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Karl Stumpff
Karl Johann Nikolaus Stumpff (May 17, 1895 – November 10, 1970) was a German astronomer. The Stumpff functions, used in the universal variable formulation of the two-body problem, are named after him. Works * ''Analyse periodischer Vorgänge''. Gebrüder Borntraeger: Berlin 1927 * ''Grundlagen und Methoden der Periodenforschung''. Berlin 1937 * ''Ermittlung und Realität von Periodizitäten. Korrelationsrechnung.'' In: ''Handbuch der Geophysik.'' 1940 * ''Tafeln und Aufgaben zur Harmonischen Analyse und Periodogrammrechnung.'' Berlin 1939 * ''Neue Theorie und Methoden der Ephemeridenrechnung.'' Abhandlungen der Deutschen Akademie der Wissenschaften 1947 * ''Neue Wege zur Bahnberechnung der Himmelskörper.'' In: ''Fortschritte der Physik.'' vol.1, 1954, pp. 557–596 * ''Geographische Ortsbestimmungen.'' In: ''Hochschulbücher für Physik.'' Berlin 1955 * ''Himmelsmechanik.'' 3 vols., Deutscher Verlag der Wissenschaften (DVW) (English: ''German Publisher of Sciences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, galaxies – in either observational astronomy, observational (by analyzing the data) or theoretical astronomy. Examples of topics or fields astronomers study include planetary science, Sun, solar astronomy, the Star formation, origin or stellar evolution, evolution of stars, or the galaxy formation and evolution, formation of galaxies. A related but distinct subject is physical cosmology, which studies the Universe as a whole. Types Astronomers usually fall under either of two main types: observational astronomy, observational and theoretical astronomy, theoretical. Observational astronomers make direct observations of Astronomical object, celestial objects and analyze the data. In contrast, theoretical astronomers create and investigate C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stumpff Function
In celestial mechanics, the Stumpff functions ''c''''k''(''x''), developed by Karl Stumpff, are used for analyzing orbits using the universal variable formulation. They are defined by the formula: c_k (x) = \frac - \frac + \frac - \cdots = \sum_^\infty for k = 0, 1, 2, 3,\ldots The series above converges absolutely for all real ''x''. By comparing the Taylor series expansion of the trigonometric functions sin and cos with ''c''0(''x'') and ''c''1(''x''), a relationship can be found: \begin c_0(x) &= \cos , \\ exc_1(x) &= \frac, \end \quad \textx > 0 Similarly, by comparing with the expansion of the hyperbolic functions sinh and cosh we find: \begin c_0(x) &= \cosh , \\ exc_1(x) &= \frac, \end \quad \textx < 0 The Stumpff functions satisfy the : |
Universal Variable Formulation
In orbital mechanics, the universal variable formulation is a method used to solve the two-body Kepler problem. It is a generalized form of Kepler's Equation, extending them to apply not only to elliptic orbits, but also parabolic and hyperbolic orbits. It thus is applicable to many situations in the Solar System, where orbits of widely varying eccentricities are present. Introduction A common problem in orbital mechanics is the following: given a body in an orbit and a time ''t0'', find the position of the body at any other given time ''t''. For elliptical orbits with a reasonably small eccentricity, solving Kepler's Equation by methods like Newton's method gives adequate results. However, as the orbit becomes more and more eccentric, the numerical iteration may start to converge slowly or not at all. Furthermore, Kepler's equation cannot be applied to parabolic and hyperbolic orbits, since it specifically is tailored to elliptic orbits. Derivation Although equations similar to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-body Problem
In classical mechanics, the two-body problem is to predict the motion of two massive objects which are abstractly viewed as point particles. The problem assumes that the two objects interact only with one another; the only force affecting each object arises from the other one, and all other objects are ignored. The most prominent case of the classical two-body problem is the gravitational case (see also Kepler problem), arising in astronomy for predicting the orbits (or escapes from orbit) of objects such as satellites, planets, and stars. A two-point-particle model of such a system nearly always describes its behavior well enough to provide useful insights and predictions. A simpler "one body" model, the " central-force problem", treats one object as the immobile source of a force acting on the other. One then seeks to predict the motion of the single remaining mobile object. Such an approximation can give useful results when one object is much more massive than the other (as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deutscher Verlag Der Wissenschaften
(DVW) (English: ''German Publisher of Sciences'') was a scientific publishing house in the former German Democratic Republic (GDR/). Situated in Berlin, DVW was founded as (VEB) on 1 January 1954 as the successor of the main department of "university literature" of the publisher (VWV). During the first ten years, DVW, for the most part, published mathematical and scientific literature aimed at university education. About 780 titles were introduced with a total print run of some 3.7 million books. In 1964, DVW took over parts of the programme of and also published textbooks on topics of philosophy, history and sociology. DVW was among the publishers of the (MSB). Whilst more than a third of the production was distributed into Western foreign countries, the publisher still did not make a profit due to the fixed low book prices, politically motivated so called ' (PAOs) dictated by the East German government. In 1988, with a turnaround of 8.4 million East German mark, DVW los ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1895 Births
Events January–March * January 5 – Dreyfus affair: French officer Alfred Dreyfus is stripped of his army rank, and sentenced to life imprisonment on Devil's Island. * January 12 – The National Trust for Places of Historic Interest or Natural Beauty is founded in England by Octavia Hill, Robert Hunter and Canon Hardwicke Rawnsley. * January 13 – First Italo-Ethiopian War: Battle of Coatit – Italian forces defeat the Ethiopians. * January 17 – Félix Faure is elected President of the French Republic, after the resignation of Jean Casimir-Perier. * February 9 – Mintonette, later known as volleyball, is created by William G. Morgan at Holyoke, Massachusetts. * February 11 – The lowest ever UK temperature of is recorded at Braemar, in Aberdeenshire. This record is equalled in 1982, and again in 1995. * February 14 – Oscar Wilde's last play, the comedy ''The Importance of Being Earnest'', is first shown at St Jam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
