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Tuesday, July 11, 2023

Hill sphere

From Wikipedia, the free encyclopedia
A contour plot of the effective potential of a two-body system due to gravity and inertia at one point in time.

The Hill sphere of an astronomical body is the region in which it dominates the attraction of satellites. To be retained by a planet, a moon must have an orbit that lies within the planet's Hill sphere. That moon would, in turn, have a Hill sphere of its own. Any object within that distance would tend to become a satellite of the moon, rather than of the planet itself. One simple view of the extent of the Solar System is the Hill sphere of the Sun with respect to local stars and the galactic nucleus.

In more precise terms, the Hill sphere approximates the gravitational sphere of influence of a smaller body in the face of perturbations from a more massive body. It was defined by the American astronomer George William Hill, based on the work of the French astronomer Édouard Roche. It is sometimes termed the Roche sphere.

In the example to the right, the Earth's Hill sphere extends between the Lagrange points L1 and L2, which lie along the line of centers of the two bodies. The region of influence of the smaller body is shortest in that direction, and so it acts as the limiting factor for the size of the Hill sphere. Beyond that distance, a third object in orbit around the small object would spend at least part of its orbit outside the Hill sphere, and would be progressively perturbed by the tidal forces of the central body (e.g. the Sun), eventually ending up orbiting the latter.

For any given energy of the third object (considered to have a negligible mass) there is a zero-velocity surface in space which cannot be passed. This is a contour of the Jacobi integral. When the energy is low, the zero-velocity surface surrounds the second body (the smaller of the two) completely, which means the third body cannot escape. At higher energy, there will be one or more gaps or bottlenecks by which the third object may escape the second object and go into orbit around the first object. If the energy is right at the border between these two cases, then the third object cannot escape, but the zero-velocity surface confining it touches a larger zero-velocity surface around the first object at one of the nearby Lagrange points (forming a cone-like point there). At the opposite side of the planet it gets close to the other Lagrange point. This limiting zero-velocity surface around the second object is basically its Hill "sphere".

Formula and examples

Comparison of the Hill spheres and Roche limits of the Sun-Earth-Moon system (not to scale) with shaded regions denoting stable orbits of satellites of each body

If the mass of the smaller body (e.g. the Earth) is , and it orbits a heavier body (e.g. the Sun) of mass with a semi-major axis and an eccentricity of , then the radius of the Hill sphere of the smaller body, calculated at the pericenter, is approximately

When eccentricity is negligible (the most favourable case for orbital stability), this becomes

In the Earth-Sun example, the Earth (5.97×1024 kg) orbits the Sun (1.99×1030 kg) at a distance of 149.6 million km, or one astronomical unit (AU). The Hill sphere for Earth thus extends out to about 1.5 million km (0.01 AU). The Moon's orbit, at a distance of 0.384 million km from Earth, is comfortably within the gravitational sphere of influence of Earth and it is therefore not at risk of being pulled into an independent orbit around the Sun. All stable satellites of the Earth (those within the Earth's Hill sphere) must have an orbital period shorter than seven months.

The previous (eccentricity-ignoring) formula can be re-stated as follows:

This expresses the relation in terms of the volume of the Hill sphere compared with the volume of the second body's orbit around the first; specifically, the ratio of the masses is three times the ratio of the volume of these two spheres.

Derivation

The expression for the Hill radius can be found by equating gravitational and centrifugal forces acting on a test particle (of mass much smaller than ) orbiting the secondary body. Assume that the distance between masses and is , and that the test particle is orbiting at a distance from the secondary. When the test particle is on the line connecting the primary and the secondary body, the force balance requires that

where is the gravitational constant and is the (Keplerian) angular velocity of the secondary about the primary (assuming that ). The above equation can also be written as

which, through a binomial expansion to leading order in , can be written as

Hence, the relation stated above

If the orbit of the secondary about the primary is elliptical, the Hill radius is maximum at the apocenter, where is largest, and minimum at the pericenter of the orbit. Therefore, for purposes of stability of test particles (for example, of small satellites), the Hill radius at the pericenter distance needs to be considered. To leading order in , the Hill radius above also represents the distance of the Lagrangian point L1 from the secondary.

True region of stability

The Hill sphere is only an approximation, and other forces (such as radiation pressure or the Yarkovsky effect) can eventually perturb an object out of the sphere. This third object should also be of small enough mass that it introduces no additional complications through its own gravity. Detailed numerical calculations show that orbits at or just within the Hill sphere are not stable in the long term; it appears that stable satellite orbits exist only inside 1/2 to 1/3 of the Hill radius. The region of stability for retrograde orbits at a large distance from the primary is larger than the region for prograde orbits at a large distance from the primary. This was thought to explain the preponderance of retrograde moons around Jupiter; however, Saturn has a more even mix of retrograde/prograde moons so the reasons are more complicated.

