Lunar Coordinates Research Articles

Television observations from Surveyor 3

Television observations from Surveyor 3

A comparison of the American and Soviet coordinate system for the lunar far side

A comparison between the representative charts of the Far Side of the Moon was made with respect to their systems of selenographic coordinates. A systematic relative shift reaching 7° in longitude was found, in addition to local errors attaining 1°–2°. The uncertainty in the positions should be kept in view in discussions about the lunar nomenclature on the Lunar Far Side.

Transformations of the lunar coordinates and orbital parameters

view Abstract Citations (37) References (2) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Transformations of the lunar coordinates and orbital parameters Eckert, W. J. ; Walker, M. J. ; Eckert, D. Abstract Because of its high quality and long acceptance as the standard of comparison, Brown's lunar theory will, for years to come, play a key role in the discussion of the observed lunar motion and in the critical examina- tion of new, more precise theoretical developments. In the modification of Brown's basic solution to facilitate the comparison with observation the full precision of the solution was not preserved since this was not then considered necessary. Some of this loss of precision was regained by the Improved Lunar Ephemeris in 1952. The purpose of this paper is to make the full accuracy of Brown's solution available for the comparison with observation and to increase the precision of the relations between the computed coordinates and the param- ters on which they are based. The precision of the solar terms in sin parallax is improved by more than an order of magnitude. Publication: The Astronomical Journal Pub Date: June 1966 DOI: 10.1086/109923 Bibcode: 1966AJ.....71..314E full text sources ADS |

A computer program for the transformation of lunar observations from celestial to selenographic coordinates

A program has been devised which is suitable for mapping observations onto the nighttime surface of the Moon. It can be extracted from the present paper without being understood in detail, and familiarity with computer programming is not required. The basic data used in the program are the universal times, right ascensions, and declinations of points of interest on the Moon which are recorded from the telescope's coordinate circles and a Greenwich clock. Focal plane precision screw coordinates may be substituted if desired. In addition, for part of these points, selenographic coordinates are input. This subset, necessarily contained on the sunlit portion of the Moon, is used as a set of standards from which to derive a function describing the translation of the center of the Moon on the celestial sphere relative to the vernal equinox. The balance of input data are limiting conditions which may be read directly without interpolation from the ephemeris. Results are presented from test data which show an average geodesic residual of 0.5 degrees fairly independently of which of several versions of the computer program are used. The error is thus random gear train error in the telescope, which can be expected to decrease in future applications inasmuch as the test data were gathered when the telescope installation was new and not yet tightly adjusted.

LUNAR RADIO BEACON LOCATION BY DOPPLER MEASUREMENTS

A feasibility analysis points up the fact that, although the overall Doppler shift of a signal originating from a beacon on the moon is quite significant, the portion of the shift which is sensitive to the selenographic latitude and longitude of the beacon is much smaller. In fact, the basic transmitter frequency would have to be held constant (including noise) to one part in 10 for even marginal performance of the beacon location system. The feasibility analysis also shows, qualitatively, that there exist optimum times of the month for most accurately determining the selenographic coordinates of a beacon. The detailed formalism for a differential correction procedure is given in which the first-estimate values of the beacon coordinates are obtained, e.g., from the trajectory ephemeris of the vehicle setting the beacon upon the moon.

The measurement of lunar altitudes by photography—I. Estimating the true lengths of shadows

Abstract This paper provides a discussion of all known sources of error in the apparent length of a lunar shadow recorded photographically and measured with a microdensitometer. The discussion is general but is illustrated by reference to sunrise shadows of various lengths cast by the lunar Straight Wall. Measurements of shadow lengths made between half-density points of a microdensitometric scan along a shadow may contain systematic errors due to the non-linearity of the characteristic of the photographic emulsion. The most important sources of systematic-error are seeing (especially in the case of short shadows), penumbrae, and uncertain selenographic coordinates. Other errors, due to seeing, effects at a shadow-tip, and procedures of measurement, are also important but probably apply in a more nearly random manner.

Schematic Chart of the Far Side of the Moon

The photographs of the far side of the Moon, obtained on 7 October 1959 by the automatic interplanetary station, were studied at the Pulkovo Observatory independently from other observatories. The purpose of this work was to detect authentic objects on the far side of the Moon, to determine their selenographic coordinates, and to draw—on this basis—a schematic chart with an approximate distribution of the brightness of detected features. In contrast with the work conducted at the Sternberg Astronomical Institute [1], the Pulkovo Observatory did not apply the method consisting of an artificial increase of the contrast of features within a specific range of densities (the so-called method of photometric cross-sections). Therefore, we detected only the topographically most distinctive features, which can be examined directly on photographs and compared with others.

