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How Do Scientists Measure How Long One Spin of the Earth Takes?

Category: Space & Astronomy

A day is 24 hours. But if you could watch the Earth from far away and count how long it takes to turn all the way around once, you would get about 23 hours and 56 minutes. Four minutes short.

That raises two puzzles. Where do the four minutes go? And how do you time a spin when you are standing on the thing that is spinning? The short answer: pick a marker that stays put, and count the time until the Earth faces it again with a clock you can trust. The surprise is that, for a long time, the clock was the Earth itself.

1. One Full Spin Takes About Four Minutes Less Than a Day

Our everyday day is measured from one noon to the next, that is, from the moment the Sun is highest in the sky to the next time it is highest. That is a solar day, 24 hours on average. A spin measured against distant stars is called a sidereal day. The International Earth Rotation and Reference Systems Service (IERS) gives its length as 86,164.09 seconds, which is 23 hours 56 minutes 4 seconds[1].

The gap comes from the Earth's trip around the Sun. In one day the Earth also moves about 1 degree along its orbit. So after one full spin, the Sun has not yet come back to the same spot in the sky. The Earth has to turn a little extra, and that extra turning takes nearly 4 minutes[2].

So "how long is one spin?" really means "how long until the Earth faces the same far-away direction again?" Everything below is about choosing that direction and counting the time.

2. You Need Two Things: A Marker That Stays Put and a Clock

Think of a spinning chair in a room. To time one turn, you watch for a mark on the far wall, such as a poster, to pass in front of you again. Then you read a clock. If the poster drifted along the wall, or if the clock sped up and slowed down, your answer would be off.

Measuring the Earth has exactly these two problems. The marker must be so far away that it hardly seems to move. The clock must tick steadily, whatever the Earth is doing. For centuries the first part was easy: stars are far away. The second part was the hard one.

3. For a Long Time the Clock Was the Earth, So Its Wobbles Were Hidden

Before atomic clocks, time was defined by the sky. A day, and the hours and seconds cut from it, came from the Earth's turning. A clock was checked against the stars and the Sun and kept in step with them.

Here is the trap. If you set your clock by the Earth's spin and then use that clock to time the spin, the answer is always "steady." Suppose the Earth sped up a little. Your clock would speed up with it, and nothing would look different. NIST describes the root of the problem in one line: "The day length changes unpredictably as Earth's rotation slows and speeds up"[3]. To catch the changes, scientists needed a clock that did not depend on the spin at all.

4. Atomic Clocks Gave Scientists a Clock That Ignores the Earth

In May 1955, the physicist Louis Essen unveiled a cesium atomic clock at the National Physical Laboratory in the United Kingdom. NIST calls it the first atomic clock stable enough to be used as a time standard[3]. Essen later wrote that he had invited his laboratory's director to "come and witness the death of the astronomical second and the birth of atomic time"[3].

In 1967 the General Conference on Weights and Measures redefined the second as 9,192,631,770 cycles of the microwave radiation from a cesium-133 atom[3]. From then on, the second was defined using an atom, not the Earth's motion.

The roles flipped. Now atomic clocks provide the steady time standard, and the Earth is the thing being measured. Any difference between "time set by the Earth's turning" (called UT1) and "time kept by atomic clocks" shows how the spin speed changes[4].

5. Radio Telescopes Use Distant Quasars as Markers That Hardly Move

Today the main method uses radio telescopes spread around the world. They detect radio signals from quasars, extremely distant objects, and treat them as fixed markers. As the Earth turns, the telescopes' positions relative to each quasar change, and the radio signals reach different dishes at slightly different times. Timing those arrivals with atomic clocks and analyzing them together with the telescopes' positions and the quasars' directions gives how far the Earth has turned[5]. This family of methods is called very long baseline interferometry, or VLBI. Wikipedia, citing the Paris Observatory's IERS centers, says VLBI is the main way Earth's rotation is monitored[1].

One limit: these methods give one value averaged over a whole day[6]. Good for tracking the slow changes, but not for catching what happens within a day.

6. A Ring of Laser Beams Can Feel the Earth Turn Without Looking at the Sky

In 2023, a team led by K. Ulrich Schreiber reported a different approach. Their instrument, called G, sits in an underground lab at the Geodetic Observatory Wettzell in Germany. Inside it, one laser beam travels clockwise around a square ring and another travels counterclockwise. Because the Earth turns underneath, the two beams do not match exactly. Mixing them makes a "beat," like two slightly out-of-tune notes, and the beat frequency reveals the rotation rate[5].

