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Planetary reference systems and time

Planetary reference systems and time


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I am researching into how coordinate systems of solar systems objects are created by reading some of the reports written by the Working Group on Cartographic Coordinates and Rotational Elements (e.g. 2009). However, I am finding it difficult to completley understand the role of time in defining reference systems.

When observing at a planet from Earth, for example Jupiter, there are a variety of factors that make it difficult to construct a reference system (including no solid surface and planetary precession), so we use geometry to define a reference system. However, because our perspective is dynamic, meaning Jupiter's surface changes and the planet's move, we say that at time J2000 we know the precise orientation and position of Earth and therefore can say from position defined at J2000 this is the coordinate reference system for Jupiter.

So, does incorporating time (e.g. J2000) mean we can say a coordinate reference system is based on the situation of an object, Jupiter in this example, at a given moment?


Look at J2000 Solar System Barycentric (spatial reference) and Barycentric Dynamical Time (TDB). Together they are good space and time coordinate system. NASA/JPL has some good info and data on these.

In terms of time, TDB is rescaled so that from the Earth, it appears to be close to the same as TT (roughly ~UTC). The rescaling is due to the fact we are in a gravitational well, as well as moving at 30 km/s with respect to the solar system barycentre, due to relativity. The original unscaled is called Barycentric Coordinate Time (TCB) and differs by ~0.5seconds / year.


We need a system to describe "where things are in the sky". Even a cursory glance at the sky will find that "things move across the sky daily". So instead of describing where something is directly, we will describe where it is relative to the stars.

However some of the stars move (due to their actual motion relative to the sun) and appear to wobble (due the motion of the Earth around the sun). So let us consider those objects that are so far that any such motion is undetectable. For example, quasars. Other distant stars are also suitable as they don't have a measurable motion. I'll call these sources "fixed stars". The goal is to describe a system of coordinates in which the fixed stars don't move.

For our coordinate system we will use the plane of the Earth's equator on the March Equinox (chosen in part so the plane passes through the sun). Declension is defined as the angle relative to this plane. Right Ascension is then the angle between the line through the Earth and Sun, and the line formed by projecting the object onto the plane. For very distant objects, it doesn't matter if we use the sun or the Earth as the centre as the angle will be the same to any reasonable level of accuracy.

However, choosing the March equinox in this way causes a problem, because the plane of the Earth's equator is slowly changing, and this means that the position relative to this plane will also slowly change. The RA and Dec of a quasar will slowly change due to this precession.

The solution to this issue is to define the coordinate system on a particular date "Jan 1st 2000". With this convention we can assign a position to the quasar, and it won't change. This is a coordinate system that can describe the position of any object relative to the fixed stars.

We can now define the position of any object in the same coordinates. For nearby stars we can describe their proper and apparent motion relative to this coordinate system. For planets the position relative to the fixed stars varies from day to day, due to the relative motion of the planets. It also depends on the location of the observer. So I can talk about the location of Jupiter at midnight on 28 June 2018, from Perth, WA, using the J2000.0 coordinates.

The 2000.0 defines exactly which fixed coordinate system we are using. But to describe the location of Jupiter in the sky we also need to use an observation time and date and location.


Learners can expect to find careers in fields that value scientific knowledge and complex problem-solving skills. This includes the ability to use modern statistical data analysis techniques. Graduates may find jobs within K-12 STEM teaching, writing and journalism, science policy or statistical data analysis and computer programming.

This online astronomy degree is ideal for individuals who would like to gain a solid understanding of astronomy and planetary science. Because this program focuses on critical thinking and innovative problem-solving, it may prepare you for law school or other graduate school opportunities related to this skill set.

However, if you plan to apply to a graduate program in astronomy or astrophysics or pursue a path as a university professor or professional astronomer, you’ll need additional advanced coursework in mathematics and physics and in-person research experience not currently provided in this degree. You may want to consider ASU’s campus Bachelor of Science in earth and space exploration.