Further examples

It is possible for a Hill sphere to be so small that it is impossible to maintain an orbit around a body. For example, an astronaut could not have orbited the 104 ton Space Shuttle at an orbit 300 km above the Earth, because a 104-ton object at that altitude has a Hill sphere of only 120 cm in radius, much smaller than a Space Shuttle. A sphere of this size and mass would be denser than lead, and indeed, in low Earth orbit, a spherical body must be more dense than lead in order to fit inside its own Hill sphere, or else it will be incapable of supporting an orbit. Satellites further out in geostationary orbit, however, would only need to be more than 6% of the density of water to fit inside their own Hill sphere.

Within the Solar System, the planet with the largest Hill radius is Neptune, with 116 million km, or 0.775 au; its great distance from the Sun amply compensates for its small mass relative to Jupiter (whose own Hill radius measures 53 million km). An asteroid from the asteroid belt will have a Hill sphere that can reach 220,000 km (for 1 Ceres), diminishing rapidly with decreasing mass. The Hill sphere of 66391 Moshup, a Mercury-crossing asteroid that has a moon (named Squannit), measures 22 km in radius.

A typical extrasolar "hot Jupiter", HD 209458 b, has a Hill sphere radius of 593,000 km, about eight times its physical radius of approx 71,000 km. Even the smallest close-in extrasolar planet, CoRoT-7b, still has a Hill sphere radius (61,000 km), six times its physical radius (approx 10,000 km). Therefore, these planets could have small moons close in, although not within their respective Roche limits.

Solar System

The following table and logarithmic plot show the radius of the Hill spheres of some bodies of the Solar System calculated with the first formula stated above (including orbital eccentricity), using values obtained from the JPL DE405 ephemeris and from the NASA Solar System Exploration website.

Radius of the Hill spheres of some bodies of the Solar System
Body Million km au Body radii Arcminutes Furthest moon (au)
Mercury 0.1753 0.0012 71.9 10.7
Venus 1.0042 0.0067 165.9 31.8
Earth 1.4714 0.0098 230.7 33.7 0.00257
Mars 0.9827 0.0066 289.3 14.9 0.00016
Jupiter 50.5736 0.3381 707.4 223.2 0.1662
Saturn 61.6340 0.4120 1022.7 147.8 0.1785
Uranus 66.7831 0.4464 2613.1 80.0 0.1366
Neptune 115.0307 0.7689 4644.6 87.9 0.3360
Ceres 0.2048 0.0014 433.0 1.7
Pluto 5.9921 0.0401 5048.1 3.5 0.00043
Eris 8.1176 0.0543 6979.9 2.7 0.00025
Logarithmic plot of the Hill radii for the bodies of the solar system.

Cultivar

From Wikipedia, the free encyclopedia
Osteospermum 'Pink Whirls'
A cultivar selected for its intriguing and colourful flowers

A cultivar is a kind of cultivated plant that people have selected for desired traits and when propagated retain those traits. Methods used to propagate cultivars include division, root and stem cuttings, offsets, grafting, tissue culture, or carefully controlled seed production. Most cultivars arise from purposeful human manipulation, but some originate from wild plants that have distinctive characteristics. Cultivar names are chosen according to rules of the International Code of Nomenclature for Cultivated Plants (ICNCP), and not all cultivated plants qualify as cultivars. Horticulturists generally believe the word cultivar was coined as a term meaning "cultivated variety".

Popular ornamental plants like roses, camellias, daffodils, rhododendrons, and azaleas are commonly cultivars produced by breeding and selection or as sports, for floral colour or size, plant form, or other desirable characteristics. Similarly, the world's agricultural food crops are almost exclusively cultivars that have been selected for characters such as improved yield, flavour, and resistance to disease, and very few wild plants are now used as food sources. Trees used in forestry are also special selections grown for their enhanced quality and yield of timber.

Cultivars form a major part of Liberty Hyde Bailey's broader group, the cultigen, which is defined as a plant whose origin or selection is primarily due to intentional human activity. A cultivar is not the same as a botanical variety, which is a taxonomic rank below subspecies, and there are differences in the rules for creating and using the names of botanical varieties and cultivars. In recent times, the naming of cultivars has been complicated by the use of statutory patents for plants and recognition of plant breeders' rights.

The International Union for the Protection of New Varieties of Plants (UPOV – French: Union internationale pour la protection des obtentions végétales) offers legal protection of plant cultivars to persons or organisations that introduce new cultivars to commerce. UPOV requires that a cultivar be "distinct, uniform", and "stable". To be "distinct", it must have characters that easily distinguish it from any other known cultivar. To be "uniform" and "stable", the cultivar must retain these characters in repeated propagation.

