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In-depth
Period

Many natural phenomena are cyclical: they repeat in the same manner after nearly equal time intervals. The term period (from the Greek peri-odeyo = turn around) denotes the lapse of time after which the objects involved in the cyclical phenomenon, starting from a given initial configuration, will return to it. The best known and most easily reproducible cyclical phenomenon is the movement of the pendulum; but the most visible examples are found in astronomy.

Pendulum period

The simple pendulum consists of a flexible, non-elastic string of negligible mass, fastened at one end, carrying a heavy object of negligible size. The heavy object is swung when the string forms a given initial angle with the vertical. The period of the simple pendulum is the time taken by the heavy object to return to its starting point. The period—as Galileo (1564-1642) was the first to establish—is proportional to the square root of the length of the string; but it does not change if the mass of the object changes. Galileo observed that, for small oscillations, the pendulum period is also independent of the value of the initial angle (isochronism).

Period of Earth's rotation

The Earth rotates on its axis from west to east. Its rotation period can be determined by measuring the time between two successive observations of the same celestial body at the local meridian. If we take the Sun as the reference, the period of c. 24 hours is called solar day. If we take a star as the reference instead, the period of c. 23 hours and 56 minutes is called sidereal day (from the Latin sideralis = pertaining to the stars). The difference between the lengths of the two days is due to the Earth's concomitant shift along the orbit. The shift causes the Sun to be projected farther east on the Zodiac by about 1° per day and thus delays its observation at the meridian by about 4 minutes with respect to a star.

In ancient geocentric astronomy, which held the Earth to be immobile, the measured durations of the solar day and sidereal day were similar to the present ones; but the phenomena responsible for the two periods were different. Owing to the different perspective, the diurnal rotation of the sphere of the fixed stars from east to west determined the length of the sidereal day, while the slightly slower rotation of Sun, also from east to west, determined the solar day.

Period of terrestrial revolution

The Earth completes its orbit in a revolution period that can be determined with respect to the Sun or the stars. The term sidereal year denotes the period of 365 days, 6 hours, and 48 minutes elapsed between two successive observations of the Sun at the same point in the Zodiac. The term tropical year denotes the period of 365 days, 6 hours, and 28 minutes elapsed between two successive observations of the Sun at the spring equinox. The twenty-minute difference between the two years is due to the precession of the equinoxes. By shifting the direction of the terrestrial axis, precession moves up the positions of the equinoxes on the Zodiac by about 50" of arc per year.

In ancient geocentric astronomy, which held the Earth to be immobile, the measured durations of the sidereal year and the tropical year were similar to the present ones; but the phenomena responsible for the two periods were different. Starting at the spring equinox, the Sun objectively traveled along the ecliptic from west to east and returned to the equinox after a tropical year. A few minutes later, the sidereal year was completed; the Sun reached those fixed stars that were located at the equinox in the previous year but had shifted slightly eastward owing to the precession of the equinoxes (interpreted as an intrinsic motion of the sphere of fixed stars).

Periods of the planets

Two periods of planetary motion are defined: the first relative to the Sun, the second relative to the fixed stars. The synodic period (from the Greek *synodikós = relating to conjunction) is the mean time after which the planet, starting from a given angular distance from the Sun (elongation), returns to that distance. The sidereal period is the mean time between two successive passages of the planet at the same point of the Zodiac.

In present-day heliocentric astronomy, in which planets move around the Sun, the sidereal period is equivalent to the planet's orbital period. In ancient geocentric astronomy, in which planets moved around the immobile Earth, the measured durations of sidereal periods were similar to the present ones for the three planets superior to the Sun then known: Mars, Jupiter, and Saturn (we now describe the three as external to the terrestrial orbit). By contrast, the sidereal periods of Mercury and Venus were different. The two inferior planets—which we now call internal—apparently never moved very far from the Sun and hence seemed to have the same annual sidereal motion as the Sun.

Planet / Sidereal period / Synodic period

- Mercury / 88 d (geocentric: 1 yr) / 116 d

- Venus / 225 d (geocentric: 1 yr) / 219 d

- Mars /1 yr 322 d / 2 yr 49 d

- Jupiter / 11 yr 315 d / 1 yr 34 d

- Saturn / 29 yr 167 d / 1 yr 13 d

- Uranus / 84 yr 7 d / 1 yr 4 d

- Neptune / 164 yr 280 d / 1 yr 2 d

- Pluto / 247 yr 249 d / 1 yr 1 d