Modifying the atlas of low lunar orbits using inert tethers

For long enough tethers, the coupling of the attitude and orbital dynamics may show non-negligible effects in the orbital motion of a tethered satellite about a central body. In the case of fast rotating tethers the attitude remains constant, on average, up to second order effects. Besides, for a tether rotating in a plane parallel to the equatorial plane of the central body, the attitude?orbit coupling effect is formally equal to the perturbation of the Keplerian motion produced by the oblateness of the central body and, therefore, may have a stabilizing effect in the orbital dynamics. In the case of a tethered satellite in a low lunar orbit, it is demonstrated that feasible tether lengths can help in modifying the actual map of lunar frozen orbits

Outreach Testing of Ancient Astronomy

This work is an outreach approach to an ubiquitous recent problem in secondary-school education: how to face back the decreasing interest in natural sciences shown by students under ‘pressure’ of convenient resources in digital devices/applications. The approach rests on two features. First, empowering of teen-age students to understand regular natural events around, as very few educated people they meet could do. Secondly, an understanding that rests on personal capability to test and verify experimental results from the oldest science, astronomy, with simple instruments as used from antiquity down to the Renaissance (a capability restricted to just solar and lunar motions). Because lengths in astronomy and daily life are so disparate, astronomy basically involved observing and registering values of angles (along with times), measurements being of two types, of angles on the ground and of angles in space, from the ground. First, the gnomon, a simple vertical stick introduced in Babylonia and Egypt, and then in Greece, is used to understand solar motion. The gnomon shadow turns around during any given day, varying in length and thus angle between solar ray and vertical as it turns, going through a minimum (noon time, at a meridian direction) while sweeping some angular range from sunrise to sunset. Further, the shadow minimum length varies through the year, with times when shortest and sun closest to vertical, at summer solstice, and times when longest, at winter solstice six months later. The extreme directions at sunset and sunrise correspond to the solstices, swept angular range greatest at summer, over 180 degrees, and the opposite at winter, with less daytime hours; in between, spring and fall equinoxes occur, marked by collinear shadow directions at sunrise and sunset. The gnomon allows students to determine, in addition to latitude (about 40.4° North at Madrid, say), the inclination of earth equator to plane of its orbit around the sun (ecliptic), this fundamental quantity being given by half the difference between solar distances to vertical at winter and summer solstices, with value about 23.5°. Day and year periods greatly differing by about 2 ½ orders of magnitude, 1 day against 365 days, helps students to correctly visualize and interpret the experimental measurements. Since the gnomon serves to observe at night the moon shadow too, students can also determine the inclination of the lunar orbital plane, as about 5 degrees away from the ecliptic, thus explaining why eclipses are infrequent. Independently, earth taking longer between spring and fall equinoxes than from fall to spring (the solar anomaly), as again verified by the students, was explained in ancient Greek science, which posited orbits universally as circles or their combination, by introducing the eccentric circle, with earth placed some distance away from the orbital centre when considering the relative motion of the sun, which would be closer to the earth in winter. In a sense, this can be seen as hint and approximation of the elliptic orbit proposed by Kepler many centuries later.

Institutes of natural philosophy, theoretical and practical. With some corrections; change in the order of the branches; and the addition of an appendix to the astronomical part, selected from Mr. Ewing's Practical astronomy.

"Appendix to the astronomy. Containing solar and lunar tables, with their explanation and use, and the projection of eclipses, selected from 'Ewing's Practical astronomy'": [233]-297.

Where no man has gone before [microform] : a history of Apollo lunar exploration missions /

Mode of access: Internet.

Conceptual design of a lunar colony.

"NASA grant NGT 44-005-114."

Catalog of lunar positions : based on the lunar Positional Reference System (1974) /

Photocopy.

An experimental investigation of lunar and auroral scattered signals; final report,

"AFCRL-65-78."

El lunar de la marquesa. Comedia en cuatro actos y en verso. [Microform]

Microopaque.

Principales tables de Mr de Mendoza pour la très-prompte réduction des distances... = Mr de Mendoza's principal tables for deducing very readily the longitude from lunar distances..

Edición bilingue inglés-francés.

Anatomia de todo lo visible e invisible : compendio universal de ambos mundos : viaje fantastico... : noticia de los movimientos, y naturaleza de los cuerpos terrestres, y celestiales, y ciencia de los influxos de los eclipses de sol, y luna, hasta el fin del mundo... /

Mode of access: Internet.

La hermosura sin lunar, qual es la del alma y cuerpo de Maria Santisima significada en su vida : escrita en estancias de cancion real y segun la reveló la Señora a su sierva la M. Maria de Jesus de Agreda /

Mode of access: Internet.

Lunar flight handbook.

"Prepared for the George C. Marshall Space Flight Center, Huntsville, Alabama under contract NAS 8-5031."

An introductory treatise on the lunar theory,

"Index of authors quoted": p. 274.