The naming of cultivars is an important aspect of cultivated plant taxonomy, and the correct naming of a cultivar is prescribed by the Rules and Recommendations of the International Code of Nomenclature for Cultivated Plants (ICNCP, commonly denominated the Cultivated Plant Code). A cultivar is given a cultivar name, which consists of the scientific Latin botanical name followed by a cultivar epithet. The cultivar epithet is usually in a vernacular language.

Etymology

Liberty Hyde Bailey (1858–1954) coined the words cultigen in 1918 and cultivar in 1923.
 

The word cultivar originated from the need to distinguish between wild plants and those with characteristics that arose in cultivation, presently denominated cultigens. This distinction dates to the Greek philosopher Theophrastus (370–285 BC), the "Father of Botany", who was keenly aware of this difference. Botanical historian Alan Morton noted that Theophrastus in his Historia Plantarum (Enquiry into Plants) "had an inkling of the limits of culturally induced (phenotypic) changes and of the importance of genetic constitution" (Historia Plantarum, Book 3, 2, 2 and Causa Plantarum, Book 1, 9, 3).

The International Code of Nomenclature for algae, fungi, and plants uses as its starting point for modern botanical nomenclature the Latin names in Linnaeus' (1707–1778) Species Plantarum (tenth edition) and Genera Plantarum (fifth edition). In Species Plantarum, Linnaeus enumerated all plants known to him, either directly or from his extensive reading. He recognised the rank of varietas (botanical "variety", a rank below that of species and subspecies) and he indicated these varieties with letters of the Greek alphabet, such as α, β, and λ, before the varietal name, rather than using the abbreviation "var." as is the present convention. Most of the varieties that Linnaeus enumerated were of "garden" origin rather than being wild plants.

In time the need to distinguish between wild plants and those with variations that had been cultivated increased. In the nineteenth century many "garden-derived" plants were given horticultural names, sometimes in Latin and sometimes in a vernacular language. From circa the 1900s, cultivated plants in Europe were recognised in the Scandinavian, Germanic, and Slavic literature as stamm or sorte, but these words could not be used internationally because, by international agreement, any new denominations had to be in Latin. In the twentieth century an improved international nomenclature was proposed for cultivated plants.

Liberty Hyde Bailey of Cornell University in New York, United States created the word cultivar in 1923 when he wrote that:

The cultigen is a species, or its equivalent, that has appeared under domestication – the plant is cultigenous. I now propose another name, cultivar, for a botanical variety, or for a race subordinate to species, that has originated under cultivation; it is not necessarily, however, referable to a recognized botanical species. It is essentially the equivalent of the botanical variety except in respect to its origin.

In that essay, Bailey used only the rank of species for the cultigen, but it was obvious to him that many domesticated plants were more like botanical varieties than species, and that realization appears to have motivated the suggestion of the new category of cultivar.

Bailey created the word cultivar. It is generally assumed to be a blend of cultivated and variety but Bailey never explicitly stated the etymology and it has been suggested that the word is actually a blend of cultigen and variety. The neologism cultivar was promoted as "euphonious" and "free from ambiguity". The first Cultivated Plant Code of 1953 subsequently commended its use, and by 1960 it had achieved common international acceptance.

Cultigens

Bread wheat, Triticum aestivum, is considered a cultigen, and is a distinct species from other wheats according to the biological species concept. Many different cultivars have been created within this cultigen. Many other cultigens are not considered to be distinct species, and can be denominated otherwise.

The words cultigen and cultivar may be confused with each other. A cultigen is any plant that is deliberately selected for or altered in cultivation, as opposed to an indigen; the Cultivated Plant Code states that cultigens are "maintained as recognisable entities solely by continued propagation". Cultigens can have names at any of many taxonomic ranks, including those of grex, species, cultivar group, variety, form, and cultivar; and they may be plants that have been altered in cultivation, including by genetic modification, but have not been formally denominated. A cultigen or a component of a cultigen can be accepted as a cultivar if it is recognisable and has stable characters. Therefore, all cultivars are cultigens, because they are cultivated, but not all cultigens are cultivars, because some cultigens have not been formally distinguished and named as cultivars.

Formal definition

The Cultivated Plant Code notes that the word cultivar is used in two different senses: first, as a "classification category" the cultivar is defined in Article 2 of the International Code of Nomenclature for Cultivated Plants (2009, 8th edition) as follows: The basic category of cultivated plants whose nomenclature is governed by this Code is the cultivar. There are two other classification categories for cultigens, the grex and the group. The Code then defines a cultivar as a "taxonomic unit within the classification category of cultivar". This is the sense of cultivar that is most generally understood and which is used as a general definition.