What makes this exciting is what it does not need. Schreiber is quoted as saying that a gyroscope measures rotation in an absolute way, with no outside reference[5]. The team reported variations in rotation rate of about five parts per billion over three months of continuous running, with each data point built from more than three hours of data[6]. Science News describes the result as measuring the length of a day to better than a millisecond[5]. Future versions may help scientists understand how air and ocean flows nudge the spin[6].

7. The Measurements Decide When Clocks Get a Leap Second

Time based on atomic clocks (UTC) and time based on the Earth's own turning (UT1) slowly drift apart, because the spin speed is not constant. Leap seconds keep the difference under 0.9 seconds[4]. When the corrections began in 1972, ten seconds had to be added at once[4]. The IERS, which measures the Earth's rotation, is the body whose data underlies this[4].

So the loop closes. We invented atomic clocks to measure a spinning planet, and the planet's measured wobble tells us when to nudge the clocks.

Check the Four-Minute Gap Yourself

  • Watch a bright star disappear behind a fixed spot. With an adult, pick a clear evening and a safe spot where a bright star slips behind a chimney or roof edge. Write down the time, using a clock set from the internet. Each clear night, watch the same star from the same spot and the same roof edge. The star should vanish about 4 minutes earlier each night. That is the gap between the solar and the sidereal day.
  • Keep the same spot and the same star. Stand in exactly the same place every time. Moving a few steps changes the time. After about ten nights you should see the trend. Stay with an adult at night, and avoid roads and dangerous places.
  • Read an original. Science News and Physics Today, linked below, describe the laser ring in plain language. The 2023 paper is in Nature Photonics.

Sources

This article is a personal summary based on the public sources listed below. I could not reach every primary page, so each note says how far I read.

  1. Wikipedia, "Earth's rotation." https://en.wikipedia.org/wiki/Earth%27s_rotation (Source for the sidereal day of 86,164.09 seconds and for VLBI being the main way Earth's rotation is monitored. It is a secondary source; the figures it cites come from IERS and Paris Observatory pages, which I could not open myself. Read through a summarizing fetch tool.)
  2. Wikipedia, "Sidereal time." https://en.wikipedia.org/wiki/Sidereal_time (Source for the Earth moving about 1 degree along its orbit per day and the solar day being nearly 4 minutes longer than the sidereal day. Secondary source, citing the Explanatory Supplement to the Astronomical Almanac. Read through a summarizing fetch tool.)
  3. NIST, "A Brief History of Atomic Time." https://www.nist.gov/atomic-clocks/brief-history-atomic-time (Source for day length changing unpredictably, Essen's May 1955 clock, his "death of the astronomical second" remark, and the 1967 definition of the second. A U.S. government page. Read through a summarizing fetch tool, not line by line.)
  4. NIST, "Leap Seconds FAQs." https://www.nist.gov/pml/time-and-frequency-division/leap-seconds-faqs (Source for UT1 versus UTC, the 0.9-second limit, the ten seconds added when corrections began in 1972, and the IERS measuring Earth's rotation. This page does not mention VLBI. Read through a summarizing fetch tool.)
  5. Emily Conover, Science News, "A laser gyroscope measured tiny variations in the lengths of days on Earth," September 18, 2023. https://www.sciencenews.org/article/laser-gyroscope-length-day-earth-physics (Source for the ring laser G, the beat signal, the better-than-a-millisecond result, and telescope methods using quasars as fixed references. News report on the Schreiber et al. paper; I could not open the paper itself, which is behind a login redirect. Read through a summarizing fetch tool.)
  6. Physics Today, "Laser gyroscope measures the variations in Earth's rotation rate," DOI 10.1063/PT.6.1.20230928a. https://physicstoday.aip.org/news/laser-gyroscope-measures-the-variations-in-earths-rotation-rate (Source for one daily-average value from satellite and radio-telescope methods, five parts per billion over three months, and more than three hours per data point. It describes the ring as 16 m around, with 4 m on each side, while Science News says 4 m per side; this article gives no size. Read in an extract.)

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