Planetary and Space Science

Planetary and Space Science publishes original articles as well as short communications (letters). Ground-based and space-borne instrumentation and laboratory simulation of solar system processes are included. The following fields of planetary and solar system research are covered:

Planetary and Space Science publishes original articles as well as short communications (letters). Ground-based and space-borne instrumentation and laboratory simulation of solar system processes are included. The following fields of planetary and solar system research are covered:

&bull Celestial mechanics, including dynamical evolution of the solar system, gravitational captures and resonances, relativistic effects, tracking and dynamics

&bull Cosmochemistry and origin, including all aspects of the formation and initial physical and chemical evolution of the solar system

&bull Terrestrial planets and satellites, including the physics of the interiors, geology and morphology of the surfaces, tectonics, mineralogy and dating

&bull Outer planets and satellites, including formation and evolution, remote sensing at all wavelengths and in situ measurements

&bull Planetary atmospheres, including formation and evolution, circulation and meteorology, boundary layers, remote sensing and laboratory simulation

&bull Planetary magnetospheres and ionospheres, including origin of magnetic fields, magnetospheric plasma and radiation belts, and their interaction with the sun, the solar wind and satellites

&bull Small bodies, dust and rings, including asteroids, comets and zodiacal light and their interaction with the solar radiation and the solar wind

&bull Exobiology, including origin of life, detection of planetary ecosystems and pre-biological phenomena in the solar system and laboratory simulations

&bull Extrasolar systems, including the detection and/or the detectability of exoplanets and planetary systems, their formation and evolution, the physical and chemical properties of the exoplanets


The Milky Way

The Milky Way is the galaxy that contains our Solar System. Its name “milky” is derived from its appearance as a dim glowing band arching across the night sky in which the naked eye cannot distinguish individual stars. The term “Milky Way” is a translation of the Latin via lactea, from the Greek γαλαξίας κύκλος (galaxías kýklos, “milky circle”). From Earth, the Milky Way appears as a band because its disk-shaped structure is viewed from within. Galileo Galilei first resolved the band of light into individual stars with his telescope in 1610. Up until the early 1920s, most astronomers thought that all of the stars in the universe were contained inside of the Milky Way. Following the 1920 Great Debate between the astronomers Harlow Shapley and Heber Curtis, observations by Edwin Hubble definitively showed that the Milky Way is just one of many billions of galaxies.

The Milky Way is a barred spiral galaxy some 100,000–120,000 light-years in diameter, which contains 100–400 billion stars. It may contain at least as many planets as well. The Solar System is located within the disk, about 27,000 light-years away from the Galactic Center, on the inner edge of one of the spiral-shaped concentrations of gas and dust called the Orion Arm. The stars in the inner ≈10,000 light-years form a bulge and one or more bars that radiate from the bulge. The very center is marked by an intense radio source, named Sagittarius A*, which is likely to be a supermassive black hole.

Stars and gases at a wide range of distances from the Galactic Center orbit at approximately 220 kilometers per second. The constant rotation speed contradicts the laws of Keplerian dynamics and suggests that much of the mass of the Milky Way does not emit or absorb electromagnetic radiation. This mass has been given the name “dark matter”. The rotational period is about 240 million years at the position of the Sun. The Milky Way as a whole is moving at a velocity of approximately 600 km per second with respect to extragalactic frames of reference. The oldest known star in the Milky Way is at least 13.82 billion years old and thus must have formed shortly after the Big Bang.

Surrounded by several smaller satellite galaxies, the Milky Way is part of the Local Group of galaxies, which forms a subcomponent of the Virgo Supercluster, which again forms a subcomponent of the Laniakea Supercluster.


An Introduction to Galaxies

NGC 4414, a typical spiral galaxy in the constellation Coma Berenices, is about 55,000 light-years in diameter and approximately 60 million light-years away from Earth. NASA

Galaxies 101:

A galaxy is a massive, gravitationally bound system consisting of stars, stellar remnants, an interstellar medium of gas and dust, and, dark matter, an important but poorly understood component. The word galaxy is derived from the Greek galaxias (γαλαξίας), literally “milky”, a reference to the Milky Way. Examples of galaxies range from dwarfs with as few as ten million (107) stars to giants with a hundred trillion (1014) stars, each orbiting their galaxy’s own center of mass.

Galaxies contain varying numbers of star systems, star clusters and types of interstellar clouds. In between these objects is a sparse interstellar medium of gas, dust, and cosmic rays. Supermassive black holes reside at the center of all galaxies. They are thought to be the primary driver of active galactic nuclei found at the core of some galaxies. The Milky Way galaxy is known to harbor at least one such object.