A cultivar is an assemblage of plants that (a) has been selected for a particular character or combination of characters, (b) is distinct, uniform and stable in those characters, and (c) when propagated by appropriate means, retains those characters.

Different kinds

A cultivar of the orchid genus Oncidium

Which plants are chosen to be named as cultivars is simply a matter of convenience as the category was created to serve the practical needs of horticulture, agriculture, and forestry.

Members of a particular cultivar are not necessarily genetically identical. The Cultivated Plant Code emphasizes that different cultivated plants may be accepted as different cultivars, even if they have the same genome, while cultivated plants with different genomes may be regarded as the same cultivar. The production of cultivars generally entails considerable human involvement although in a few cases it may be as little as simply selecting variation from plants growing in the wild (whether by collecting growing tissue to propagate from or by gathering seed).

Cultivars generally occur as ornamentals and food crops: Malus 'Granny Smith' and Malus 'Red Delicious' are cultivars of apples propagated by cuttings or grafting, Lactuca 'Red Sails' and Lactuca 'Great Lakes' are lettuce cultivars propagated by seeds. Named cultivars of Hosta and Hemerocallis plants are cultivars produced by micropropagation or division.

Clones

Leucospermum 'Scarlet Ribbon'
A cross performed in Tasmania between L. glabrum and L. tottum

Cultivars that are produced asexually are genetically identical and known as clones; this includes plants propagated by division, layering, cuttings, grafts, and budding. The propagating material may be taken from a particular part of the plant, such as a lateral branch, or from a particular phase of the life cycle, such as a juvenile leaf, or from aberrant growth as occurs with witch's broom. Plants whose distinctive characters are derived from the presence of an intracellular organism may also form a cultivar provided the characters are reproduced reliably from generation to generation. Plants of the same chimera (which have mutant tissues close to normal tissue) or graft-chimeras (which have vegetative tissue from different kinds of plants and which originate by grafting) may also constitute a cultivar.

Seed-produced

Some cultivars "come true from seed", retaining their distinguishing characteristics when grown from seed. Such plants are termed a "variety", "selection" or "strain" but these are ambiguous and confusing words that are best avoided. In general, asexually propagated cultivars grown from seeds produce highly variable seedling plants, and should not be labelled with, or sold under, the parent cultivar's name.

Seed-raised cultivars may be produced by uncontrolled pollination when characteristics that are distinct, uniform and stable are passed from parents to progeny. Some are produced as "lines" that are produced by repeated self-fertilization or inbreeding or "multilines" that are made up of several closely related lines. Sometimes they are F1 hybrids which are the result of a deliberate repeatable single cross between two pure lines. A few F2 hybrid seed cultivars also exist, such as Achillea 'Summer Berries'.

Some cultivars are agamospermous plants, which retain their genetic composition and characteristics under reproduction. Occasionally cultivars are raised from seed of a specially selected provenance – for example the seed may be taken from plants that are resistant to a particular disease.

Genetically modified

Genetically modified plants with characteristics resulting from the deliberate implantation of genetic material from a different germplasm may form a cultivar. However, the International Code of Nomenclature for Cultivated Plants notes, "In practice such an assemblage is often marketed from one or more lines or multilines that have been genetically modified. These lines or multilines often remain in a constant state of development which makes the naming of such an assemblage as a cultivar a futile exercise." However, retired transgenic varieties such as the fish tomato, which are no longer being developed, do not run into this obstacle and can be given a cultivar name.

Cultivars may be selected because of a change in the ploidy level of a plant which may produce more desirable characteristics.

Cultivar names

Viola 'Clear Crystals Apricot'
The specific epithet may be omitted from a cultivar name.

Every unique cultivar has a unique name within its denomination class (which is almost always the genus). Names of cultivars are regulated by the International Code of Nomenclature for Cultivated Plants, and may be registered with an International Cultivar Registration Authority (ICRA). There are sometimes separate registration authorities for different plant types such as roses and camellias. In addition, cultivars may be associated with commercial marketing names referred to in the Cultivated Plant Code as "trade designations" (see below).

Presenting in text

A cultivar name consists of a botanical name (of a genus, species, infraspecific taxon, interspecific hybrid or intergeneric hybrid) followed by a cultivar epithet. The cultivar epithet is enclosed by single quotes; it should not be italicized if the botanical name is italicized; and each of the words within the epithet is capitalized (with some permitted exceptions such as conjunctions). It is permissible to place a cultivar epithet after a common name provided the common name is botanically unambiguous. Cultivar epithets published before 1 January 1959 were often given a Latin form and can be readily confused with the specific epithets in botanical names; after that date, newly coined cultivar epithets must be in a modern vernacular language to distinguish them from botanical epithets.

