An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

1) The fact that the Sun, which contains 99.9% of the mass of the → solar system, accounts for about 2% of the total → angular momentum of the solar system. The problem of outward → angular momentum transfer has been a main topic of interest for models attempting to explain the origin of the solar system.
2) More generally, in star formation studies, the question of the origin of the angular momentum of a star and the evolution of its distribution during the early history of a star. Consider a filamentary molecular cloud with a length of 10 pc and a radius of 0.2 pc, rotating about its long axis with a typical → angular velocity of Ω = 10^-15 s^-1. At a matter density of 20 cm^-3, the cloud is about 1 → solar mass. The cloud collapses to form a star with radius of 6 x 10¹⁰ cm. The conservation of angular momentum (∝ ΩR²) requires that as the radius decreases from 0.2 pc to the stellar value, a factor of 10⁷, the value of Ω must increase by 14 orders of magnitude to 10^-1 s^-1. The star's rotational velocity will be 20% the speed of light and the ratio of → centrifugal force to gravity at the equator will be about 10⁴. Observational data, however, indicate that the youngest stars are in fact rotating quite slowly, with rotational velocities of 10% of the → break-up velocity. The angular momentum problem was first studied in the context of single stars forming in isolation (L. Mestel, 1965, Quart. J. R. Astron. Soc. 6, 161). For more information see, e.g., P. Bodenheimer, 1995, ARAA 33, 199; H. Zinnecker, 2004, RevMexAA 22, 77; R. B. Larson, 2010, Rep. Prog. Phys. 73, 014901, and references therein.

→ angular; → momentum; → problem.

The impressive discrepancy of about 120 orders of magnitude between the theoretical value of the → cosmological constant and its observed value. → Quantum field theory interprets the cosmological constant as the density of the → vacuum energy. This density can be derived from the maximum energy at which the theory is valid, i.e. the → Planck energy scale (10¹⁸ GeV). The theoretical vacuum → energy density is (10¹⁸ GeV)⁴ = (10²⁷ eV)⁴ = 10¹¹² erg cm^-3. On the other hand, the observed vacuum energy density is estimated to be about (10^-3 eV)⁴ = 10^-8 erg cm^-3. There is, therefore, a discrepancy of about 120 orders of magnitude.

→ cosmological; → constant; → problem.

A problem encountered by the → cold dark matter (CDM) model of galaxy formation. The numerical simulations with CDM predict a large concentration of dark matter in the center of galaxies, with a peaked density distribution, in contrast to the real, observed galaxies. See also: → angular momentum catastrophe; → missing dwarfs.

→ cusp; → problem.

Math: The question of whether a → solution to a given → problem exists.

→ existence; → problem.

A computer experiment that was aimed to study the → thermalization process of a → solid. In other words, the goal was to see whether there is an approximate → equipartition of energy in the system, which would mean that the motion is → chaotic. Using computer simulation, Fermi-Pasta-Ulam studied the behavior of a chain of 64 mass particles connected by → nonlinear springs. In fact, they were looking for a theoretical physics problem suitable for an investigation with one of the very first computers, the he MANIAC (Mathematical Analyzer, Numerical Integrator and Computer). They decided to study how a → crystal evolves toward → thermal equilibrium by simulating a chain of particles, linked by a quadratic interaction potential, but also by a weak nonlinear interaction. Fermi-Pasta-Ulam assumed that if the interaction in the chain were nonlinear, then an exchange of energy among the normal modes would occur, and this would bring forth the equipartition of energy, i.e. the thermalization. Contrary to expectations, the energy revealed no tendency toward equipartition. The system had a simple quasi-periodic behavior, and no → chaoticity was observed. This result, known as the Fermi-Pasta-Ulam paradox, shows that → nonlinearity is not enough to guarantee the equipartition of energy (see, e.g., Dauxois et al., 2005, Eur. J. Phys., 26, S3).

E. Fermi, J. Pasta, S. Ulam, 1955, Los Alamos report LA-1940; → problem.

The observed fact that the → geometry of the → Universe is very nearly flat, in other words its density is very close to the → critical density. This would be an extreme coincidence because a → flat Universe is a special case. Many attempts have been made to explain the flatness problem, and modern theories now include the idea of → inflation.

→ flat; → problem.

The discrepancy between observed galaxy → rotation curves and the theoretical prediction, assuming a centrally dominated mass associated with the observed luminous material.

→ galactic; → rotation; → problem.

A problem with the standard cosmological model of the Big Bang related to the observational fact that regions of the Universe that are separated by vast distances nevertheless have nearly identical properties such as temperature. This contradicts the fact that light moves with a finite speed and, as a result, certain events which occur in the Universe are completely independent of each other. Inflationary cosmology offers a possible solution.

→ horizon; → problem.

1) Given the trajectory of a particle moving in a → central force field, determine the law governing the central force.
2) Inversely, considering a central force -k/r², determine the trajectory a particle moving in the field will take.

