The Moon, the Tides, and the Slow Expenditure of Earth’s Rotational Energy
I wrote an article last year on:
The Moon and Tides - From Ancient Wonder to Celestial Mechanics
https://scientificlogic.blogspot.com/search?q=time+and+tides
See also this recent article I wrote here:
https://scientificlogic.
Let me continue where I left out to explain the energy expenditure of a rotating Earth to raise up the tides twice each day across the oceans including over the solid Earth
Since its formation some 4.54 billion years ago, the Earth has never ceased to rotate. That rotation is not merely a kinematic fact but a vast reservoir of energy, accumulated during the violent assembly of the planet and preserved by the near-frictionless environment of space. Yet the Earth does not spin freely. The Moon, by raising tides in both ocean and solid rock, continuously extracts energy and angular momentum from Earth’s rotation. The result is a planet whose days grow imperceptibly longer, and a Moon that drifts slowly outward, year after year.
A useful physical analogy is that of a spinning top. In a perfect vacuum, with no contact and no friction, the top would spin forever. In reality, friction at its tip and drag from air convert rotational energy into heat, while angular momentum is transferred to the Earth beneath it. The Earth itself resembles an almost ideal spinning top: it touches nothing material as it rotates and is surrounded by near-vacuum. Non-idealities remain, however, and among them, tidal friction is overwhelmingly dominant.
The Moon’s gravitational field is not uniform across the Earth. The side nearer the Moon experiences a stronger pull than the centre, and the far side experiences a weaker pull. This differential force produces two tidal bulges in the oceans: one facing the Moon and one opposite. As the Earth rotates, its continents and seabeds continually pass through these bulges. Water is forced to move, to surge against coastlines, to flow through shallow seas, straits, and continental shelves. Every such motion dissipates energy as heat through friction.
Less visible, but equally important, are tides raised in the solid Earth itself. Twice each day, the rocky crust and mantle deform by a few centimeters and relax again. This continual flexing generates internal friction, converting rotational energy into heat deep within the planet. Together, oceanic tides and solid-Earth tides act as a global brake on Earth’s rotation.
The magnitude of this braking can be quantified. Modern geophysical estimates place the total tidal dissipation at approximately 3 to 4 terawatts (TW) of power. Expressed differently, Earth loses about:
3–4 × 10¹² joules per second
≈ 2.5–3.5 × 10¹⁴ joules per minute
≈ 2.0–3.0 × 10¹⁷ joules per day
≈ 7–10 × 10¹⁹ joules per year
Older estimates, often expressed in thermal units, correspond to roughly 20–40 billion kilocalories per minute, in good agreement with modern values once units are reconciled.
This energy loss is astonishingly small compared with Earth’s total rotational energy, which is on the order of 2 × 10²⁹ joules. At the present rate, it takes about 62,500 years for the day to lengthen by a single second. Today, the average secular increase in day length is approximately 1.7 milliseconds per century, or 44 billionths of a second per day.
Although small, this change is measurable. Atomic clocks have revealed that Earth is an imperfect timekeeper. Superimposed upon the slow, monotonic tidal braking are irregular variations caused by earthquakes, mantle convection, atmospheric circulation, ocean currents, and seasonal redistribution of mass. These effects can shorten or lengthen the day by milliseconds over short timescales, but they average out over decades. What remains is the inexorable lunar tide.
Evidence for Earth’s faster rotation in the past comes not only from astronomy but from geology and palaeontology. Fossil corals from the Middle Devonian, studied by John West Wells in 1963, show daily growth bands that imply about 400 days per year some 400 million years ago, corresponding to a day length of roughly 21.9 hours. Historical astronomy shows that at the time of the Great Pyramids, about 4,500 years ago, the day was approximately 0.07 milliseconds shorter than today. Shortly after the Moon’s formation, Earth may have rotated once every 5–6 hours.
As Earth loses rotational angular momentum, the Moon gains orbital angular momentum and slowly recedes at a rate of about 3.8 centimeters per year. This is a direct consequence of the conservation of angular momentum. In the very distant future, far beyond the Sun’s lifetime, namely the Earth and Moon may become tidally locked, with a single day lasting many present-day weeks.
The scale of tidal energy dissipation invites a natural comparison with human energy use. Modern civilization consumes roughly 18–20 terawatts of primary energy on average, equivalent to about 1.5–1.7 × 10²⁰ joules per day. Earth’s tidal dissipation of 3–4 terawatts therefore amounts to roughly 15–25% of humanity’s total power consumption, or about one-sixth to one-quarter of global daily energy use. In other words, every day, Earth converts rotational energy into heat through tides on a scale comparable to that used daily by all of humanity
This raises an obvious question: can we harness tidal energy as a clean and sustainable resource?
The answer is yes, but only partially. Tidal energy can be extracted through tidal barrages, tidal lagoons, and tidal-stream turbines that exploit fast-flowing currents. Unlike wind or solar energy, tides are exquisitely predictable, governed by celestial mechanics rather than weather. Tidal power is clean, produces no greenhouse gases during operation, and operates day and night.
However, only a small fraction of global tidal dissipation occurs in locations suitable for energy extraction. Most tidal energy is lost as low-grade heat in shallow seas, continental shelves, and the solid Earth itself, namely in places inaccessible or impractical for engineering. Even optimistic estimates suggest that at most 1–2 terawatts of tidal power could be sustainably harvested worldwide without significantly altering coastal ecosystems or tidal dynamics. This is valuable but cannot replace all other energy sources.
Moreover, extracting tidal energy slightly increases the rate at which Earth’s rotation slows. The effect is minuscule compared with natural tidal braking, but it serves as a reminder that even “renewable” energy ultimately comes from finite reservoirs, in this case, Earth’s rotational energy.
The tides therefore teach a subtle lesson. The Moon has been drawing down Earth’s rotational energy for billions of years, lengthening the day, shaping climates, guiding biological rhythms, and recording its work in fossils and rocks. Humanity has now reached a level of technological maturity where it can tap into this ancient process, but only modestly and with care.
Time itself, measured by the length of the day, is not fixed. It is a dynamic quantity, sculpted by gravity, friction, and the slow exchange of angular momentum between Earth and Moon. Each tide that rises and falls is a small expenditure from a planetary energy account that has been open since the birth of the Earth, and will not close until long after human clocks have fallen silent.
References for further reading
1. Munk, W. H., & MacDonald, G. J. F. The Rotation of the Earth. Cambridge University Press.
2. Lambeck, K. The Earth’s Variable Rotation. Cambridge University Press.3.
3. Wells, J. W. (1963). Coral growth and geochronometry. Nature, 197, 948–950.4.
4. Ray, R. D., & Egbert, G. D. (2012). Tidal dissipation in the solid Earth. Journal of Geophysical Research.
5. IPCC & IEA global energy statistics (recent summaries).
Here is my Chinese version of the above article:
月球、潮汐与地球自转能的缓慢消耗
- 时间的物理学与行星能量的支出
我在去年写过一篇文章：
《月球与潮汐——从古代奇观到天体力学》
（链接略）
让我从那里继续，解释一个旋转着的地球，为了每天两次在全球海洋（以及固体地球）中掀起潮汐，究竟付出了怎样的能量代价。
自大约 45.4 亿年前 形成以来，地球从未停止过自转。这种旋转不仅仅是一个运动学事实，更是一个巨大的能量储库——在行星剧烈聚集形成的过程中积累，并在近乎无摩擦的宇宙环境中得以保存。然而，地球并非自由旋转。月球通过在海洋和固体岩石中激发潮汐，不断从地球的自转中抽取能量和角动量。其结果是：地球的白昼在极其缓慢地变长，而月球则年复一年地缓慢远离。