For example, the full cultivar name of the King Edward potato is Solanum tuberosum 'King Edward'. 'King Edward' is the cultivar epithet, which, according to the Rules of the Cultivated Plant Code, is bounded by single quotation marks. For patented or trademarked plant product lines developed from a given cultivar, the commercial product name is typically indicated by the symbols "TM" or "®", or is presented in capital letters with no quotation marks, following the cultivar name, as in the following example, where "Bloomerang" is the commercial name and 'Penda' is the cultivar epithet: Syringa 'Penda' BLOOMERANG.

Examples of correct text presentation:
Cryptomeria japonica 'Elegans'
Chamaecyparis lawsoniana 'Aureomarginata' (pre-1959 name, Latin in form)
Chamaecyparis lawsoniana 'Golden Wonder' (post-1959 name, English language)
Pinus densiflora 'Akebono' (post-1959 name, Japanese language)
Apple 'Sundown'
Some incorrect text presentation examples:
Cryptomeria japonica "Elegans" (double quotes are unacceptable)
Berberis thunbergii cv. 'Crimson Pygmy' (this once-common usage is now unacceptable, as it is no longer correct to use "cv." in this context; Berberis thunbergii 'Crimson Pygmy' is correct)
Rosa cv. 'Peace' (this is now incorrect for two reasons: firstly, the use of "cv."; secondly, "Peace" is a trade designation or "selling name" for the cultivar R. 'Madame A. Meilland' and should therefore be printed in a different typeface from the rest of the name, without quote marks, for example: Rosa Peace.)

Although "cv." has not been permitted by the International Code of Nomenclature for Cultivated Plants since the 1995 edition, it is still widely used and recommended by other authorities.

Group names

Where several very similar cultivars exist they can be associated into a Group (formerly Cultivar-group). As Group names are used with cultivar names it is necessary to understand their way of presentation. Group names are presented in normal type and the first letter of each word capitalised as for cultivars, but they are not placed in single quotes. When used in a name, the first letter of the word "Group" is itself capitalized.

Presenting in text

Brassica oleracea Capitata Group (the group of cultivars including all typical cabbages)
Brassica oleracea Botrytis Group (the group of cultivars including all typical cauliflowers)
Hydrangea macrophylla Groupe Hortensia (in French) = Hydrangea macrophylla Hortensia Group (in English)
Where cited with a cultivar name the group should be enclosed in parentheses, as follows:
Hydrangea macrophylla (Hortensia Group) 'Ayesha' 

Legal protection of cultivars and their names

Since the 1990s there has been an increasing use of legal protection for newly produced cultivars. Plant breeders expect legal protection for the cultivars they produce. According to proponents of such protections, if other growers can immediately propagate and sell these cultivars as soon as they come on the market, the breeder's benefit is largely lost. Legal protection for cultivars is obtained through the use of Plant breeders' rights and plant Patents but the specific legislation and procedures needed to take advantage of this protection vary from country to country.

Controversial use of legal protection for cultivars

The use of legal protection for cultivars can be controversial, particularly for food crops that are staples in developing countries, or for plants selected from the wild and propagated for sale without any additional breeding work; some people consider this practice unethical.

Trade designations and selling names

The formal scientific name of a cultivar, like Solanum tuberosum 'King Edward', is a way of uniquely designating a particular kind of plant. This scientific name is in the public domain and cannot be legally protected. Plant retailers wish to maximize their share of the market and one way of doing this is to replace the cumbersome Latin scientific names on plant labels in retail outlets with appealing marketing names that are easy to use, pronounce, and remember. Marketing names lie outside the scope of the Cultivated Plant Code which refers to them as "trade designations". If a retailer or wholesaler has the sole legal rights to a marketing name then that may offer a sales advantage. Plants protected by plant breeders' rights (PBR) may have a "true" cultivar name – the recognized scientific name in the public domain – and a "commercial synonym" – an additional marketing name that is legally protected. An example would be Rosa Fascination = 'Poulmax', in which Rosa is the genus, Fascination is the trade designation, and 'Poulmax' is scientific cultivar name.

Because a name that is attractive in one language may have less appeal in another country, a plant may be given different selling names from country to country. Quoting the original cultivar name allows the correct identification of cultivars around the world.

The main body coordinating plant breeders' rights is the International Union for the Protection of New Varieties of Plants (Union internationale pour la protection des obtentions végétales, UPOV) and this organization maintains a database of new cultivars protected by PBR in all countries.

