# Angular momentum of the earth

We know the tidal waves are decreasing the spin rate of the earth which causes the days to longer, so as the angular momentum of the earth decreases it means it rotational kinetic energy also decreases since energy is always conserved the translational kinetic energy of earth must increase now right? Then that would cause number of days in a year to decrease as we right?

since energy is always conserved the translational kinetic energy of earth must increase now right?

Energy is conserved, but kinetic energy is not necessarily conserved. In this case, the tidal drag converts some of the kinetic energy of the earth-moon system into thermal energy.

It's very similar to simple friction in other contexts. If you slide a book across a table, it comes to a stop. Momentum (of the earth-book system) is conserved, but kinetic energy is not.

Then that would cause number of days in a year to decrease as we right?

Maybe you should read this article as a lot more goes into the kinematics of the earth around the sun,

Earth rotates faster than the moon orbits it, so the watery tidal bulge travels ahead of the moon's relative position. This displaced mass gravitationally tugs the moon forward, imparting energy and giving the satellite an orbital boost, whereas friction along the seafloor curbs Earth's rotation.

.....

Hints of inconsistent Earthly timekeeping come through natural calendars preserved in fossils. Corals, for example, go through daily and seasonal growing cycles that form bands akin to growth rings in trees; counting them shows how many days passed in a year. In the early Carboniferous period some 350 million years ago an Earth year was around 385 days, ancient corals indicate, meaning not that it took longer for the planet to revolve around the sun, but that a day–night cycle was less than 23 hours long

Etc.

Note that energy can be radiated into space as heat, while angular momentum is harder to get rid of. The total angular momentum of the Earth-Moon-Sun system is approximately constant, even as Earth's daily spin rate slows slightly.

• Does it not approximately decrease by the amount the earth slows down?
– user257090
Commented May 16, 2020 at 6:07
• @DoctorNuu no. The slowing rotation of the earth is balanced mostly by the moon's increasing orbit. Commented May 16, 2020 at 6:48
• Mostly. hmm. Approximately. Any intuitive argument why the moon speeds up? By how much? Seems to be a hard one. cds.cern.ch/record/636493/files/0308162.pdf
– user257090
Commented May 16, 2020 at 7:13
• @DoctorNuu The moon slows down, not speeds up. The angular momentum of the orbit increases because the Earth-Moon distance gets larger. Your link gives historical values for the length of the day and the month; both used to be faster.
– rob
Commented May 16, 2020 at 14:57
• All not easy. One of us should probably use this to build a perpetuum mobile. Why did you not just state that angular momentum is conserved? Why the approximately?
– user257090
Commented May 16, 2020 at 19:40