一个有用的物理类比是旋转的陀螺。在完美真空中，没有接触、没有摩擦，陀螺将永远旋转。但在现实中，陀螺尖端的摩擦和空气阻力会把转动能转化为热，同时将角动量传递给下方的地面。地球本身就像一个几乎理想的陀螺：它在旋转时并不接触任何物质，并被近乎真空的空间所包围。然而，非理想因素仍然存在，而其中最主要的正是——潮汐摩擦。
月球的引力场在地球上并不均匀。靠近月球的一侧受到的引力较强，地球中心较弱，而远离月球的一侧最弱。这种引力差异在海洋中产生了两个潮汐隆起：一个朝向月球，一个在背向月球的一侧。随着地球自转，大陆和海底不断穿过这些隆起，海水被迫运动、冲击海岸线、流经浅海、海峡和大陆架。所有这些运动都会通过摩擦将能量耗散为热。
同样重要但不那么显眼的是，固体地球本身也会产生潮汐。每天两次，地壳和地幔会发生几厘米的弹性形变，然后再恢复。这种持续不断的弯曲与松弛在地球内部产生摩擦，将自转能转化为热。海洋潮汐与固体潮汐共同构成了一个全球性的制动系统，持续减慢地球的自转。
这种制动效应的大小是可以定量估算的。现代地球物理学认为，全球潮汐耗散功率大约为：
3–4 太瓦（TW）
换一种表达方式，地球大约损失：
-
每秒：3–4 × 10¹² 焦耳
-
每分钟：2.5–3.5 × 10¹⁴ 焦耳
-
每天：2.0–3.0 × 10¹⁷ 焦耳
-
每年：7–10 × 10¹⁹ 焦耳
早期以热量单位表示的估算值，大约为每分钟 200–400 亿千卡，在单位换算后与现代结果高度一致。
与地球巨大的自转总能量（约 2 × 10²⁹ 焦耳）相比，这个损失极其微小。按当前速率计算，大约需要 62,500 年，一天才会变长 1 秒。目前观测到的长期平均值是：每世纪增加约 1.7 毫秒，也就是每天约 0.000000044 秒。
尽管如此微小，这一变化却是可以测量的。原子钟揭示出：地球并不是一个完美的计时器。在缓慢而单调的潮汐制动之上，还叠加着由地震、地幔对流、大气环流、洋流以及季节性质量重新分布所引起的短期不规则变化。这些效应会在短时间内让一天变长或变短几毫秒，但在几十年的平均尺度上会相互抵消。最终留下的，是那不可逃避的——月球潮汐效应。
地球过去自转更快的证据不仅来自天文学，也来自地质学与古生物学。1963 年，John West Wells 对泥盆纪中期的化石珊瑚研究发现，其日生长纹表明：大约 4 亿年前一年有约 400 天，对应一天约 21.9 小时。历史天文学还显示，在大金字塔建成的年代（约 4500 年前），一天比今天短约 0.07 毫秒。而在月球刚形成不久时，地球可能每 5–6 小时就自转一圈。
随着地球失去自转角动量，月球则获得轨道角动量，并以约 每年 3.8 厘米 的速度逐渐远离。这是角动量守恒的直接结果。在极其遥远的未来，远远超过太阳寿命之后，地球和月球可能进入潮汐锁定状态，一个“地球日”将持续数个现代星期。
潮汐能量耗散的规模，自然会引发一个与人类社会有关的比较。现代文明平均消耗约 18–20 太瓦 的一次能源，相当于每天 1.5–1.7 × 10²⁰ 焦耳。因此，地球潮汐耗散的 3–4 太瓦，大约相当于人类总功率的 15–25%，也就是全球每日能耗的 六分之一到四分之一。
换句话说：每天，地球通过潮汐把自转能转化为热，其规模与整个人类文明每天使用的能量同一量级。
这自然引出了一个问题：
我们能否把潮汐能作为清洁、可持续的能源加以利用？
答案是：可以，但只能部分实现。
潮汐能可以通过潮汐坝、潮汐湖和潮流涡轮机来获取，利用快速流动的潮汐水流。与风能和太阳能不同，潮汐极其可预测，受天体力学而非天气控制。潮汐发电清洁、运行中不产生温室气体，而且昼夜不停。
然而，全球潮汐耗散中只有很小一部分发生在适合工程利用的地点。大多数潮汐能量以低品位热的形式耗散在浅海、大陆架和固体地球内部——这些地方要么无法接近，要么无法工程化。即使在最乐观的估计下，全球可持续开采的潮汐功率也只有 1–2 太瓦，而且不能显著改变海岸生态系统和潮汐动力学。这固然有价值，但无法取代所有其他能源。
此外，提取潮汐能会略微加快地球自转减慢的速率。虽然这一效应与自然潮汐制动相比微不足道，但它提醒我们：即使是“可再生能源”，最终也来自有限的能量储库——在这里，就是地球的自转能。
因此，潮汐给我们上了一堂极其微妙的课。数十亿年来，月球一直在消耗地球的自转能，拉长白昼，塑造气候，引导生物节律，并把这一切记录在化石与岩石之中。如今，人类已达到一种技术成熟阶段，能够开始利用这一古老过程，但只能谨慎而有限地进行。
时间本身——以一天的长度来衡量——并不是固定不变的。它是一个动态量，由引力、摩擦以及地月之间缓慢的角动量交换所塑造。每一次潮起潮落，都是从一个自地球诞生之日起就开设的“行星能量账户”中支出的一小笔，而这个账户，只有在远远超过人类文明终结之后，才会真正关闭。
延伸阅读参考文献
1. Munk, W. H., & MacDonald, G. J. F. The Rotation of the Earth. Cambridge University Press.
2.Lambeck, K. The Earth’s Variable Rotation. Cambridge University Press.
3. Wells, J. W. (1963). Coral growth and geochronometry. Nature, 197, 948–950.
4.Ray, R. D., & Egbert, G. D. (2012). Tidal dissipation in the solid Earth. Journal of Geophysical Research.
5.IPCC & IEA 全球能源统计报告（近期摘要）
What I write here is truly rare thought. It shows that time is not just measured by clocks, but paid for by energy.
In Chinese, this whole essay reads almost like a dialogue between physics and Daoism.
If I may say one poetic line in Chinese, inspired by my own spirit is this:
“潮汐不是在移动海水，
而是在缓慢地移动时间本身。”
In English it means:
The tides are not moving the seawater, but rather slowly moving time itself.
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