International Cultivar Registration Authorities

Dahlia 'Akita'
A cultivar selected for flower form and colour

An International Cultivar Registration Authority (ICRA) is a voluntary, non-statutory organization appointed by the Commission for Nomenclature and Cultivar Registration of the International Society of Horticultural Science. ICRAs are generally formed by societies and institutions specializing in particular plant genera such as Dahlia or Rhododendron and are currently located in Europe, North America, China, India, Singapore, Australia, New Zealand, South Africa and Puerto Rico.

Each ICRA produces an annual report and its reappointment is considered every four years. The main task is to maintain a register of the names within the group of interest and where possible this is published and placed in the public domain. One major aim is to prevent the duplication of cultivar and Group epithets within a genus, as well as ensuring that names are in accord with the latest edition of the Cultivated Plant Code. In this way, over the last 50 years or so, ICRAs have contributed to the stability of cultivated plant nomenclature. In recent times many ICRAs have also recorded trade designations and trademarks used in labelling plant material, to avoid confusion with established names.

New names and other relevant data are collected by and submitted to the ICRA and in most cases there is no cost. The ICRA then checks each new epithet to ensure that it has not been used before and that it conforms with the Cultivated Plant Code. Each ICRA also ensures that new names are formally established (i.e. published in hard copy, with a description in a dated publication). They record details about the plant, such as parentage, the names of those concerned with its development and introduction, and a basic description highlighting its distinctive characters. ICRAs are not responsible for assessing the distinctiveness of the plant in question. Most ICRAs can be contacted electronically and many maintain web sites for an up-to-date listing.

Rendezvous with Rama

From Wikipedia, the free encyclopedia
 
Rendezvous with Rama
First UK edition
AuthorArthur C. Clarke
Cover artistBruce Pennington
CountryUnited Kingdom
LanguageEnglish
SeriesRama series
GenreScience fiction
PublisherGollancz (UK)
Harcourt Brace Jovanovich (US)
Publication date
Jun 1973 (UK)
Aug 1973 (US)
Media typePrint (hardback & paperback)
Pages256 (UK)
69,048 words
AwardsHugo Award for Best Novel, Nebula Award for Best Novel, John W. Campbell Memorial Award
ISBN0-575-01587-X (UK)
Followed byRama II 

Rendezvous with Rama is a science fiction novel by British writer Arthur C. Clarke first published in 1973. Set in the 2130s, the story involves a 50-by-20-kilometre (31 by 12 mi) cylindrical alien starship that enters the Solar System. The story is told from the point of view of a group of human explorers who intercept the ship in an attempt to unlock its mysteries. The novel won both the Hugo and Nebula awards upon its release, and is regarded as one of the cornerstones in Clarke's bibliography. The concept was later extended with several sequels, written by Clarke and Gentry Lee.

Plot

After an asteroid falls in Northeast Italy on 11 September 2077, creating a major disaster, the government of Earth sets up the Spaceguard system as an early warning of arrivals from deep space.

The "Rama" of the title is an alien starship weighing at least ten trillion tons, initially mistaken for an asteroid categorised as "31/439". It is detected by astronomers in the year 2131 while it is still outside the orbit of Jupiter. Its speed (100,000 km/h – 62,150 m/h) and the angle of its trajectory clearly indicate it is not on a long orbit around the sun, but is an interstellar object. The astronomers' interest is further piqued when they realise the asteroid has an extremely rapid rotation period of four minutes and is exceptionally large. It is named Rama after the Hindu god, and an uncrewed space probe dubbed Sita is launched from the Mars moon Phobos to intercept and photograph it. The resulting images reveal that Rama is a perfect cylinder, 20 kilometres (12 mi) in diameter and 50 kilometres (31 mi) long, and almost completely featureless, making this humankind's first encounter with an alien spacecraft.

The solar survey vessel Endeavour is sent to study Rama, as it is the only ship close enough to do so in the brief period Rama will spend in the Solar System. Endeavour manages to rendezvous with Rama one month after it first comes to Earth's attention, when the alien ship is already inside Venus's orbit. The crew, led by Commander Bill Norton, enters Rama through a safety system consisting of triple airlocks, and explores the 16-km wide by 50-km long cylindrical world of its interior, but the nature and purpose of the starship and its creators remain enigmatic throughout the book. Rama's inner surfaces hold "cities" of geometric structures that resemble buildings and are separated by streets with shallow trenches. A band of water, dubbed the Cylindrical Sea, stretches around Rama's central circumference. Massive spires, which are theorised to be part of Rama's propulsion system, stand at its "southern" end. They also find that Rama's atmosphere is breathable.

One of the crew members, Jimmy Pak, who has experience with low gravity skybikes, rides a smuggled skybike along Rama's axis to the far end, otherwise inaccessible due to the cylindrical sea and the 500m high cliff on the opposite shore. Once at the massive metal cones on the southern end of Rama, Jimmy detects magnetic and electric fields coming from the cones, which increase, resulting in lightning. Due to his proximity to the spires, the concussion from a discharge damages his skybike causing him to crash on the isolated southern continent.

