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Study Guide: Planetary Coordinate Systems and Geodesy

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Planetary Coordinate Systems and Geodesy Study Guide

Fundamentals of Planetary Coordinate Systems

A planetary coordinate system is exclusively used for gas giants, as solid bodies utilize a different nomenclature.

Answer: False

Explanation: Planetary coordinate systems are generalized systems used for all celestial bodies other than Earth, including both solid bodies and gas giants, though the specific reference points differ.

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Selenographic coordinates are specifically used to define locations on Earth's Moon.

Answer: True

Explanation: The term 'selenographic coordinates' is specifically designated for defining locations on Earth's Moon, analogous to geographic coordinates for Earth.

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Merton E. Davies of the Rand Corporation was primarily responsible for establishing coordinate systems for Earth's oceans, not other Solar System bodies.

Answer: False

Explanation: Merton E. Davies of the Rand Corporation was, in fact, responsible for establishing coordinate systems for almost all solid bodies throughout the Solar System, not primarily Earth's oceans.

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A planetary datum requires the specification of physical reference points or surfaces with fixed coordinates, such as a specific crater for a reference meridian.

Answer: True

Explanation: A planetary datum, a generalization of geodetic datums, fundamentally requires the specification of physical reference points or surfaces with precisely fixed coordinates, such as a designated crater for a reference meridian.

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The Equator, or zero latitude plane, for celestial bodies is defined as being parallel to the mean axis of rotation.

Answer: False

Explanation: The Equator, or zero latitude plane, for celestial bodies is defined as being orthogonal (perpendicular) to the mean axis of rotation, not parallel to it.

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Which of the following is NOT an alternative name for a planetary coordinate system?

Answer: Geocentric

Explanation: Planetographic, planetodetic, and planetocentric are all alternative names for a planetary coordinate system. Geocentric refers specifically to Earth-centered coordinates.

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What specific term is used for coordinate systems defined for the Moon?

Answer: Selenographic coordinates

Explanation: Coordinate systems specifically defined for Earth's Moon are known as selenographic coordinates.

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Who was responsible for establishing coordinate systems for almost all solid bodies in the Solar System?

Answer: Merton E. Davies

Explanation: Merton E. Davies of the Rand Corporation was the key figure responsible for establishing coordinate systems for nearly all solid bodies within the Solar System.

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What is a key requirement for the specification of a planetary datum?

Answer: Physical reference points or surfaces with fixed coordinates.

Explanation: A fundamental requirement for specifying a planetary datum is the establishment of physical reference points or surfaces with precisely fixed coordinates.

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How is the zero latitude plane, or Equator, defined for a celestial body?

Answer: As being orthogonal (perpendicular) to the mean axis of rotation.

Explanation: The zero latitude plane, or Equator, for a celestial body is defined as being orthogonal (perpendicular) to its mean axis of rotation.

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Defining Poles, Meridians, and Rotation

The prime meridian for the Moon is located at the center of its far side, according to the source material.

Answer: False

Explanation: The source material indicates that the prime meridian for the Moon is located at the center of its near side, not its far side.

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For most celestial bodies with observable rigid surfaces, longitude systems are defined by referencing a specific surface feature like an impact crater.

Answer: True

Explanation: Longitude systems for most celestial bodies with observable rigid surfaces are indeed defined by referencing a specific, identifiable surface feature, such as an impact crater, to establish the prime meridian.

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The north pole of rotation for a celestial body is defined as the pole that lies on the south side of the Solar System's invariable plane.

Answer: False

Explanation: The north pole of rotation for a celestial body is defined as the pole that lies on the north side of the Solar System's invariable plane.

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Precession, a slow wobble in an object's rotational axis, can cause the location of a body's prime meridian and north pole to change over time.

Answer: True

Explanation: Precession, which is a slow wobble in a celestial body's rotational axis, is a known phenomenon that can cause the location of both the prime meridian and the north pole to shift over extended periods.

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If the position angle of a body's prime meridian decreases with time, the body is said to have a direct, or prograde, rotation.

Answer: False

Explanation: If the position angle of a body's prime meridian decreases with time, its rotation is classified as retrograde, not direct or prograde.

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For Mercury and most satellites, in the absence of other information, their axis of rotation is assumed to be normal to their mean orbital plane.

Answer: True

Explanation: In the absence of specific data, it is a standard assumption that the axis of rotation for Mercury and most satellites is normal (perpendicular) to their mean orbital plane.

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The rotation of surface features is the primary reference for defining coordinate systems on giant planets.

Answer: False

Explanation: For giant planets, the rotation of their magnetic fields, rather than their constantly changing surface features, is used as the primary reference for defining coordinate systems.

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For the Sun, an agreed-upon value for the rotation of its equator is used as a reference because its magnetic field is too complex and unsteady.

Answer: True

Explanation: Due to the Sun's complex and unsteady magnetic field, an agreed-upon value for the rotation of its equator is utilized as the reference for its coordinate system.

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Planetographic longitude is measured positively to the east when a body has a prograde rotation.

Answer: False

Explanation: Planetographic longitude is measured positively to the west when a body exhibits prograde (direct) rotation, not to the east.

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Planetocentric longitude is consistently measured positively to the east, regardless of the planet's rotation direction.

Answer: True

Explanation: Planetocentric longitude maintains a consistent measurement convention, always being measured positively to the east, irrespective of the celestial body's rotational direction.

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The modern standard for maps of Mars since 2002 is to use planetographic coordinates, with its prime meridian at the Airy-0 crater.

Answer: False

Explanation: Since approximately 2002, the modern standard for maps of Mars utilizes planetocentric coordinates, not planetographic, with its prime meridian established at the Airy-0 crater.

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Mercury's prime meridian is defined by a thermocentric coordinate system, running through the point on the equator with the highest temperatures.

Answer: True

Explanation: Mercury's prime meridian is indeed defined using a thermocentric coordinate system, specifically passing through the point on its equator that experiences the highest temperatures.

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Where is the prime meridian for the Moon located, according to the source material?

Answer: At the center of its near side.

Explanation: The source material specifies that the prime meridian for Earth's Moon is located at the center of its near side.

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How are longitude systems for most celestial bodies with observable rigid surfaces defined?

Answer: By referencing a specific surface feature, such as an impact crater.

Explanation: For most celestial bodies with observable rigid surfaces, longitude systems are defined by referencing a specific surface feature, such as an impact crater, to establish the prime meridian.

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How is the north pole of rotation defined for a celestial body?

Answer: The pole that lies on the north side of the Solar System's invariable plane.

Explanation: The north pole of rotation for a celestial body is defined as the pole that is situated on the north side of the Solar System's invariable plane.

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What phenomenon can cause a body's prime meridian and north pole position to change over time?

Answer: Precession

Explanation: Precession, a slow wobble in an object's rotational axis, is the phenomenon that can cause the location of a body's prime meridian and north pole position to change over time.

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How is a body's rotation classified if the position angle of its prime meridian decreases with time?

Answer: Retrograde rotation

Explanation: If the position angle of a body's prime meridian decreases with time, its rotation is classified as retrograde.

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In the absence of specific information, what is assumed about the axis of rotation for Mercury and most satellites?

Answer: It is normal to their mean orbital plane.

Explanation: In the absence of specific information, the axis of rotation for Mercury and most satellites is assumed to be normal (perpendicular) to their mean orbital plane.

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What is used as the primary reference for defining coordinate systems for giant planets?

Answer: The rotation of their magnetic fields.

Explanation: For giant planets, the rotation of their magnetic fields serves as the primary reference for defining their coordinate systems, given their dynamic and variable surface features.

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Why does the Sun use an agreed-upon value for its equator's rotation as a reference?

Answer: Its magnetic field is too complex and unsteady.

Explanation: The Sun utilizes an agreed-upon value for its equator's rotation as a reference because its magnetic field is too complex and unsteady to serve as a reliable coordinate system reference.

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How is planetographic longitude measured for a body with prograde (direct) rotation?

Answer: Positively to the west.

Explanation: For a body with prograde (direct) rotation, planetographic longitude is measured positively to the west.

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In planetocentric longitude, how is 'east' defined when viewed from above the body's north pole?

Answer: Counterclockwise direction.

Explanation: In planetocentric longitude, 'east' is defined as the counterclockwise direction when viewed from above the body's north pole.

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What is the modern standard for maps of Mars since approximately 2002?

Answer: Planetocentric coordinates with the prime meridian at the Airy-0 crater.

Explanation: Since approximately 2002, the modern standard for maps of Mars employs planetocentric coordinates, with its prime meridian precisely located at the Airy-0 crater.

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How is the prime meridian defined for Mercury?

Answer: Through the point on the equator that experiences the highest temperatures.

Explanation: For Mercury, the prime meridian is defined thermocentrically, passing through the point on its equator that experiences the highest temperatures.

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Reference Surfaces: Ellipsoids and Geoids

For planets like Earth and Mars, the reference surfaces used are oblate spheroids, which are ellipsoids of revolution with an equatorial bulge.

Answer: True

Explanation: For planets such as Earth and Mars, the standard reference surfaces are oblate spheroids, which are ellipsoids of revolution characterized by an equatorial bulge and polar flattening.

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Vertical position in a planetary coordinate system is expressed only through altitude/elevation measurements above a geoid.

Answer: False

Explanation: Vertical position in a planetary coordinate system can be expressed in multiple ways, including relative to a specified vertical datum using physical quantities or through altitude/elevation measurements above or below a geoid.

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The 'areoid' is the term for the geoid of Mars, measured using satellite missions like Mariner 9 and Viking.

Answer: True

Explanation: The 'areoid' is indeed the term for the geoid of Mars, and its measurement has been accomplished through satellite missions such as Mariner 9 and Viking.

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The main gravitational departures from an ideal ellipsoid on Mars are primarily due to its extensive polar ice caps.

Answer: False

Explanation: The primary gravitational departures from an ideal ellipsoid on Mars are attributed to the Tharsis volcanic plateau and its antipodal points, not primarily its polar ice caps.

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The 'selenoid' is the term for the geoid of the Moon, measured gravimetrically by the GRAIL twin satellites.

Answer: True

Explanation: The 'selenoid' is the correct term for the geoid of Earth's Moon, and its gravitational field was precisely mapped gravimetrically by the GRAIL twin satellites.

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Reference ellipsoids are only useful for large planets and are not typically applied to smaller bodies like asteroids or comet nuclei.

Answer: False

Explanation: Reference ellipsoids are useful for defining geodetic coordinates and mapping a wide range of celestial bodies, including planets, their satellites, asteroids, and comet nuclei, not just large planets.

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For rigid-surface, nearly-spherical bodies, ellipsoids are defined based on their axis of rotation and their mean surface height, excluding any atmosphere.

Answer: True

Explanation: For rigid-surface, nearly-spherical celestial bodies, ellipsoids are defined by considering their axis of rotation and their mean surface height, explicitly excluding any atmospheric influence.

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Mars is perfectly spherical, making its north and south polar radii identical.

Answer: False

Explanation: Mars is not perfectly spherical; it is described as egg-shaped, with its north and south polar radii differing by approximately 6 kilometers.

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For gaseous planets, an effective surface for an ellipsoid is chosen as the equal-pressure boundary of one bar, and prime meridians are determined by mathematical rules.

Answer: True

Explanation: For gaseous planets lacking a solid surface, the effective surface for an ellipsoid is defined as the one-bar equal-pressure boundary, and their prime meridians are established through mathematical rules due to the absence of permanent physical features.

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What type of reference surface is typically used for planets like Earth and Mars?

Answer: Oblate spheroids

Explanation: For planets such as Earth and Mars, the typical reference surfaces employed are oblate spheroids, which are ellipsoids of revolution with an equatorial bulge.

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How can vertical position be expressed in a planetary coordinate system?

Answer: Relative to a specified vertical datum, using physical quantities or altitude/elevation measurements.

Explanation: Vertical position in a planetary coordinate system can be expressed relative to a specified vertical datum, utilizing physical quantities or altitude/elevation measurements above or below a geoid.

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What is the 'areoid'?

Answer: The term for the geoid of Mars.

Explanation: The 'areoid' is the specific term used to refer to the geoid of Mars, representing its theoretical mean sea level surface based on gravity.

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What are the main gravitational departures from an ideal ellipsoid on Mars attributed to?

Answer: The Tharsis volcanic plateau and its antipodes.

Explanation: The primary gravitational departures from an ideal ellipsoid on Mars are attributed to the Tharsis volcanic plateau and its antipodal points.

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How was the 'selenoid' measured?

Answer: Gravimetrically by the GRAIL twin satellites.

Explanation: The 'selenoid,' representing the Moon's gravitational equipotential surface, was measured gravimetrically by the GRAIL twin satellites.

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For what types of celestial bodies are reference ellipsoids useful?

Answer: Planets, their satellites, asteroids, and comet nuclei.

Explanation: Reference ellipsoids are valuable for defining geodetic coordinates and mapping a broad spectrum of celestial bodies, including planets, their satellites, asteroids, and comet nuclei.

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How are ellipsoids defined for rigid-surface, nearly-spherical bodies?

Answer: Based on their axis of rotation and their mean surface height, excluding any atmosphere.

Explanation: For rigid-surface, nearly-spherical bodies, ellipsoids are defined based on their axis of rotation and their mean surface height, specifically excluding any atmospheric considerations.

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What is notable about Mars' shape in relation to its ellipsoid definition?

Answer: It is egg-shaped, with differing north and south polar radii.

Explanation: Mars is notable for its egg-shaped morphology, characterized by differing north and south polar radii, although an average polar radius is used for its reference ellipsoid.

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For gaseous planets, what is chosen as the effective surface for an ellipsoid?

Answer: The equal-pressure boundary of one bar.

Explanation: For gaseous planets, the effective surface for an ellipsoid is chosen as the equal-pressure boundary of one bar, serving as a consistent reference in the absence of a solid surface.

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Planetary Shape: Flattening and Equatorial Bulges

Earth's flattening is often exaggerated in illustrations because the actual difference between its major and minor semi-axes is very small, making it appear almost perfectly spherical.

Answer: True

Explanation: Earth's flattening is frequently exaggerated in visual representations because the actual difference between its equatorial and polar semi-axes is minimal, causing the planet to appear nearly perfectly spherical.

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Saturn has a flattening value of approximately 1/900, similar to the Moon.

Answer: False

Explanation: Saturn has a flattening value of approximately 1/10, whereas the Moon's flattening is about 1/900, indicating a significant difference.

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Isaac Newton proved that rotating fluid bodies in equilibrium take the form of an oblate ellipsoid in his 'Principia' in 1687.

Answer: True

Explanation: Isaac Newton, in his 1687 publication 'Principia,' provided the initial proof that a rotating, self-gravitating fluid body in equilibrium naturally assumes the shape of an oblate ellipsoid.

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The amount of flattening in a celestial body is solely determined by its rotation rate, irrespective of its density.

Answer: False

Explanation: The amount of flattening in a celestial body is determined by both its density and the intricate balance between its gravitational force and the centrifugal force resulting from its rotation.

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Any rotating celestial body massive enough to become spherical will develop an equatorial bulge corresponding to its rotation rate.

Answer: True

Explanation: A rotating celestial body with sufficient mass to achieve a spherical or nearly spherical shape will invariably develop an equatorial bulge, the extent of which is directly related to its rotation rate.

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Jupiter has the largest equatorial bulge in the Solar System, measuring 11,808 kilometers.

Answer: False

Explanation: Saturn, not Jupiter, possesses the largest equatorial bulge in the Solar System, measuring 11,808 kilometers.

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Earth's equatorial bulge is 42.6 km, while Mars's is 40 km.

Answer: True

Explanation: According to the provided data, Earth's equatorial bulge is 42.6 km, and Mars's equatorial bulge is 40 km.

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What is the inverse flattening (1/f) value for Earth's WGS84 ellipsoid?

Answer: 298.257223563

Explanation: For Earth's WGS84 ellipsoid, the inverse flattening (1/f) value is precisely 298.257223563.

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Which Solar System body has an approximate flattening value of 1/10?

Answer: Saturn

Explanation: Saturn has an approximate flattening value of 1/10, making it one of the most oblate bodies in the Solar System.

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Who first proved that rotating fluid bodies in equilibrium take the form of an oblate ellipsoid?

Answer: Isaac Newton

Explanation: Isaac Newton was the first to mathematically prove that rotating fluid bodies in equilibrium naturally assume the shape of an oblate ellipsoid.

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What two factors determine the amount of flattening in a celestial body?

Answer: Its density and the balance between gravitational and centrifugal forces.

Explanation: The amount of flattening in a celestial body is determined by its intrinsic density and the dynamic balance between its gravitational pull and the centrifugal force generated by its rotation.

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What is the general cause of an equatorial bulge in a sufficiently massive, rotating celestial body?

Answer: Centrifugal force pushing material outward at the equator.

Explanation: The general cause of an equatorial bulge in a sufficiently massive, rotating celestial body is the centrifugal force, which pushes material outward at the equator.

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Which planet in the Solar System has the largest equatorial bulge?

Answer: Saturn

Explanation: Saturn holds the distinction of having the largest equatorial bulge in the Solar System, measuring 11,808 kilometers.

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What is Earth's equatorial bulge?

Answer: 42.6 km

Explanation: Earth's equatorial bulge is 42.6 kilometers, representing the difference between its equatorial and polar diameters.

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Irregular Bodies and Unique Surface Features

For tidally-locked bodies, 180° longitude is the center of the leading hemisphere.

Answer: False

Explanation: For tidally-locked bodies, 90° longitude corresponds to the center of the leading hemisphere, while 180° longitude marks the center of the anti-primary hemisphere.

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Libration causes the natural reference point on tidally-locked bodies to trace a path similar to an analemma.

Answer: True

Explanation: Libration, an apparent wobble in a celestial body's motion, causes the natural reference point on tidally-locked bodies to trace a path resembling an analemma around any fixed point.

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Equatorial ridges are the same as gravitational equatorial bulges, both resulting from a body's rotation.

Answer: False

Explanation: Equatorial ridges are distinct surface features and should not be confused with gravitational equatorial bulges, which are general shape deformations resulting from a body's rotation.

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Only Iapetus and Atlas among Saturn's moons are known to have equatorial ridges.

Answer: False

Explanation: At least four of Saturn's moons are known to possess equatorial ridges: Iapetus, Atlas, Pan, and Daphnis.

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The Cassini probe discovered the equatorial ridges on Iapetus, Atlas, and Pan in 2005.

Answer: True

Explanation: The Cassini probe indeed discovered the equatorial ridges on Iapetus, Atlas, and Pan in 2005, with the ridge on Daphnis being discovered later.

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The equatorial ridge on Iapetus is a minor feature, only a few meters high and wide.

Answer: False

Explanation: The equatorial ridge on Iapetus is a substantial feature, measuring approximately 20 kilometers wide and 13 kilometers high, extending for 1300 kilometers.

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A triaxial ellipsoid is a three-dimensional shape with three unequal axes, making it a better fit for small, irregularly shaped bodies like asteroids.

Answer: True

Explanation: A triaxial ellipsoid, characterized by three unequal axes, offers a more accurate geometric model for small, irregularly shaped celestial bodies such as asteroids and comet nuclei.

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For highly irregular bodies, a reference ellipsoid is always the most useful model for precise mapping.

Answer: False

Explanation: For highly irregular bodies, a reference ellipsoid may not be the most useful model for precise mapping due to significant deviations from a smooth ellipsoid; a simpler spherical reference is sometimes preferred.

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Triaxial ellipsoids simplify map projections and maintain elegant properties compared to spherical references.

Answer: False

Explanation: Triaxial ellipsoids actually complicate many computations and cause map projections to lose their elegant and popular properties, making spherical references often preferred despite potentially less accurate shape representation.

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For non-convex bodies like the asteroid Eros, latitude and longitude coordinates may not always uniquely identify a single surface location.

Answer: True

Explanation: For non-convex bodies such as the asteroid Eros, the use of latitude and longitude coordinates can be problematic, as they may not consistently identify a unique single surface location.

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For tidally-locked bodies, what longitude corresponds to the center of the leading hemisphere?

Answer: 90°

Explanation: For tidally-locked bodies, 90° longitude corresponds to the center of the leading hemisphere.

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What phenomenon causes the natural reference point on tidally-locked bodies to move around any fixed point, tracing a path similar to an analemma?

Answer: Libration

Explanation: Libration is the phenomenon that causes the natural reference point on tidally-locked bodies to oscillate, tracing a path similar to an analemma around a fixed point.

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How do equatorial ridges differ from equatorial bulges?

Answer: Ridges are distinct surface features, while bulges are general shape deformations from rotation.

Explanation: Equatorial ridges are distinct, localized surface features, whereas equatorial bulges are broader, gravitational deformations of a body's overall shape resulting from its rotation.

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Which of Saturn's moons were discovered by the Cassini probe in 2005 to have equatorial ridges?

Answer: Iapetus, Atlas, and Pan

Explanation: The Cassini probe discovered equatorial ridges on Saturn's moons Iapetus, Atlas, and Pan in 2005.

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What are the approximate dimensions of the equatorial ridge on Iapetus?

Answer: 20 km wide, 13 km high, 1300 km long.

Explanation: The equatorial ridge on Iapetus is approximately 20 kilometers wide, 13 kilometers high, and extends for 1300 kilometers in length.

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For what types of bodies is a triaxial ellipsoid a better fit than an oblate spheroid?

Answer: Small moons, asteroids, and comet nuclei with irregular shapes.

Explanation: A triaxial ellipsoid provides a more accurate geometric representation than an oblate spheroid for small moons, asteroids, and comet nuclei that frequently exhibit irregular shapes.

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Why might the concept of a reference ellipsoid be less useful for highly irregular bodies?

Answer: Their shapes deviate significantly from a smooth ellipsoid.

Explanation: The concept of a reference ellipsoid becomes less useful for highly irregular bodies because their shapes deviate significantly from a smooth ellipsoid, making a simpler spherical reference sometimes more practical.

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What challenge do triaxial ellipsoids present for map projections?

Answer: They cause many projections to lose their elegant and popular properties.

Explanation: Triaxial ellipsoids complicate map projections, often causing many projections to lose their elegant and popular properties, which is why spherical references are frequently used instead.

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What problem can arise with latitude and longitude for non-convex bodies like the asteroid Eros?

Answer: They may not always uniquely identify a single surface location.

Explanation: For non-convex bodies such as the asteroid Eros, latitude and longitude coordinates may not always uniquely identify a single surface location, posing a challenge for precise mapping.

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