Prograde and retrograde motion: Encyclopedia - Prograde and retrograde motion

Prograde and retrograde motion

Prograde motion is the rotational or orbital motion of a body in a direction similar to that of other bodies within a given system, and is sometimes called direct motion. Retrograde motion is in the contrary direction. The word 'retrograde' derives from the Latin words retro, backwards, and gradus, step.

Prograde and retrograde motion - Two notations

The north orbital pole of a celestial body is defined by the right-hand rule: If you curve the fingers of your right hand along the direction of orbital motion, with your thumb extended parallel to the orbital axis, the direction your thumb points is defined to be north.

Similarly, the north rotational pole of a body is defined by the direction of your thumb if you were to wrap your fingers around its 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.

It is more common to keep the orbital or rotational period positive and let the inclination vary between 90° and 180° for retrograde motion, and between 0° and 90° for prograde motion, but when this inclination isn't listed, a negative orbital period is the only indication that an object is retrograde. (See natural satellite.)

Prograde and retrograde motion - Retrograde orbits

In the Solar system, most bodies orbit in a similar (prograde) 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 comets, which generally have highly disturbed orbits.

Prograde and retrograde motion - Retrograde rotation

Most planets, including Earth, spin in the prograde 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 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 prograde 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 187° 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 the Earth (so-called diurnal motion). However, objects such as the Space Shuttle and many artificial satellites appear to move from west to east. These are direct satellites (they actually orbit the Earth in the same direction as the Moon), but they orbit the Earth faster than the Earth itself rotates, and so appear to move in the opposite direction. Mars has a natural moon, Phobos, with a similar orbit. It appears to move in the opposite direction to the 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 is longer than a Terrestrial day. There are also smaller numbers of truely retrograde artificial satellites orbiting the Earth which paradoxically appear to move westward, in the same direction as the Moon.

Prograde and retrograde motion - Retrogradation or apparent retrograde motion

Retrograde motion should not be confused with retrogradation. The latter term is used in reference to the motion of the outer planets (Mars, Jupiter, Saturn, Neptune, Uranus, and Pluto). Though these planets appear to move from east to west on a nightly basis in response to the spin of Earth, they are most of the time drifting slowly eastward with respect to the background of stars, which can be observed by noting the position of these planets for several nights in a row. This motion is normal for these planets, so it is called direct motion (not retrograde). However, since Earth completes its orbit in a shorter period of time than these outer planets, we occasionally overtake an outer planet, like a faster car on a multiple-lane highway. When this occurs, the planet we are passing will first appear to stop its eastward drift, and it will then appear to drift back toward the west. This is retrogradation, since the planet seems to be moving in a direction opposite to that which is typical for planets. Finally as Earth swings past the planet in its orbit, it appears to resume its normal west-to-east drift on successive nights.

Mars goes through retrogradation about every 25.7 months. The more distant outer planets retrograde more frequently. The period between such retrogradations is the synodic period of the planet.

This retrogradation puzzled ancient astronomers, and was one reason why they named these bodies 'planets' which in Greek means 'wanderers'. In the geocentric model of the solar system, this motion was accounted for by having the planets travel in deferents and epicycles. In modern astronomy, the term retrograde motion refers to objects which are actually moving in a direction opposite that which is normal to spatial bodies within a given system, as opposed to merely observed phenomena (retrogradation) such as that described above.

Prograde and retrograde motion - 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 to 90°, and can be considered to be rotating in a retrograde direction depending on one's interpretation.

Prograde and retrograde motion - Reference

This article originated from Jason Harris' Astroinfo which comes along with KStars, a Desktop Planetarium for Linux/KDE. See http://edu.kde.org/kstars/index.phtml

See also: Hipparchus, positional astronomy, Ptolemy

Categories: Astrodynamics | Celestial mechanics

Adapted from the Wikipedia article "Prograde and retrograde motion", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki