What is a planetary coordinate system, and what are its alternative names?

A planetary coordinate system is a generalized system used to define locations on planets other than Earth. It is also referred to as planetographic, planetodetic, or planetocentric, extending the concepts of geographic, geodetic, and geocentric coordinate systems used for Earth.

How are coordinate systems for other celestial bodies, like the Moon, referred to?

Similar coordinate systems are defined for other solid celestial bodies, such as the Moon, where they are specifically known as selenographic coordinates.

Who was instrumental in establishing the coordinate systems for most solid bodies in the Solar System?

Merton E. Davies of the Rand Corporation was responsible for establishing the coordinate systems for almost all solid bodies in the Solar System. This includes planets like Mercury, Venus, and Mars, as well as several moons such as Jupiter's four Galilean moons and Neptune's largest moon, Triton.

What is a planetary datum, and what does it require for specification?

A planetary datum is a generalization of geodetic datums for other planetary bodies, such as the Mars datum. It requires the specification of physical reference points or surfaces with fixed coordinates, for instance, a specific crater for the reference meridian or the best-fitting equigeopotential as a zero-level surface.

What does the image of lunar maria illustrate regarding planetary coordinate systems?

The source material includes a chart depicting the lunar maria, which are large, dark, basaltic plains on Earth's Moon, overlaid with lines of longitude and latitude. This chart indicates that the prime meridian for the Moon is located at the center of its near side, serving as a reference point for measuring longitude.

How are the longitude systems of most solid bodies with observable rigid surfaces defined?

The longitude systems for most celestial bodies possessing observable rigid surfaces are defined by referencing a specific surface feature, such as an impact crater, to establish a prime meridian.

What factors can cause the location of a body's prime meridian and north pole to change over time?

The location of a body's prime meridian and the position of its north pole on the celestial sphere can change over time due to the precession of the planet's (or satellite's) axis of rotation. Precession is a slow wobble or change in the orientation of an object's rotational axis.

How is the direction of a body's rotation classified based on its prime meridian?

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

What assumptions are made about the axis of rotation and rotation rate for Mercury and most satellites when other information is absent?

In the absence of other specific information, the axis of rotation for bodies like Mercury and most satellites is assumed to be normal (perpendicular) to their mean orbital plane. Additionally, for many satellites, it is assumed that their rotation rate is equal to their mean orbital period, a condition often associated with tidal locking.

How is the rotation reference established for giant planets?

For giant planets, whose surface features are constantly changing and moving at various rates, the rotation of their magnetic fields is used as the primary reference for defining their coordinate systems.

What criterion is used to define the rotation of the Sun?

For the Sun, even the magnetic field criterion fails due to its complex and unsteady magnetosphere. Therefore, an agreed-upon value for the rotation of its equator is used as a reference.

How is planetographic longitude measured, and what is its convention regarding rotation direction?

Planetographic longitude is measured positively to the west when a body has a prograde (direct) rotation, and positively to the east when the rotation is retrograde. This convention means that for an observer in the plane of the planet's equator, a point that passes later in time has a higher planetographic longitude.

How is planetocentric longitude defined and measured?

Planetocentric longitude is consistently measured positively to the east, regardless of the planet's rotation direction. East is defined as the counterclockwise direction when viewed from above the body's north pole, which is the pole that aligns more closely with Earth's north pole. Longitudes are traditionally indicated with 'E' or 'W' rather than '+' or '-' to specify polarity, where, for example, -91°, 91°W, +269°, and 269°E all represent the same location.

What is the modern standard for maps of Mars regarding longitude, and where is its prime meridian located?

Since approximately 2002, the modern standard for maps of Mars is to use planetocentric coordinates. The prime meridian of Mars was established by Merton E. Davies at the Airy-0 crater, guided by the work of historical astronomers.

How is the prime meridian defined for Mercury?

For Mercury, which is the only other planet with a solid surface visible from Earth, a thermocentric coordinate system is used. Its prime meridian runs through the point on the equator that experiences the highest temperatures, which is defined as exactly twenty degrees of longitude east of the Hun Kal crater.

What is the natural reference longitude for tidally-locked bodies?