→ Kepler; → problem.

Low-mass → protostars are about an order of magnitude less luminous than expected. Two possible solutions are that → low-mass stars form slowly, and/or protostellar → accretion is episodic. The latter accounts for less than half the missing luminosity. The solution to this problem relates directly to the fundamental question of the time required to form a low-mass star (McKee & Offner, 2010, astro-ph/1010.4307).

→ luminosity; → problem.

A problem concerning the compatibility of grand unified theories (→ GUTs) with standard cosmology. If standard cosmology was combined with grand unified theories, far too many → magnetic monopoles would have been produced in the early Universe. The → inflation hypothesis aims at explaining the observed scarcity of monopoles. The inflation has deceased their density by a huge factor.

→ magnetic; → monopole; → problem.

The mathematical problem of solving the equations of motions of any number of bodies which interact gravitationally. More specifically, to find their positions and velocities at any point in the future or the past, given their present positions, masses, and velocities.

Many, from M.E. mani, meni, O.E. monig, manig; → body; → problem.

The observed underabundance, by one or two orders of magnitude, of → dwarf galaxies orbiting → spiral galaxies compared to their number predicted by the standard model. The → cold dark matter (CDM) model predicts that dwarf galaxies are the building blocks of large galaxies like the Milky Way and should largely outnumber them. Dwarf galaxies form first, they merge into bigger and bigger galaxies, and galaxies into groups of galaxies. The dark matter halos, however, are very dense, and dwarf halos are not destroyed in the merging, resulting in their large predicted number, in numerical simulations.

Probably first dealt with in an article entitled "Where Are the Missing Galactic Satellites?" (Lypin et al. 1999, ApJ 522, 82); → missing mass; → satellite; → problem.

The mathematical problem of studying the behavior (e.g., velocities, positions) of any number of objects moving under their mutual gravitational attraction for any time in the past or future. Same as the → many-body problem.

→ body; → problem.

1) Any question or matter involving doubt, uncertainty, or difficulty.
2) Math.: A statement requiring a solution, usually by means of a mathematical operation or geometric construction.

M.E., from O.Fr. problème, from L. problema, from Gk. problema "a problem, a question," literally "thing put forward," from proballein "to propose," from → pro- "forward" + ballein "to throw," → ballistics.

Parâsé, from pərəs- present tense stem of Av. fras- "to ask, question, inquire," pərəsaiti "asks," to which is related Mod.Pers. pors-, porsidan "to ask;" Mid.Pers. pursidan; O.Pers. prs-, fraθ- "to ask, examine, investigate, punish;" Sogd. anfrāsē "question, enquiry;" cf. Skt. praś- "to ask, long for;" Tokharian prak-/prek- "to ask;" L. prex "request," precor "to ask, to pray;" Lith. prašyti "to ask, to demand;" Ger. fragen "to ask;" PIE base *prek- "to ask."

1) Posing a problem; difficult to solve.
2) Open to doubt; debatable.
3) Not settled; unresolved or dubious (TheFreeDictionary.com).

From M.Fr. problematique, from L. problematicus, from Gk. problematikos "pertaining to a problem," from → problem.

A special case of the → three-body problem in which the → mass of one of the bodies is negligible compared to that of the two others. If the relative motion of the two massive components is a circle, the situation is referred to as the → circular restricted three-body problem. An example would be a space probe moving in the → gravitational fields of the → Earth and the → Moon, which revolve very nearly in circles about their common → center of mass.

→ restrict; → three; → body; → problem.

The combination of a → partial differential equation and a → piecewise constant → initial condition. The Riemann problem is a basic tool in a number of numerical methods for wave propagation problems. The canonical form of the Riemann problem is: ∂u/∂t + ∂f(u)/∂x = 0, x ∈ R, t > 0, u(x,0) = u_l if x < 0, and u(x,0) = u_r if x > 0 .

→ Riemann's geometry; → problem.

A major discrepancy between the flux of neutrinos detected at Earth from the solar core and that predicted by current models of solar nuclear fusion and our understanding of neutrinos themselves. The problem, lasting from the mid-1960s to about 2002, was a considerably lesser detected number of neutrons compared with theoretical predictions. The discrepancy has since been resolved by new understanding of neutrino physics, requiring a modification of the → standard model of particle physics, in particular → neutrino oscillation.

→ solar; → neutrino; → problem.

The mathematical problem of studying the positions and velocities of three mutually attracting bodies (such as the Sun, Earth and Moon) and the stability of their motion. This problem is surprisingly difficult to solve, even in the simple case, called → restricted three-body problem, where one of the masses is taken to be negligibly small so that the problem simplifies to finding the behavior of the mass-less body in the combined gravitational field of the other two. See also → two-body problem, → n-body problem.

→ three; → body; → problem.