler's Laws) hasn't changed much in that interval, but that instead the day has gotten longer due to the Earth-Moon tidal interaction, that means that 430 My ago there were about 20.9 hours in each day.

Linear extrapolation in between says that only about one-sixth of that change has taken place in the past 73 My, which would give a day length of about 23.5 hours.

In a comment, JohnHoltz cautiously extrapolates your currently-known slowing of 0.0016 seconds/century over that interval, which gives an ancient day length of closer to 23.7 hours.

JohnHoltz's estimate is probably better. Tidal slowing is occurring as the mean distance between the Earth and Moon increases, which makes all tidal effects (including tidal slowing) weaker. So a linear extrapolation from today's well-measured rate of rotational slowing is probably more accurate for recent times than a linear extrapolation over a much longer period that probably includes more rapid slowing in the past. It inspires confidence that the two methods come out close to each other, though.

$$~\quad~$$ A quick Google search after daylength dinosaurs reveals the following relevant results :

Period : Upper Cretaceous – Age (years) : 70 million – Days per year : 370 – Hours per day : 23.7NASA

If we say the "time of the dinosaurs" started about 200 million years ago, then the years has lengthened by 1.2 million seconds in that time - or just under an hour a day less than today. To get all the way to a day of 17 hours, you need to go back a little before the dinosaurs - about 2 billion years.Physics Stack Exchange

This means, for instance, that 100m years ago, when dinosaurs ruled Earth, a day was nearer 23 than 24 hours.The Economist

Fossil evidence informs us about how the day-length has changed over geological time. When the dinosaurs first walked the Earth there were about 375 days in a year, 10 more than at present, each day more than 30 minutes shorter than now.Independent

For Jurassic-era stegosauruses 200 million years ago, the day was perhaps 23 hours long and each year had about 385 days. Two hundred million years from now, the daily dramas for whatever we evolve into will unfold during 25-hour days and 335-day years.The Washington Post

Meyers and a colleague recently showed that 1.4 billion years ago, a single “day” lasted only about 18 hours. Back in the Proterozoic, a few million years after multicellular life appeared on the planet, the moon was about 211,825 miles away from Earth—about 21,000 miles closer than it is today. This, they figured out, compressed the length of a day down to 18.68 hours. By the time land plants evolved about 470 million years ago, the days had stretched to 21.46 hours. And when the dinosaurs showed up 225 million years ago, the days lasted 22.68 hours. The roughly 24-hour day we have now was almost in place as the first ice sheets bloomed near the Northern Hemisphere’s poles about 3.5 million years ago.National Geographic

So would the day length during the age of the dinosaurs have been 21 hours? "The dinosaurs were around 100 million years ago, which at the current rate [ of day lengthening ] adds up to 2000 seconds, which is less than an hour." Geological evidence for increasing day length can help us pin this time down more accurately. Tidal records laid down in ancient estuaries can show daily, monthly and seasonal cycles in alternating deposits of sand and silt. They indicate that 620 million years ago the day was 21 hours, says Mardling. Since the dinosaurs lived during the Mesozoic era, from 250 million years ago to 65 million years ago, day length would have been longer than 21 hours and probably closer to 23 hours.ABC Science