Definitions

# Deferents and epicycles

Direct motion is the motion of a planetary body in a direction similar to that of other bodies within its system, and is sometimes called prograde motion. Retrograde motion is motion in the opposite direction. In the case of celestial bodies, such motion may be real, defined by the inherent rotation or orbit of the body, or apparent, as seen in the skies from Earth.

While the terms direct and prograde are equivalent in this context, the former is the traditional term in astronomy. Prograde was first seen in an abstract of an astronomy-related professional article in 1963 (J. Geophys. Res. 68, 4979).

The word retrograde derives from the Latin words retro, backwards, and gradus, step

Inherent retrogradation is defined by motion relative to an axis of rotation or orbit.

The north orbital pole of a celestial body is defined by the right-hand rule: If one curves the fingers of the right hand along the direction of orbital motion, with the thumb extended parallel to the orbital axis, the direction the thumb points is defined to be south. (The International Astronomical Union has defined a different convention for planetary bodies in the solar system. According to this definition, the north pole is the one that points north of the invariable plane.)

Similarly, the north rotational pole of a body is defined by the direction of the thumb if one were to wrap the fingers around the body's equator in the direction it spins.

There are two notations for retrograde motion that are mathematically equivalent: The body can be considered to orbit backwards, or it can be considered to orbit forwards, but with its orbit upside-down. For example, a moon in a retrograde orbit that is inclined from the pole of its planet by 10°, and with a 6-hour orbital period, could be said to have the orbital parameters of:

• 10° (rightside-up) and −6 h (backwards),

in which case no inclination would ever exceed 90° (anything more than 90° would be upside-down), or of:

• 170° (upside-down) and +6 h (forwards), in which case no period would ever be negative.

Similarly, a moon spinning backwards on an axis inclined by 10° from the axis of its orbit can instead be described as being flipped upside-down and spinning forwards.

The choice between these two notations is largely arbitrary. It is more common to keep the period positive and let the inclination vary between 90° and 180° for retrograde motion, and between 0° and 90° for direct motion, but when this inclination is not listed, a negative period is the only indication that an orbit or rotation is retrograde. Thus it is common to see negative periods in tables of data (See natural satellite).

In the Solar system, most bodies orbit in a similar (direct) direction to the rotation of the Sun. All planets and most smaller bodies orbit the Sun counterclockwise as seen from a position above the Sun's north pole. The exceptions are mostly long-period and nonperiodic comets, which can have any inclination.

Similarly, the moons that are larger and closer to their parent planet orbit in the same direction as the planets' rotation, and are therefore also direct. However, the gas giant planets have large numbers of small "irregular" moons in highly inclined or elliptical orbits, thought to be captured asteroids or Kuiper belt objects (or fragments thereof), and the majority of these exhibit retrograde motion: 48 retrograde to 7 direct for Jupiter, 29 to 9 for Saturn, and 8 to 1 for Uranus. One of the largest of these is the Saturnian moon Phoebe. Neptune is somewhat different: it seems to have captured its only surviving large moon, the retrograde but otherwise regular Triton, from the Kuiper Belt. The six irregular moons beyond Triton's orbit are evenly divided between direct and retrograde motion; some of these may be original Neptunian moons whose orbits were disturbed by Triton's capture, rather than being captured bodies themselves.

Most planets, including Earth, spin in the direct sense: they spin in the same direction as they orbit the Sun (that is, their north rotational pole and north orbital pole point in similar directions, more or less in the direction of the Solar north pole). The exceptions are Venus, Uranus and the planetoid Pluto. Uranus rotates nearly on its side relative to its orbit. It has been described as having an axial tilt of 82° and a negative rotation of −17 hours, or, equivalently, of having an axis tilted at 98° and a positive rotation. Since current speculation is that Uranus started off with a typical direct orientation and was knocked on its side by a large impact early in its history, it is most commonly described as having the higher axial tilt and positive rotation. (Since Uranus' moons are considered relative to Uranus itself, their description is unaffected by the choice made for the planet.)

