On Astronomy - The Slow Theft of Time:
Earth’s Rotational Energy, Tidal Friction, and the Fate of the Day
By blogger lim ju boo, alias lin ru wu (林 如 武)
Post-doctoral - University of Oxford
Abstract
Earth’s rotation stores an immense reservoir of kinetic energy, accumulated since planetary formation. Yet this energy is not conserved within Earth itself: through tidal interactions with the Moon, a small but relentless fraction is dissipated as heat in the oceans and crust.
This article quantifies Earth’s rotational kinetic energy, estimates the rate at which it is lost to tidal friction, and explores the long-term dynamical consequence, namely the gradual lengthening of the day and Earth’s eventual tidal locking. Though imperceptible on human timescales, this process provides one of the most elegant examples of slow cosmic evolution governed by classical mechanics.
1. Rotational kinetic energy of the Earth
For a rotating rigid body,
Krot = 1/2 Iω2
Where
I, is the moment of inertia and
ω (omega) is the angular velocity.
Earth parameters
Mass (M) = 5.972×10 24 kg
(That's almost 6 followed by 24 zeros kg)
Mean radius (R) = 6.371 × 10 6 m
Angular velocity (sidereal rotation):
ω = 7.292×10−5 rad s−1
Because Earth is centrally condensed, its measured moment of inertia is
I = 0.3307 MR2 ≈ 8.04×1037 kg m2
Thus,
Krot = 1/2 (8.04×1037)(7.292×10−5)2
≈2.1×1029 joules
(Those unfamiliar with mathematics, that means, 2 followed by a whopping, whooping 29 zeros joules of energy - I can't even dream that amount of energy the rotating Earth is endowed with by the Creator - can you?)
This is the stored mechanical energy of Earth’s spin, independent of orbital motion or internal heat.
2. The mechanism of tidal energy loss
The Moon raises tidal bulges on Earth’s oceans and, to a lesser extent, its solid body. Because Earth rotates faster than the Moon orbits, these bulges are carried slightly ahead of the Earth–Moon line. The Moon’s gravity pulls backward on them, exerting a torque that:
1. Slows Earth’s rotation
2. Transfers angular momentum to the Moon
3. .Dissipates energy as heat via oceanic and crustal friction
This process obeys angular momentum conservation but not energy conservation, the “missing” energy is thermalised.
3. Measured rate of tidal dissipation
Geophysical measurements give the present tidal dissipation power as:
Ptides ≈ 3.7×1012 w
That is, 3.7 terawatts, comparable to human civilization total power consumption.
Energy lost per day:
Eday = P × 86400 ≈ 3.2×1017 Joules
Fraction of Earth’s rotational energy lost per day:
E day / K rot ≈ 3.2 x 10 17 / 2.1 x 10 29 ≈ 1.5 x 10 - 12
That is:
0.00000000015% per day
4. Observable consequences today
Despite the tiny fraction, the effects are measurable:
Length of day increases by
~1.7 milliseconds per century
Moon recedes at ~ 3.8 cm per year
Ancient coral growth rings show ~ 400 days per year hundreds of millions of years ago. This confirms that the process has been active throughout geological history.
5. How long until Earth “comes to a halt”?
Strictly speaking, Earth will never stop rotating in an absolute sense.
Instead, it will approach a tidally locked state with the Moon.
Final configuration:
One Earth day = one lunar month
Earth always shows the same face to the Moon
No lunar tides (only solar tides remain)
Current estimates place this timescale at:
30–50 billion years.
This far exceeds the Sun’s remaining lifetime (~5 billion years).
Earth’s habitability window.
Even the Sun’s red-giant phase
Thus, Earth will be uninhabitable long before its rotation is exhausted.
6. A subtle but profound insight
Angular momentum is conserved.
Energy is not.
Earth’s lost rotational energy does not vanish:
It warms the oceans
It stirs currents
It fractures crustal rock
It drives geological evolution
Time itself, measured by the length of the day, is slowly forged by friction.
7. The poetry of slow physics
Earth is not running down like a wound clock.
It is participating in a quiet celestial dialogue with the Moon.
Each tide whispers away an infinitesimal portion of spin,
stretching the day,
moving the Moon outward,
and reminding us that even the most stable rhythms of nature are temporary.
As the Moon continues its slow recession, the exquisite geometric coincidence that allows total solar eclipses will eventually be lost. The Moon’s apparent angular diameter will shrink below that of the Sun, and totality will give way forever to annular eclipses. Humanity happens to live in a brief cosmic window, a grace period measured in hundreds of millions of years, during which such perfection is possible.
That alone is a thought worthy of quiet reverence.
This is not decay. It is cosmic patience.
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