Illustration by Matt Zang

Pace of the Planets

 

The orbital periods of the planets grow longer with increasing distance from the sun. Sluggish Saturn completes a fraction of an orbit in the same time it takes Mercury to complete one circuit. The planets’ widely varying, nonrhythmic motions explain why even approximate alignments are so unusual.

From mid-March through early April, all five “naked-eye” planets will be aligned across the evening sky. Mercury will hover low but bright in the western twilight, and Venus will dance above it. Mars, Saturn, and Jupiter are higher up, arrayed like a ragged chorus line. A similar apparition will grace the morning sky this December. After that, we will have to wait a dozen years before anything even remotely like this happens again.

Alignments are rare simply because the solar system as a whole does not follow neat mathematical patterns: The planets have widely varying orbital periods that aren’t evenly divisible by each other. The slowest-moving bright planets, Jupiter and Saturn, meet up just once every 19.85 years. Mars’s orbital period of 1.88 years means that if it is on the same side of the sun as one Jupiter-Saturn meeting, it will be nearly on the opposite side the next time around. Adding in the variables of when Venus and Mercury are invisibly close to the sun reveals why the current lineup is an unusual treat.


Nonetheless, there are many synchronicities hidden within the solar system’s apparent disorder. For instance, although the sun and the moon have drastically different diameters, they appear the same size in the sky. The sun is 400 times larger than the moon, but it is also 400 times farther from Earth. Both the sun and the moon rotate in nearly the same 27-day period. All of this is chance, nothing more.

Other patterns are rooted in physics. Take, for instance, the three big inner Jovian moons, now visible through binoculars as Jupiter reaches its closest approach to Earth on March 4. They orbit in a precise 1:2:4 rhythm: While Io whizzes around Jupiter four times, Europa orbits twice and Ganymede once. Gravitational interactions between the moons produce tides that have nudged them into orderly orbits over billions of years.

Even planets are not immune to the relentless action of tides. Mercury, now making its best appearance of the year, rotates in 58.6 days and orbits the sun every 88 days. The former number is exactly two-thirds of the latter, so the planet presents the same side to the sun, and to us, every other revolution. Repeatedly seeing the same features, astronomers mistakenly deduced that the sun’s gravity caused Mercury to rotate and revolve at the same rate, just as Earth’s pull keeps one face of the moon pointed our way. In 1965 radar measurements revealed Mercury’s true two-thirds rotation pattern, a similar but less complete type of gravitational synchrony.

Every major satellite rotates in step with its orbit, so that one side is forever pointed toward its parent planet. Pluto is the only planet that follows the reverse pattern, keeping one side locked toward its satellite, Charon. As a result, Pluto’s “day” and its “month” are the same, 6.4 Earth days long.
Other patterns seem less like science and more like fun with numbers. A wonderful example was discovered by German astronomer Johann Daniel Titius in 1766. Take the sequence 0, 3, 6, 12, 24, 48, 96, in which the numbers double after zero. Add 4 to each number, divide by 10, and you get .4, .7, 1, 1.6, 2.8, 5.2, 10. That sequence closely matches the spacing of the planets when expressed as multiples of Earth’s distance from the sun. Mercury is .4 times as far, Venus is .7, Earth is 1, Mars is 1.6, the asteroids are 2.8, Jupiter is 5.2, and Saturn is 9.5. This match is now regarded as nothing more than coincidence.

Another German astronomer, Johannes Kepler, had more success with his numerical dabblings. He noticed the cube of any planet’s relative distance from the sun equals the square of its orbital period. Jupiter, for example, lies at 5.2 Earth distances. The cube of 5.2 is 140.6, the same as the square of Jupiter’s 11.86-year orbit.

Decades later, Isaac Newton showed that this mathematical curiosity is a consequence of the way the force of gravity decreases with distance. Newton’s discovery was a true physical law, a fascinating example of the inherent mathematical harmony hidden in the same spheres now arrayed so strikingly across the heavens.