A third-order intermediate orbit for planetary theory

We compare numerical efficiency of the two kinds of series for the first-order intermediate orbit for general planetary theory: (1) the classical expansion involving mean longitudes of the planets; (2) an expansion resulting from the theory of elliptic functions. We conclude that mutual perturbations of close couples of planets (the ratio of major semi-axes ∼ 1) can be represented in more compact form with the aid of the second kind of series.

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Third-order Jupiter ? Saturn planetary theory

Earth Moon and Planets ◽

10.1007/bf00056332 ◽

1989 ◽

Vol 47 (1) ◽

pp. 73-89 ◽

Cited By ~ 1

Author(s):

Osman M. Kamel

Keyword(s):

Planetary Theory ◽

Third Order

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On the expansions of intermediate orbit for general planetary theory

Celestial Mechanics and Dynamical Astronomy ◽

10.1007/bf00049377 ◽

1997 ◽

Vol 66 (4) ◽

pp. 345-363 ◽

Cited By ~ 1

Author(s):

Sergei A. Klioner

Keyword(s):

Planetary Theory ◽

Intermediate Orbit ◽

General Planetary Theory

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Third order uranus-neptune planetary theory

Earth Moon and Planets ◽

10.1007/bf00192646 ◽

1988 ◽

Vol 40 (3) ◽

Author(s):

OsmanM. Kamel ◽

AbdelAziz Bakry

Keyword(s):

Planetary Theory ◽

Third Order

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Probe size and 5th-order aberration

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100125609 ◽

1987 ◽

Vol 45 ◽

pp. 134-135 ◽

Cited By ~ 1

Author(s):

Zhifeng Shao

Keyword(s):

Electron Probe ◽

Spherical Aberration ◽

Wave Length ◽

Cylindrical Symmetry ◽

Electron Wave ◽

Third Order ◽

The Third ◽

Probe Radius ◽

Small Probe ◽

Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

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Children’s Recall of Approximations to English

Journal of Speech and Hearing Research ◽

10.1044/jshr.1602.201 ◽

1973 ◽

Vol 16 (2) ◽

pp. 201-212 ◽

Cited By ~ 3

Author(s):

Elizabeth Carrow ◽

Michael Mauldin

Keyword(s):

Language Development ◽

Fourth Order ◽

Third Order ◽

Memory Processes ◽

The Third ◽

General Index ◽

General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

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