Tidally-locked bodies, which have one side permanently facing their parent body, have a natural reference longitude passing through the point nearest to their parent. Specifically, 0° is the center of the primary-facing hemisphere, 90° is the center of the leading hemisphere, 180° is the center of the anti-primary hemisphere, and 270° is the center of the trailing hemisphere.

How does libration affect the reference longitude of tidally-locked bodies?

Libration, which is an apparent wobble or oscillation in the motion of a celestial body, caused by non-circular orbits or axial tilts, causes the natural reference point on tidally-locked bodies to move around any fixed point on the celestial body, tracing a path similar to an analemma.

How are planetographic and planetocentric latitudes defined, and what defines the zero latitude plane?

Planetographic latitude and planetocentric latitude are similarly defined to their longitude counterparts. The zero latitude plane, known as the Equator, is defined as being orthogonal (perpendicular) to the mean axis of rotation of the celestial body.

How is vertical position expressed in a planetary coordinate system?

Vertical position in a planetary coordinate system can be expressed relative to a specified vertical datum. This is done using physical quantities analogous to the topographical geocentric distance, which compares to a nominal Earth radius or the varying geocentric radius of a reference ellipsoid surface, or by using altitude/elevation measurements above and below a geoid.

What is the 'areoid,' and how was it measured?

The 'areoid' is the term for the geoid of Mars, which represents its theoretical mean sea level surface based on gravity. It has been measured using the flight paths of satellite missions such as Mariner 9 and Viking.

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

The main departures from the ellipsoid shape expected of an ideal fluid on Mars are attributed to the Tharsis volcanic plateau, a continent-sized region of elevated terrain, and its antipodes, which are points on the opposite side of the planet.

What is the 'selenoid,' and how was it measured?

The 'selenoid' is the term for the geoid of the Moon, representing its gravitational equipotential surface. It has been measured gravimetrically by the GRAIL twin satellites, which precisely mapped the Moon's gravitational field.

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

For rigid-surface, nearly-spherical bodies, such as rocky planets and many moons, ellipsoids are defined based on their axis of rotation and their mean surface height, excluding any atmosphere. A fixed observable surface feature is typically used to define a reference meridian.

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

Mars is actually egg-shaped, with its north and south polar radii differing by approximately 6 kilometers (4 miles). However, this difference is considered small enough that the average polar radius is used to define its reference ellipsoid.

How is the effective surface and prime meridian chosen for gaseous planets?

For gaseous planets like Jupiter, which lack a solid surface, an effective surface for an ellipsoid is chosen as the equal-pressure boundary of one bar. Since these planets have no permanent observable features, their prime meridians are determined according to mathematical rules rather than physical landmarks.

What are the defining values for the Earth's WGS84 ellipsoid?

For the WGS84 ellipsoid, which models Earth, the defining values are an equatorial radius (a) of 6,378,137.0 meters and an inverse flattening (1/f) of 298.257223563. From these, a polar radius (b) of 6,356,752.3142 meters is derived.

What is the difference between Earth's major and minor semi-axes, and why is flattening often exaggerated in illustrations?

The difference between Earth's major (equatorial) and minor (polar) semi-axes is 21.385 kilometers (13 miles), which is only 0.335% of the major axis. This small difference makes Earth appear almost perfectly spherical, so illustrations typically greatly exaggerate the flattening to visually emphasize the concept of a planet's oblateness.

What are the approximate flattening values for Jupiter, Saturn, the Moon, and the Sun?

The approximate flattening values for other Solar System bodies are 1/16 for Jupiter, 1/10 for Saturn, 1/900 for the Moon, and about 9×10^-6 for the Sun.

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

The amount of flattening in a celestial body depends on its density and the balance between its gravitational force, which pulls matter inward, and its centrifugal force, which pushes matter outward due to rotation.

What is the general cause of an equatorial bulge in celestial bodies?

Generally, any celestial body that is rotating and is sufficiently massive to pull itself into a spherical or nearly spherical shape will develop an equatorial bulge that corresponds to its rotation rate. This bulge is a result of centrifugal force pushing material outward at the equator.

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

Saturn has the largest equatorial bulge in the Solar System, measuring 11,808 kilometers, which is a significant difference between its equatorial and polar diameters.

What are the equatorial and polar diameters, equatorial bulge, and rotation period for Earth?

Earth has an equatorial diameter of 12,756.2 km, a polar diameter of 12,713.6 km, an equatorial bulge of 42.6 km, and a rotation period of 23.936 hours.

What are the equatorial and polar diameters, equatorial bulge, and rotation period for Mars?

Mars has an equatorial diameter of 6,792.4 km, a polar diameter of 6,752.4 km, an equatorial bulge of 40 km, and a rotation period of 24.632 hours.

What are the equatorial and polar diameters, equatorial bulge, and rotation period for Jupiter?

Jupiter has an equatorial diameter of 142,984 km, a polar diameter of 133,708 km, an equatorial bulge of 9,276 km, and a rotation period of 9.925 hours.

What are the equatorial and polar diameters, equatorial bulge, and rotation period for Saturn?

Saturn has an equatorial diameter of 120,536 km, a polar diameter of 108,728 km, an equatorial bulge of 11,808 km, and a rotation period of 10.56 hours.

What are equatorial ridges, and how do they differ from equatorial bulges?

Equatorial ridges are distinct surface features that closely follow the equators of certain moons, and they should not be confused with the broader, gravitational equatorial bulges that result from a body's rotation. Ridges are physical formations, while bulges are a general shape deformation.

Which of Saturn's moons are known to have equatorial ridges?

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

When and by whom were the equatorial ridges on Saturn's moons discovered?

The equatorial ridges on Iapetus, Atlas, and Pan were discovered by the Cassini probe in 2005, while the ridge on Daphnis was discovered more recently in 2017.

Describe the characteristics of the equatorial ridge on Iapetus.

The equatorial ridge on Iapetus is a prominent feature, measuring nearly 20 kilometers wide, 13 kilometers high, and extending 1300 kilometers in length.

How does the equatorial ridge on Atlas compare to that of Iapetus?

The equatorial ridge on Atlas is proportionally even more remarkable than Iapetus's, given Atlas's much smaller size, and contributes to its distinctive disk-like shape.

What is a triaxial ellipsoid, and for what types of bodies is it a better fit?

A triaxial ellipsoid is a three-dimensional shape with three unequal axes, making it a better fit than an oblate spheroid for small moons, asteroids, and comet nuclei that frequently have irregular shapes. Jupiter's moon Io is an example of a body better approximated by a scalene (triaxial) ellipsoid.

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

For highly irregular bodies, the concept of a reference ellipsoid may not have useful value because their shapes deviate significantly from a smooth ellipsoid. In such cases, a spherical reference is sometimes used instead, with points identified by planetocentric latitude and longitude.

What challenges do triaxial ellipsoids present for computations and map projections?

Triaxial ellipsoids complicate many computations, particularly those related to map projections, as many projections would lose their elegant and popular properties. For this reason, spherical reference surfaces are frequently used in mapping programs despite triaxial ellipsoids potentially offering a better fit for some bodies.

What problem can arise with latitude and longitude for non-convex bodies?

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 and navigation.

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Overview

Generalizing Earth's Systems

A planetary coordinate system extends the familiar geographic, geodetic, and geocentric coordinate systems of Earth to other celestial bodies. These systems are essential for precisely locating features on planets, moons, asteroids, and even comets, enabling detailed mapping and scientific analysis.

Nomenclature and Scope

Depending on the specific reference frame, these systems are often termed planetographic, planetodetic, or planetocentric. While the principles are universal, specific applications include selenographic coordinates for the Moon, areographic coordinates for Mars, and so forth. Such systems are crucial for any solid celestial body within our Solar System.

Pioneering Cartography

The foundational work for coordinate systems across nearly all solid bodies in the Solar System was largely established by Merton E. Davies of the Rand Corporation. His contributions provided the framework for mapping Mercury, Venus, Mars, Jupiter's four Galilean moons, and Neptune's largest moon, Triton, among others.

Defining Planetary Datums

Analogous to Earth's geodetic datums, a planetary datum specifies physical reference points or surfaces with fixed coordinates for other celestial bodies. This might involve designating a particular crater as the reference for the prime meridian or defining a best-fitting equigeopotential surface as the zero-level for altitude measurements, such as the Mars datum.

Longitude

Establishing the Prime Meridian

For most celestial bodies with rigid, observable surfaces, the longitude system is defined by referencing a distinct surface feature, such as an impact crater. The north pole is conventionally identified as the pole of rotation situated on the north side of the Solar System's invariable plane, typically near the ecliptic. The precise location of this prime meridian and the north pole's celestial position can shift over time due to the precession of the body's rotational axis.

Rotation and Directionality

The direction of rotation dictates how longitude is measured. If the body exhibits direct (prograde) rotation, where the position angle of the prime meridian increases with time, west longitudes are used (measured positively to the west). Conversely, for retrograde rotation, east longitudes are employed (measured positively to the east). This means that for a distant observer in the plane of the equator, a point passing later has a higher planetographic longitude.

Planetocentric vs. Planetographic

While planetographic longitude varies with rotation direction, planetocentric longitude is consistently measured positively to the east. East is defined as the counterclockwise direction when viewed from above the north pole (the pole closer to Earth's north pole). Longitudes are traditionally denoted with "E" or "W" to indicate polarity, where, for example, -91°, 91°W, +269°, and 269°E all represent the same location.

Specific Planetary Meridians

Modern Martian maps (since approximately 2002) utilize planetocentric coordinates, with the prime meridian established at the Airy-0 crater, a decision guided by historical astronomical observations by Merton E. Davies. For Mercury, a thermocentric coordinate system is used, where the prime meridian passes through the hottest point on its equator, defined as exactly twenty degrees of longitude east of the Hun Kal crater. Tidally-locked bodies, like many moons, have a natural reference longitude passing through the point nearest to their parent body (0° for the primary-facing hemisphere), though libration can cause this point to appear to move.

Latitude

Defining Vertical Position

Similar to longitude, planetographic latitude and planetocentric latitude are defined to specify vertical positions on a celestial body. The zero latitude plane, or the equator, is established as orthogonal to the mean axis of rotation, which passes through the body's poles. This fundamental definition ensures consistency in measuring angular distance from the equator towards the poles.

Reference Surfaces for Latitude

For many planets, such as Earth and Mars, the reference surfaces used for defining latitude are ellipsoids of revolution. These ellipsoids are typically oblate spheroids, meaning their equatorial radius is larger than their polar radius, reflecting the flattening caused by rotation. This geometric model provides a standardized surface against which latitude measurements are made, accounting for the body's overall shape.

Altitude

Expressing Vertical Extent

Vertical position on a celestial body can be expressed relative to a specific vertical datum. This involves using physical quantities analogous to Earth's topographical geocentric distance (compared to a nominal Earth radius or the varying geocentric radius of a reference ellipsoid surface) or altitude/elevation (measured above or below a geoid). These measurements are crucial for understanding the topography and gravitational fields of other worlds.

Planetary Geoids: Areoid and Selenoid

The concept of a geoid, which represents an equipotential surface of a planet's gravity field, is extended to other bodies. For Mars, this is known as the areoid, and for the Moon, the selenoid. These geoids have been meticulously measured using data from satellite missions, such as Mariner 9 and Viking for Mars, and the GRAIL twin satellites for the Moon. Significant departures from an ideal fluid ellipsoid, like Mars' Tharsis volcanic plateau and its antipodes, reveal important geological features and internal structures.

Planetary Shapes

Reference Ellipsoids for Mapping

Reference ellipsoids are fundamental for defining geodetic coordinates and creating accurate maps of planetary bodies, including planets, their satellites, asteroids, and comet nuclei. Well-observed bodies like the Moon and Mars now possess highly precise reference ellipsoids, which serve as the geometric basis for their cartographic representations.

Rocky Bodies: Axis and Mean Surface

For rigid-surface, nearly-spherical bodies, which encompass all rocky planets and many moons, ellipsoids are defined by their axis of rotation and the mean surface height, excluding any atmospheric effects. While Mars exhibits a slight "egg shape" with a polar radius difference of approximately 6 km, its average polar radius is used for defining its ellipsoid. The Earth's Moon, in contrast, is effectively spherical, displaying almost no equatorial bulge.

Gaseous Giants: Defining the Surface

For gaseous planets like Jupiter, which lack a solid surface, an "effective surface" for an ellipsoid is chosen. This is typically defined as the equal-pressure boundary of one bar. Since these planets do not possess permanent, observable surface features, the selection of their prime meridians is determined by mathematical rules and conventions rather than physical landmarks.