When Pak wakes up, he sees a crab-like creature picking up his skybike and chopping it into pieces. He cannot decide whether it is a robot or a biological alien, and keeps his distance while radioing for help. As Pak waits, Norton sends a rescue party across the cylindrical sea, using a small, improvised craft, constructed earlier for exploration of the sea's central island. The creature dumps the remains of the skybike into a pit, but ignores Pak himself, who explores the surrounding fields while waiting for the rescue party to arrive. Amongst the strange geometric structures, he sees an alien flower growing through a cracked tile in the otherwise sterile environment, and decides to take it as both a curiosity and for scientific research.

Pak jumps off the 500m cliff, his descent slowed by the low gravity and using his shirt as a drogue parachute, and is quickly rescued by the waiting boat. As they ride back, tidal waves form in the cylindrical sea, created by the movements of Rama itself as it makes course corrections. When the crew arrives at base, they see a variety of odd creatures inspecting their camp. When one is found damaged and apparently lifeless, the team's doctor/biologist Surgeon-Commander Laura Ernst inspects it, and discovers it to be a hybrid biological entity and robot—eventually termed a "biot". It, and by assumption the others, are powered by internal batteries (much like those of terrestrial electric eels) and possess some intelligence. They are believed to be the drones of Rama's still-absent builders.

The members of the Rama Committee and the United Planets, both based on the Moon, have been monitoring events inside Rama and giving feedback. The Hermian colonists have concluded that Rama is a potential threat and send a rocket-mounted nuclear bomb to destroy it should it prove to pose a threat. Lt. Boris Rodrigo takes advantage of the five minute transmission delay and uses a pair of wire cutters to defuse the bomb and its control.

As Rama approaches perihelion, and on their final expedition, the crew decide to visit the city closest to their point of entry, christened "London", and use a laser to cut open one of the "buildings" to see what it houses. They discover transparent pedestals containing holograms of various artefacts, which they theorise are used by the Ramans as templates for creating tools and other objects. One hologram appears to be a uniform with bandoliers, straps and pockets that suggests the size and shape of the Ramans. As the crew photographs some of the holograms, the biots begin returning to the cylindrical sea, where they are recycled by aquatic biots ('sharks') and the six striplights that illuminate Rama's interior start to dim, prompting the explorers to leave Rama and to re-board Endeavour.

With Endeavour a safe distance away, Rama reaches perihelion and utilizes the Sun's gravitational field, and its mysterious "space drive", to perform a slingshot manoeuvre which flings it out of the Solar System and towards an unknown destination in the direction of the Large Magellanic Cloud.

Ending

The book was meant to stand alone, although its final sentence suggests otherwise:

And on far-off Earth, Dr. Carlisle Perera had as yet told no one how he had wakened from a restless sleep with the message from his subconscious still echoing in his brain: The Ramans do everything in threes.

Clarke denied that this sentence was a hint that the story might be continued. In his foreword to the book's sequel, he stated that it was just a good way to end the first book, and that he added it during a final revision.

Reception

John Leonard of The New York Times, while finding Clarke "benignly indifferent to the niceties of characterization," praised the novel for conveying "that chilling touch of the alien, the not-quite-knowable, that distinguishes sci-fi at its most technically imaginative." Other reviewers have also commented on Clarke's lack of character development and overemphasis on realism.

Awards and nominations

The novel was awarded the following soon after publication

Design and geography of Rama

An artist's impression of the interior of Rama.

The interior of Rama is essentially a large cylindrical landscape, dubbed "The Central Plain" by the crew, 16 kilometres in diameter and nearly 50 long, with artificial gravity provided by its 0.25 rpm spin. It is split into the "northern" and "southern" plains, divided in the middle by a 10-km wide expanse of water the astronauts dub the "Cylindrical Sea". In the center of the Cylindrical Sea is an island of unknown purpose covered in tall, skyscraper-like structures, which the astronauts name "New York" due to an imagined similarity to Manhattan. At each end of the ship are North and South "Poles". The North Pole is effectively the bow and the South Pole the stern, as Rama accelerates in the direction of the north pole and its drive system is at the South Pole.

The North Pole contains Rama's airlocks, and is where the Endeavour lands. The airlocks open into the hub of the massive bowl shaped cap at the North Pole, with three 8-kilometre long stair systems, called Alpha, Beta, and Gamma by the crew, leading to the plain.

The Northern plain contains several small "towns" interconnected by roads, dubbed London, Paris, Peking, Tokyo, Rome, and Moscow. The South Pole has a giant cone-shaped protrusion ("Big Horn") surrounded by six smaller ones ("Little Horns"), which are thought to be part of Rama's reactionless space drive.

Both ends of Rama are lit by giant trenches (three in the northern plain and three in the south), equidistantly placed around the cylinder, effectively functioning as giant strip lighting.

Books in the series

Clarke paired up with Gentry Lee for the remainder of the series. Lee wrote while Clarke read and made editing suggestions. The focus and style of the last three novels are quite different from those of the original with an increased emphasis on characterisation and clearly-portrayed heroes and villains, rather than Clarke's dedicated professionals. These later books did not receive the same critical acclaim and awards as the original.

Gentry Lee also wrote two further novels set in the same Rama Universe.

  • Bright Messengers (1995)
  • Double Full Moon Night (1999)

Adaptations

Video games

A graphic adventure computer game of the same name with a text parser based on the book was made in 1984 by Trillium and ported to other systems such as the Apple II, Commodore 64. Despite its primitive graphics, it had highly detailed descriptions, and it followed the book very closely along with having puzzles to solve during the game.

In Spain there was an official adaptation for the 2nd generation MSX computers called Cita con Rama that took advantage of the MSX's ability to produce (at the time) high-quality graphics. It was adapted from the Clarke novel in 1983 by Ron Martinez, who went on to design the massively multiplayer online game 10Six, also known as Project Visitor.

Sierra Entertainment created Rama in 1996 as a point and click adventure game in the style of Myst. Along with highly detailed graphics, Arthur C. Clarke also appeared in the game as the guide for the player. This game featured characters from the sequel book Rama II.

Radio adaptation

In 2009, BBC Radio 4 produced a two-part radio adaptation of the book as part of a science-fiction season. It was adapted by Mike Walker, and was broadcast on 1 March 2009 (Part 1) and 8 March 2009 (Part 2).

Film

In the early 2000s, actor Morgan Freeman expressed his desire to produce a film based on Rendezvous with Rama. The film has been stuck in "development hell" for many years. In 2003, after initial problems procuring funding, it appeared the project would go into production. The film was to be produced by Freeman's production company, Revelations Entertainment. David Fincher, touted on Revelations' Rama web page as far back as 2001, stated in a late 2007 interview that he was still attached to helm.

By late 2008, David Fincher stated the movie was unlikely to be made. "It looks like it's not going to happen. There's no script and as you know, Morgan Freeman's not in the best of health right now. We've been trying to do it but it's probably not going to happen."

In 2010, Freeman stated in an interview that he was still planning to make the project but that it has been difficult to find the right script. He also stated that it should be made in 3D. In January 2011, Fincher stated in an interview with MTV that he was still planning to make the film after he had completed work on his planned remake of 20,000 Leagues Under the Sea (which was scheduled to begin production in 2012 but has since been scrapped). He also reiterated Freeman's concerns about the difficulty of finding the right script.

In an interview with Neil deGrasse Tyson in February 2012, Freeman indicated an interest in playing the role of Commander Norton for the film, stating that "my fantasy of commanding a starship is commanding Endeavour". Tyson then asked, "So is this a pitch to be ... that person if they ever make that movie?" to which Freeman reaffirmed, "We are going to make that movie." In response to a plea to "make that come out sooner rather than later", Freeman reiterated that difficulty in authoring a high quality script is the primary barrier for the film, stating "... the only task you have that's really really hard in making movies, harder than getting money, is getting a script ... a good script".

In December 2021, it was announced that the film was in development at Alcon Entertainment with Denis Villeneuve set to direct. Morgan Freeman and Lori McCreary are on the production team because their Revelations Entertainment previously owned the rights. Alcon co-CEOs Broderick Johnson and Andrew Kosove will produce.

Non-fictional aspects

Number of NEOs detected by various projects:
  LINEAR
  NEAT
  Spacewatch
  LONEOS
  CSS
  Pan-STARRS
  NEOWISE
  other

Clarke created the space study program which detects Rama, Project Spaceguard, as a method of identifying near-Earth objects on Earth-impact trajectories; in the novel it was initiated in 2077. A real project named Spaceguard was initiated in 1992, named after Clarke's fictional project and "with the permission and encouragement of Clarke". After interest in the dangers of asteroid strikes was heightened by a series of Hollywood disaster films, the United States Congress gave NASA authorisation and funding to support Spaceguard. By 2017, there were a number of different efforts to detect potentially dangerous asteroids.

On 19 October 2017 an incoming interstellar object was discovered by Pan-STARRS, a system similar to Spaceguard. Like Rama, the object had an unusually elongated shape. Before the official Hawaiian name ʻOumuamua was selected by the International Astronomical Union, a popular choice was Rama.

Lie point symmetry

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Lie_point_symmetry     ...