Radar observations of the moon at 10-cm wavelength

This note describes some of the initial results derived from observations of radar echoes from the moon obtained at 10-cm wavelength at the Royal Radar Establishment, Malvern. The radar, which has been described elsewhere [1], has a transmitter of 2 megawatts peak power with a pulse length of 5 microseconds and a pulse recurrence frequency of 260 per second. The receiver is of conventional design and has a bandwidth of 500 kc/s and a noise factor of 7.5. The aerial used is the 45-foot diameter radio telescope shown in Fig. 1. The telescope is controlled from a mechanical computer that converts the lunar coordinates into azimuth and elevation, which are then fed into a servo drive.

Calculation of the shadow path of a chosen lunar feature during an occultation.

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Calculation of the shadow path of a chosen lunar feature during an occultation. Moser, Nora B. Abstract had two serious limitations: the inaccuracy of visual observation and the influence of limb irregularities. As a development of A. E. Whitford's photoelectric measurements of stellar diameters, mobile equipment has been designed to observe an occultation photoelectrically and record it alongside radio time signals to thousandths of a second. To cancel out the effect of limb irregularities, a prominent lunar feature which will dominate the limb for several hours is selected and two or more observation posts are so placed that at each the star will disappear behind the chosen feature. A suitable occultation having been chosen, Hayn's selenographic coordinates of the edge of the moon as presented to the earth at a given time are computed by Watts' method.i The results are plotted on Hayn's contour charts of the limb region, and a prominent mountain within about 20 of the edge line is picked. The selenographic coordinates of the top of this mountain, together with more or less arbitrary times, will be the starting data for computing the shadow path along which the mountain will occult the star. To obtain maximum precision, the moon s positions, tabulated with an extra decimal place, are requested from the British Nautical Almanac Office, and the earth's selenographic coordinates (librations) are computed from basic formulas rather than interpolated from published tables. The path of the shadow axis on Bessel's fundamental plane is calculated by standard formulas. Some significant figures are lost in subtraction in this process but the relative error between points on the shadow path will be negligible. The geocentric earth's selenographic coordinates and position angle of the moon s axis are referred to the shadow axis by Watts' method for selenographic coordinates, avoiding his approximations. The selenographic coordinates of the shadow axis and of the chosen mountain are transformed to one set of rectangular coordinates fixed in the moon and then projected onto the fundamental plane, resulting in the shadow path of the mountain. Bessel's device of a parametric declination is employed in transferring the path to the earth's surface. The observation positions are tied into the U. S. first-order triangulation and may be assumed correct. The error in the moon's place will be sensibly constant during one occultation. The limb error is under control. An observation equation may be set up to solve for the correction to the lunar parallax. Acknowledgments. Walter D. Lambert of the U. S. Coast and Geodetic Survey and C. B. Watts of the U. S. Naval Observatory have furnished valuable assistance in this project. Dr. John A. O'Keefe and Mrs. Rose L. Rowen of the Army Map Service had a large part in the work described. I.A. J. 48, 170, 1940. U.S. A rmy Map Service, Washington, D. C. Publication: The Astronomical Journal Pub Date: April 1950 DOI: 10.1086/106348 Bibcode: 1950AJ.....55...75M full text sources ADS |

On the Formation of the Derivatives of the Lunar Coordinates with Respect to the Elements

On the Formation of the Derivatives of the Lunar Coordinates with Respect to the Elements

On the formation of the derivatives of the lunar coördinates with respect to the elements

In the determination of the action of the planets on the moon, it is usual to use the method of the variation of arbitrary constants. This mnethod requires the knowledge of the derivatives of the lunar coordinates with respect to the angular elements E, 7r, 0 the epochs of mean longitude, perigee and node-and also with respect to the other three elements n, e, ry -the mean motion, eccentricity and sine of the orbital inclination. If we have a theory in which the co6rdinates, so far as the actions of the sun and moon only are concerned, are expressed literally in terms of these six elements, it is a simple matter to find the derivatives. But this is practically not the case. The convergence of many of the coefficients when expressed in powers of m = n/n'the ratio of the miean motions is so slow that a literal theory with the required accuracy seems almost impossible on account of the labor required for its development; the slowness of convergence does not occur as far as powers of e, ry are concerned. The theory of Hansen is entirely numerical and therefore only the derivatives with respect to the angular elements can be obtained from it. The theory t which I hope shortly to bring to a conclusion is semi-numerical, i. e., the numerical value of mn is inserted, the other constants being left in a literal form. t In considering how this theory was to be adapted so as to be of use when considering planetary action, the only difficulty was, therefore, the formation of the derivatives with respect to n. It is this difficulty which has been solved in the following pages. The semi-numerical theory once completed, it is shown that the derivatives with respect to n can be made to depend on quadratures with respect to the time. The formulhe are put into a form ready for computation and it is shown how a simple transformation will permit us to use the advantages of canonical sets of constants without being hampered by their disadvantages for purposes of calculation.