Bulges

Quantifying Flattening

Flattening describes the degree to which a spheroid deviates from a perfect sphere. For the Earth, modeled by the WGS84 ellipsoid, the equatorial radius is 6,378,137.0 meters, and the inverse flattening is 298.257223563. This yields a polar radius of 6,356,752.3142 meters, resulting in a difference of 21.385 km between the major and minor semi-axes. This difference, only about 0.335% of the major axis, is often greatly exaggerated in illustrations to visually emphasize the concept of oblateness.

Other celestial bodies exhibit varying degrees of flattening:

Jupiter: Approximately 1/16
Saturn: Approximately 1/10
Moon: Approximately 1/900
Sun: Approximately 9 × 10⁻⁶

The Origin of Flattening

The phenomenon of flattening in rotating celestial bodies was mathematically proven by Isaac Newton in his 1687 work, Principia. He demonstrated that a rotating, self-gravitating fluid body in equilibrium naturally assumes the shape of an oblate ellipsoid of revolution, or a spheroid. The extent of this flattening is a function of the body's density and the intricate balance between its gravitational force and the centrifugal force generated by its rotation.

Equatorial Bulge of Major Bodies

Any sufficiently massive, rotating celestial body that has drawn itself into a spherical or near-spherical shape will develop an equatorial bulge proportional to its rotation rate. Saturn, with an equatorial bulge of 11,808 km, holds the distinction of having the largest equatorial bulge in our Solar System. This table provides a comparative overview of the equatorial bulge for major celestial bodies:

Body	Diameter (km)		Equatorial Bulge (km)	Flattening Ratio	Rotation Period (h)	Density (kg/m³)	f	Deviation from f
	Equatorial	Polar
Earth	12,756.2	12,713.6	42.6	1 : 299.4	23.936	5515	1 : 232	−23%
Mars	6,792.4	6,752.4	40	1 : 170	24.632	3933	1 : 175	+3%
Ceres	964.3	891.8	72.5	1 : 13.3	9.074	2162	1 : 13.1	−2%
Jupiter	142,984	133,708	9,276	1 : 15.41	9.925	1326	1 : 9.59	−38%
Saturn	120,536	108,728	11,808	1 : 10.21	10.56	687	1 : 5.62	−45%
Uranus	51,118	49,946	1,172	1 : 43.62	17.24	1270	1 : 27.71	−36%
Neptune	49,528	48,682	846	1 : 58.54	16.11	1638	1 : 31.22	−47%

Equatorial Ridges: A Unique Feature

Distinct from equatorial bulges, equatorial ridges are prominent topographical features found on at least four of Saturn's moons: the large moon Iapetus and the smaller moons Atlas, Pan, and Daphnis. These ridges closely trace the moons' equators. Discovered by the Cassini probe, the ridge on Iapetus is nearly 20 km wide, 13 km high, and 1300 km long. The ridge on Atlas is proportionally even more striking given the moon's diminutive size, contributing to its distinctive disk-like appearance. While similar structures are seen on Pan and Daphnis, their origins and the reasons for their apparent uniqueness to the Saturnian system remain subjects of ongoing scientific inquiry.

Irregular Shapes

Modeling Non-Spherical Bodies

Many small moons, asteroids, and comet nuclei possess highly irregular shapes that deviate significantly from a perfect sphere or even an oblate spheroid. For some of these, such as Jupiter's moon Io, a scalene (triaxial) ellipsoid offers a more accurate geometric approximation than a simple oblate spheroid. This more complex model accounts for three distinct axes, better capturing the non-uniformity of these celestial bodies.

Challenges in Cartography

For celestial bodies with extremely irregular or even non-convex shapes, like the asteroid 433 Eros, the traditional concept of a reference ellipsoid may lose its practical utility. In such cases, even using a spherical reference surface can be problematic, as latitude and longitude may not uniquely identify a single surface location. The complexities introduced by triaxial ellipsoids, particularly in map projections, often lead cartographers to employ simpler spherical reference surfaces in mapping programs to maintain elegant and popular projection properties, despite the geometric compromises.

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References

Davies, M. E., "Surface Coordinates and Cartography of Mercury," Journal of Geophysical Research, Vol. 80, No. 17, June 10, 1975.