Galaxies have been historically categorized according to their apparent shape, usually referred to as their visual morphology. A common form is the elliptical galaxy, which has an ellipse-shaped light profile. Spiral galaxies are disk-shaped with dusty, curving arms. Those with irregular or unusual shapes are known as irregular galaxies and typically originate from disruption by the gravitational pull of neighboring galaxies. Such interactions between nearby galaxies, which may ultimately result in a merger, sometimes induce significantly increased incidents of star formation leading to starburst galaxies. Smaller galaxies lacking a coherent structure are referred to as irregular galaxies.

There are probably more than 170 billion (1.7 × 1011) galaxies in the observable universe. Most are 1,000 to 100,000 parsecs in diameter and usually separated by distances on the order of millions of parsecs (or megaparsecs). Intergalactic space (the space between galaxies) is filled with a tenuous gas of an average density less than one atom per cubic meter. The majority of galaxies are organized into a hierarchy of associations known as groups and clusters, which, in turn usually form larger superclusters. At the largest scale, these associations are generally arranged into sheets and filaments, which are surrounded by immense voids.

On December 12, 2012, astronomers, working with the Hubble Space Telescope, reported that the most distant known galaxy, UDFj-39546284, is now estimated to be even further away than previously believed. The galaxy, which is estimated to have formed around � million years” after the Big Bang (about 13.8 billion years ago), and has a z (redshift) of 11.9 is approximately 13.42 billion light years from Earth.


Contents

The longitude systems of most of those bodies with observable rigid surfaces have been defined by references to a surface feature such as a crater. The north pole is that pole of rotation that lies on the north side of the invariable plane of the solar system (near the ecliptic). The location of the prime meridian as well as the position of the body's north pole on the celestial sphere may vary with time due to precession of the axis of rotation of the planet (or satellite). If the position angle of the body's prime meridian increases with time, the body has a direct (or prograde) rotation otherwise the rotation is said to be retrograde.

In the absence of other information, the axis of rotation is assumed to be normal to the mean orbital plane Mercury and most of the satellites are in this category. For many of the satellites, it is assumed that the rotation rate is equal to the mean orbital period. In the case of the giant planets, since their surface features are constantly changing and moving at various rates, the rotation of their magnetic fields is used as a reference instead. In the case of the Sun, even this criterion fails (because its magnetosphere is very complex and does not really rotate in a steady fashion), and an agreed-upon value for the rotation of its equator is used instead.

For planetographic longitude, west longitudes (i.e., longitudes measured positively to the west) are used when the rotation is prograde, and east longitudes (i.e., longitudes measured positively to the east) when the rotation is retrograde. In simpler terms, imagine a distant, non-orbiting observer viewing a planet as it rotates. Also suppose that this observer is within the plane of the planet's equator. A point on the Equator that passes directly in front of this observer later in time has a higher planetographic longitude than a point that did so earlier in time.

However, planetocentric longitude is always measured positively to the east, regardless of which way the planet rotates. East is defined as the counter-clockwise direction around the planet, as seen from above its north pole, and the north pole is whichever pole more closely aligns with the Earth's north pole. Longitudes traditionally have been written using "E" or "W" instead of "+" or "−" to indicate this polarity. For example, −91°, 91°W, +269° and 269°E all mean the same thing.

The modern standard for maps of Mars (since about 2002) is to use planetocentric coordinates. Guided by the works of historical astronomers, Merton E. Davies established the meridian of Mars at Airy-0 crater. [7] [8] For Mercury, the only other planet with a solid surface visible from Earth, a thermocentric coordinate is used: the prime meridian runs through the point on the equator where the planet is hottest (due to the planet's rotation and orbit, the sun briefly retrogrades at noon at this point during perihelion, giving it more sun). By convention, this meridian is defined as exactly twenty degrees of longitude east of Hun Kal. [9] [10] [11]

Tidally-locked bodies have a natural reference longitude passing through the point nearest to their parent body: 0° the center of the primary-facing hemisphere, 90° the center of the leading hemisphere, 180° the center of the anti-primary hemisphere, and 270° the center of the trailing hemisphere. [12] However, libration due to non-circular orbits or axial tilts causes this point to move around any fixed point on the celestial body like an analemma.

The zero latitude plane (Equator) can be defined as orthogonal to the mean axis of rotation (poles of astronomical bodies).