Retrograde Venus, on the other hand, has an axial tilt of less than 3°, and a very slow rotation of 243 days. Perhaps because it is easier to conceive of Venus as rotating slowly backwards than being 'upside down' relative to its near-twin Earth, but also because it is thought that an early massive impact may have resulted in Venus' current rotation while leaving its axis more or less unaffected, Venus is nearly always described as having its axis at 3° and a rotation of −243 days, rather than 177° and +243 days.

When we observe the sky, the Sun, Moon, and stars appear to move from east to west because of the rotation of Earth (so-called diurnal motion). However, objects such as the orbiter of the Space Shuttle and many artificial satellites appear to move from west to east. These are direct satellites (they actually orbit Earth in the same direction as the Moon), but they orbit Earth faster than Earth itself rotates, and so appear to move in the opposite direction. Mars has a natural satellite Phobos, with a similar orbit. From the surface of Mars it appears to move in the opposite direction to Earth's moon (Luna), even though both Phobos and Luna have direct orbits, because its orbital period is less than a Martian day, whereas Luna's orbital period (one month) is longer than a Terrestrial day. There are also smaller numbers of truly retrograde artificial satellites orbiting Earth which counter-intuitively appear to move westward, in the same direction as the Moon.

As seen from Earth, all the true planets appear to periodically switch direction as they cross the sky. Though all stars and planets appear to move from east to west on a nightly basis in response to the rotation of Earth, the outer planets generally drift slowly eastward relative to the stars. This motion is normal for the planets, and so is considered direct motion. However, since Earth completes its orbit in a shorter period of time than the planets outside its orbit, we periodically overtake them, like a faster car on a multi-lane highway. When this occurs, the planet we are passing will first appear to stop its eastward drift, and then drift back toward the west. Then, as Earth swings past the planet in its orbit, it appears to resume its normal motion west to east. Inner planets Venus and Mercury appear to move in retrograde in a similar mechanism, though their retrograde cycles are also tied to their conjunctions with the Sun. The apparent retrograde motion is explained by the same mechanism as the outer planets. Asteroids and Kuiper Belt Objects (including Pluto) also exhibit apparent retrogradation.

The more distant planets retrograde more frequently:

• Mars retrogrades for 72 days every 25.6 months.
• Jupiter for 121 days every 13.1 months.
• Saturn for 138 days every 12.4 months.
• Uranus for 151 days every 12.15 months and
• Neptune for 158 days every 12.07 months.

The period between such retrogradations is the synodic period of the planet.

This apparent retrogradation puzzled ancient astronomers, and was one reason they named these bodies 'planets' in the first place: 'Planet' comes from the Greek word for 'wanderer'. In the geocentric model of the solar system, retrograde motion was explained by having the planets travel in deferents and epicycles. It was not understood to be an illusion until the time of Copernicus. The accompanying map shows the retrograde motion of Mars for the year 2009-2010, which occurs against the background of the constellation Cancer.

## Examples

Some significant examples of retrograde motion in the solar system:

• Venus rotates slowly in the retrograde direction.
• The moons Ananke, Carme, Pasiphaë and Sinope all orbit Jupiter in a retrograde direction. Many other minor moons of Jupiter orbit retrograde.
• The moon Phoebe orbits Saturn in a retrograde direction, and is thought to be a captured Kuiper belt object.
• The moon Triton orbits Neptune in a retrograde direction, and is also thought to be a captured Kuiper belt object.
• The planet Uranus has an axial tilt of 98°, which is near 90°, and can be considered to be rotating in a retrograde direction depending on one's interpretation.

In astrology, the apparent retrograde motion of the planets was traditionally thought to be unlucky or inauspicious, as it went against the 'natural' order of movement, and a planet which was retrograde at the time of birth was considered a weak spot in the natal chart. Most modern astrologers still consider the retrograde movement of a planet to be indicative of stress or difficulty. For example, the retrograde movement of Mercury is commonly thought to signify difficulties in communication, such as post or emails going astray, verbal misunderstandings, and travel delays and frustrations. However, many astrologers do not consider retrograde movement to be of any particular significance, especially given that the outer planets are in retrograde motion for over 40% of the time.