Davies, M. E., S. E. Dwornik, D. E. Gault, and R. G. Strom, NASA Atlas of Mercury, NASA Scientific and Technical Information Office, 1978.

Davies, M. E., and R. A. Berg, "Preliminary Control Net of Mars,"Journal of Geophysical Research, Vol. 76, No. 2, pps. 373-393, January 10, 1971.

Merton E. Davies, Thomas A. Hauge, et al.: Control Networks for the Galilean Satellites: November 1979 R-2532-JPL/NASA

Davies, M. E., P. G. Rogers, and T. R. Colvin, "A Control Network of Triton," Journal of Geophysical Research, Vol. 96, E l, pp. 15, 675-15, 681, 1991.

Davies, M. E., and R. A. Berg, "Preliminary Control Net of Mars,"Journal of Geophysical Research, Vol. 76, No. 2, pps. 373-393, January 10, 1971.

Davies, M. E., "Surface Coordinates and Cartography of Mercury," Journal of Geophysical Research, Vol. 80, No. 17, June 10, 1975.

First map of extraterrestrial planet â Center of Astrophysics.

The WGS84 parameters are listed in the National Geospatial-Intelligence Agency publication TR8350.2 page 3-1.

A full list of references for this article are available at the Planetary coordinate system Wikipedia page

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Important Notice

This page was generated by an Artificial Intelligence and is intended for informational and educational purposes only. The content is based on a snapshot of publicly available data from Wikipedia and may not be entirely accurate, complete, or up-to-date.

This is not professional astronomical or cartographic advice. The information provided on this website is not a substitute for consulting official scientific publications, astronomical data archives, or professional experts in planetary science and cartography. Always refer to authoritative sources and consult with qualified professionals for specific research or project needs. Never disregard professional scientific consensus because of something you have read on this website.

The creators of this page are not responsible for any errors or omissions, or for any actions taken based on the information provided herein.

Cosmic Cartography

💡 Dive in with Flashcard Learning! 💡

Overview 🔭

🗺️ Generalizing Earth's Systems

🌌 Nomenclature and Scope

👨‍🔬 Pioneering Cartography

📍 Defining Planetary Datums

Longitude 🧭

🎯 Establishing the Prime Meridian

🔄 Rotation and Directionality

➡️ Planetocentric vs. Planetographic

📍 Specific Planetary Meridians

Latitude 📐

⬆️ Defining Vertical Position

🌐 Reference Surfaces for Latitude

Altitude ⛰️

📏 Expressing Vertical Extent

🌊 Planetary Geoids: Areoid and Selenoid

Planetary Shapes 🪐

📐 Reference Ellipsoids for Mapping

🪨 Rocky Bodies: Axis and Mean Surface

☁️ Gaseous Giants: Defining the Surface

Bulges 🌍

📏 Quantifying Flattening

🌀 The Origin of Flattening

📈 Equatorial Bulge of Major Bodies

🏔️ Equatorial Ridges: A Unique Feature

Irregular Shapes 🥔

☄️ Modeling Non-Spherical Bodies

🚧 Challenges in Cartography

Teacher's Corner 🧑‍🏫

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References

📜 References

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📜 Important Notice

Dive in with Flashcard Learning!

Overview

Generalizing Earth's Systems

Nomenclature and Scope

Pioneering Cartography

Defining Planetary Datums

Longitude

Establishing the Prime Meridian

Rotation and Directionality

Planetocentric vs. Planetographic

Specific Planetary Meridians

Latitude

Defining Vertical Position

Reference Surfaces for Latitude

Altitude

Expressing Vertical Extent

Planetary Geoids: Areoid and Selenoid

Planetary Shapes

Reference Ellipsoids for Mapping

Rocky Bodies: Axis and Mean Surface

Gaseous Giants: Defining the Surface

Bulges

Quantifying Flattening

The Origin of Flattening

Equatorial Bulge of Major Bodies

Equatorial Ridges: A Unique Feature

Irregular Shapes

Modeling Non-Spherical Bodies

Challenges in Cartography

Teacher's Corner

True or False?

Test Your Knowledge!

Gamer's Corner

Discover other topics to study!

References

Feedback & Support

Disclaimer

Important Notice