The reference surfaces for some planets (such as Earth and Mars) are ellipsoids of revolution for which the equatorial radius is larger than the polar radius, such that they are oblate spheroids.

Vertical position can be expressed with respect to a given vertical datum, by means of physical quantities analogous to the topographical geocentric distance (compared to a constant nominal Earth radius or the varying geocentric radius of the reference ellipsoid surface) or altitude/elevation (above and below the geoid). [13]

The areoid (the geoid of Mars) [14] has been measured using flight paths of satellite missions such as Mariner 9 and Viking. The main departures from the ellipsoid expected of an ideal fluid are from the Tharsis volcanic plateau, a continent-size region of elevated terrain, and its antipodes. [15]

The selenoid (the geoid of the Moon) has been measured gravimetrically by the GRAIL twin satellites. [16]

Reference ellipsoids are also useful for geodetic mapping of other planetary bodies including planets, their satellites, asteroids and comet nuclei. Some well observed bodies such as the Moon and Mars now have quite precise reference ellipsoids.

For rigid-surface nearly-spherical bodies, which includes all the rocky planets and many moons, ellipsoids are defined in terms of the axis of rotation and the mean surface height excluding any atmosphere. Mars is actually egg shaped, where its north and south polar radii differ by approximately 6 km (4 miles), however this difference is small enough that the average polar radius is used to define its ellipsoid. The Earth's Moon is effectively spherical, having almost no bulge at its equator. Where possible, a fixed observable surface feature is used when defining a reference meridian.

For gaseous planets like Jupiter, an effective surface for an ellipsoid is chosen as the equal-pressure boundary of one bar. Since they have no permanent observable features, the choices of prime meridians are made according to mathematical rules.

Flattening Edit

For the WGS84 ellipsoid to model Earth, the defining values are [17]

b (polar radius): 6 356 752.3142 m,

so that the difference of the major and minor semi-axes is 21.385 km (13 mi). This is only 0.335% of the major axis, so a representation of Earth on a computer screen would be sized as 300 pixels by 299 pixels. This is rather indistinguishable from a sphere shown as 300 pix by 300 pix. Thus illustrations typically greatly exaggerate the flattening to highlight the concept of any planet's oblateness.

Origin of flattening Edit

In 1687, Isaac Newton published the Principia in which he included a proof that a rotating self-gravitating fluid body in equilibrium takes the form of an oblate ellipsoid of revolution (a spheroid). [18] The amount of flattening depends on the density and the balance of gravitational force and centrifugal force.

Equatorial bulge Edit

Equatorial bulge of the Solar Systems major celestial bodies
Body Diameter (km) Equatorial
bulge (km)
Flattening
ratio
Rotation
period (h)
Density
(kg/m 3 )
f Deviation
from f
Equatorial Polar
Earth 0 12 756.2 0 12 713.6 00 0 42.6 1 : 299.4 23.936 5515 1 : 232 −23%
Mars 00 6 792.4 00 6 752.4 00 0 40 1 : 170 24.632 3933 1 : 175 0 +3%
Ceres 000 964.3 000 891.8 000 72.5 1 : 13.3 0 9.074 2162 1 : 13.1 0 −2%
Jupiter 142 984 133 708 0 9 276 1 : 15.41 0 9.925 1326 1 : 9.59 −38%
Saturn 120 536 108 728 11 808 1 : 10.21 10.56 0 687 1 : 5.62 −45%
Uranus 0 51 118 0 49 946 0 1 172 1 : 43.62 17.24 1270 1 : 27.71 −36%
Neptune 0 49 528 0 48 682 00 846 1 : 58.54 16.11 1638 1 : 31.22 −47%

Generally any celestial body that is rotating (and that is sufficiently massive to draw itself into spherical or near spherical shape) will have an equatorial bulge matching its rotation rate. With 11 808 km Saturn is the planet with the largest equatorial bulge in our Solar System.

Equatorial ridges Edit

Equatorial bulges should not be confused with equatorial ridges. Equatorial ridges are a feature of at least four of Saturn's moons: the large moon Iapetus and the tiny moons Atlas, Pan, and Daphnis. These ridges closely follow the moons' equators. The ridges appear to be unique to the Saturnian system, but it is uncertain whether the occurrences are related or a coincidence. The first three were discovered by the Cassini probe in 2005 the Daphnean ridge was discovered in 2017. The ridge on Iapetus is nearly 20 km wide, 13 km high and 1300 km long. The ridge on Atlas is proportionally even more remarkable given the moon's much smaller size, giving it a disk-like shape. Images of Pan show a structure similar to that of Atlas, while the one on Daphnis is less pronounced.

Small moons, asteroids, and comet nuclei frequently have irregular shapes. For some of these, such as Jupiter's Io, a scalene (triaxial) ellipsoid is a better fit than the oblate spheroid. For highly irregular bodies, the concept of a reference ellipsoid may have no useful value, so sometimes a spherical reference is used instead and points identified by planetocentric latitude and longitude. Even that can be problematic for non-convex bodies, such as Eros, in that latitude and longitude don't always uniquely identify a single surface location.

Smaller bodies (Io, Mimas, etc.) tend to be better approximated by triaxial ellipsoids however, triaxial ellipsoids would render many computations more complicated, especially those related to map projections. Many projections would lose their elegant and popular properties. For this reason spherical reference surfaces are frequently used in mapping programs.


Planets and Planetary Systems

Keeping mathematics to a minimum, assuming only a rudimentary knowledge of calculus, the book begins with a description of the basic properties of the planets in our solar systems, and then moves on to compare them with what is known about planets in other solar systems. It continues by looking at the surfaces, interiors and atmospheres of the planets and then covers the dynamics and origin of planetary systems. The book closes with a look at the role of life in planetary systems.

·        An accessible, concise introduction to planets and planetary systems

·        Uses insights from all the disciplines underlying planetary science

·        Incorporates results from recent planetary space missions, such as Cassini to Saturn and a number of missions to Mars

·        Well illustrated throughout, including a colour plate section

Planets and Planetary Systems is invaluable to students taking courses in planetary science across a wide range of disciplines and of interest to researchers and many keen amateur astronomers, needing an up-to-date introduction to this exciting subject.


Planetary reference systems and time - Astronomy

Brussels, December 28, 2020 – The Royal Observatory of Belgium and EMXYS (Spain) have been selected by the European Space Agency to provide a gravimeter for the Juventas spacecraft that will land on asteroid Dimorphos as part of the European Space Agency’s planetary defence programme.

Artist’s view of the Juventus CubeSat. Credit: ESA.

The Royal Observatory of Belgium with EMXYS will provide the GRASS instrument that will make measurements on the gravity field of the asteroid Dimorphos. The gravimeter is part of the Juventas CubeSat, manufactured by GomSpace Luxemburg, that will land on the asteroid in 2027, after travelling onboard the ESA’s Hera spacecraft to its vicinity. GRASS will be the first gravimeter ever on an asteroid.

The gravimeter is an instrument proposed, designed and developed by the Royal Observatory of Belgium in cooperation with EMXYS, which will provide the final space version of the instrument for the mission. The gravimeter is expected to send to Earth precious data on the mass distribution, internal structure and dynamics of Dimorphos. This information will improve the knowledge for setting up future diversion strategies on asteroids that may have a threat of colliding with Earth.

The exploration of solar system bodies to better understand their evolution and origin has been one of the main research areas of the Royal Observatory of Belgium who also has a strong heritage on gravimetry and geophysics.

After its participation in three space missions in orbit around Earth and one suborbital mission, this is the first time EMXYS participates in a deep space endeavour far away from Earth orbital environment.

Due to launch in 2024, Hera is the European contribution to an international double-spacecraft collaboration to a binary asteroid system: The 780 m-diameter main body Didymos is orbited by a 160 m moon, Dimorphos. NASA’s DART mission will first perform a kinetic impact on Dimorphos, then Hera will follow up with a detailed post-impact survey that will turn this grand-scale experiment into a well understood and repeatable planetary defence technique.

Özgür Karatekin, Research Scientist at the Royal Observatory of Belgium, stated that “Hera will be the first mission to perform a detailed characterisation of a binary asteroid system. GRASS will monitor surface accelerations to reveal the subsurface structure and to better constrain the spin-orbit dynamics of the binary system. The gravitational forces on such a small body, likely composed of loosely held-together mounds of debris are very small (about 6 orders of magnitude smaller than the gravity on Earth). The GRASS is designed specifically to operate in such microgravity environment and in harsh surface conditions.”

José A. Carrasco, EMXYS CEO, stated that “this mission ensures EMXYS position within the space sector, either within the Earth orbit or in Deep Space, and makes the company’s technology highly reliable to become a leading producer of high-performance satellite platforms and payloads within the New Space market”.

Ian Carnelli, Hera project manager at the European Space Agency, stated that “GRASS will allow us to gather additional information on the internal structure of Dimorphos which is crucial to calibrate the numerical impact codes for planetary defence. We are thrilled to continue this excellent collaboration with the Royal Observatory of Belgium and EMXYS. The Juventas CubeSat will now have an incredible suite of instruments.”

About the Royal Observatory of Belgium

The Royal Observatory of Belgium is a federal research institute working under the aegis of the Belgian Federal Science Policy (BELSPO). It was founded in 1826 and moved to its present location in Ukkel/Uccle in 1890. The work of the Observatory focuses on the development and dissemination of knowledge in the field of astronomy, space geodesy and geophysics by performing scientific research and services. The services (Operational Directions) are Reference Systems and Planetology, Seismology and Gravimetry, Solar Physics and Space weather and Astronomy and Astrophysics. The Service (Operational Directorate) ‘Reference Systems and Planetology’ performs research on topics including space geodesy, planetary science, Earth rotation, GNSS and time realisation. Scientists at the Royal Observatory of Belgium have been participating actively in European Space Agency planetary exploration with responsibilities on several missions including ExoMars, MarsExpress, BepiColombo and JUICE (JUpiter ICy moons Explorer).

Founded in 2007, EMXYS has over 13 years of experience in the development of advanced electronic systems and their application to the space environment, especially nanosatellite-related technologies. The company develops projects for space agencies and space-related industrial contractors, providing reliable and competitive project management, as well as research and development services. So far, 24 space projects and 4 missions have been completed. /p>

The technology company develops and produces equipment and integrated instrumentation aimed at data capture and control systems for both scientific and commercial space applications. It focuses on four technological fields: space systems, biomedical engineering, scientific instruments, and defence systems. Its R&D laboratory and administrative facilities are located in the Scientific and Business Park of the Miguel Hernández University in Elche. EMXYS is a spin-off of this university.


Planets and Planetary Systems

Keeping mathematics to a minimum, assuming only a rudimentary knowledge of calculus, the book begins with a description of the basic properties of the planets in our solar systems, and then moves on to compare them with what is known about planets in other solar systems. It continues by looking at the surfaces, interiors and atmospheres of the planets and then covers the dynamics and origin of planetary systems. The book closes with a look at the role of life in planetary systems.

· An accessible, concise introduction to planets and planetary systems

· Uses insights from all the disciplines underlying planetary science

· Incorporates results from recent planetary space missions, such as Cassini to Saturn and a number of missions to Mars

· Well illustrated throughout, including a colour plate section

Planets and Planetary Systems is invaluable to students taking courses in planetary science across a wide range of disciplines and of interest to researchers and many keen amateur astronomers, needing an up-to-date introduction to this exciting subject.

Reviews

“Planets and Planetary Systems is invaluable to students taking courses in planetary science across a wide range of disciplines and of interest to researchers and many keen amateur astronomers, needing an up-to-date introduction to this exciting subject.” (Today Books, 20 September 2012)

Author Bios

Stephen Eales is the author of Planets and Planetary Systems, published by Wiley.


Planets and Planetary Systems

Keeping mathematics to a minimum, assuming only a rudimentary knowledge of calculus, the book begins with a description of the basic properties of the planets in our solar systems, and then moves on to compare them with what is known about planets in other solar systems. It continues by looking at the surfaces, interiors and atmospheres of the planets and then covers the dynamics and origin of planetary systems. The book closes with a look at the role of life in planetary systems.

·        An accessible, concise introduction to planets and planetary systems

·        Uses insights from all the disciplines underlying planetary science

·        Incorporates results from recent planetary space missions, such as Cassini to Saturn and a number of missions to Mars

·        Well illustrated throughout, including a colour plate section

Planets and Planetary Systems is invaluable to students taking courses in planetary science across a wide range of disciplines and of interest to researchers and many keen amateur astronomers, needing an up-to-date introduction to this exciting subject.


Watch the video: TerrestrialCelestial Spheres Coordinate Systems Tutorial (May 2022).