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All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Recent results on the mass, gravitational field and moments of inertia of the moon.

Use of Doppler tracking data from the Lunar Orbiter series of spacecraft in an analysis of the spherical harmonic coefficients of the lunar gravitational field through thirteenth degree and order. The value obtained for the mass of the moon, GM = 4902.84 cu km/sec/sec, is in good agreement with previous results and with results obtained by alternate procedures. Acceleration contour plots, derived from the gravitational coefficients, show correlations with surface features on the near side of the moon, but are of questionable validity for the far side because of the lack of direct tracking data on the far side. Based on the most recent gravitational field data, the current estimate for the polar moment of inertia of the moon is C/Ma squared = 0.4019 super + 0.004 sub - 0.002. This value indicates that the interior of the moon can be homogeneous, but some results presented strongly suggest that the moon is differentiated, with an excess of mass in the direction toward the earth.

Michael, W. H., Jr.↗
NASA NTRS1973

Parameter estimation supplement to the Mission Analysis Evaluation and Space Trajectory Operations program (MAESTRO)

This Parameter Estimation Supplement describes the PEST computer program and gives instructions for its use in determination of lunar gravitation field coefficients. PEST was developed for use in the RAE-B lunar orbiting mission as a means of lunar field recovery. The observations processed by PEST are short-arc osculating orbital elements. These observations are the end product of an orbit determination process obtained with another program. PEST's end product it a set of harmonic coefficients to be used in long-term prediction of the lunar orbit. PEST employs some novel techniques in its estimation process, notably a square batch estimator and linear variational equations in the orbital elements (both osculating and mean) for measurement sensitivities. The program's capabilities are described, and operating instructions and input/output examples are given. PEST utilizes MAESTRO routines for its trajectory propagation. PEST's program structure and subroutines which are not common to MAESTRO are described. Some of the theoretical background information for the estimation process, and a derivation of linear variational equations for the Method 7 elements are included.

Bjorkman, W. S.↗
NASA NTRS1994

Lifetimes of lunar satellite orbits

The Space Exploration Initiative has generated a renewed interest in lunar mission planning. The lunar missions currently under study, unlike the Apollo missions, involve long stay times. Several lunar gravity models have been formulated, but mission planners do not have enough confidence in the proposed models to conduct detailed studies of missions with long stay times. In this report, a particular lunar gravitational model, the Ferrari 5 x 5 model, was chosen to determine the lifetimes for 100-km and 300-km perilune altitude, near-circular parking orbits. The need to analyze orbital lifetimes for a large number of initial orbital parameters was the motivation for the formulation of a simplified gravitational model from the original model. Using this model, orbital lifetimes were found to be heavily dependent on the initial conditions of the nearly circular orbits, particularly the initial inclination and argument of perilune. This selected model yielded lifetime predictions of less than 40 days for some orbits, and other orbits had lifetimes exceeding a year. Although inconsistencies and limitations are inherent in all existing lunar gravity models, primarily because of a lack of information about the far side of the moon, the methods presented in this analysis are suitable for incorporating the moon's nonspherical gravitational effects on the preliminary design level for future lunar mission planning.

Meyer, Kurt W.↗
NASA NTRS1977

The Soviet-American Conference on Cosmochemistry of the Moon and Planets, Part 1

The basic goal of the conference was consideration of the origin of the planets of the solar system, based on the physical and chemical data obtained by study of the material of the moon and planets. Papers at the conference were presented in the following sessions: (1) Differentiation of the material of the moon and planets; (2) The thermal history of the moon; (3) Lunar gravitation and magnetism; (4) Chronology of the moon, planets, and meteorites; (5) The role of exogenic factors in the formation of the lunar surface; (6) Cosmochemical hypotheses about the origin and evolution of the moon and planets; and (7) New data about the planets Mercury, Venus, Mars, and Jupiter.

Pomeroy, J. H.↗
NASA NTRS1972

Constant tension device for gravity simulation

Mechanical device for simulating lunar gravitation is described. Details of construction are illustrated and example of application is provided. Device works opposite to effects of earth gravity and produces effects similar to lunar conditions by providing mechanical lifting forces.

Orlowski, W. F.↗
NASA NTRS1971

An Empirical Method for Determining the Lunar Gravity Field

A method has been devised to determine the spherical harmonic coefficients of the lunar gravity field. This method consists of a two-step data reduction and estimation process. In the first step, a weighted least-squares empirical orbit determination scheme is applied to Doppler tracking data from lunar orbits to estimate long-period Kepler elements and rates. Each of the Kepler elements is represented by an independent function of time. The long-period perturbing effects of the earth, sun, and solar radiation are explicitly modeled in this scheme. Kepler element variations estimated by this empirical processor are ascribed to the non-central lunar gravitation features. Doppler data are reduced in this manner for as many orbits as are available. In the second step, the Kepler element rates are used as input to a second least-squares processor that estimates lunar gravity coefficients using the long-period Lagrange perturbation equations.

Ferrari, A. J.↗
NASA NTRS1973

Lunar gravity derived from long-period satellite motion - A proposed method.

A new method has been devised to determine the spherical harmonic coefficients of the lunar gravity field. This method consists of a two-step data reduction and estimation process. In the first step, a weighted least-squares empirical orbit determination scheme is applied to Doppler tracking data from lunar orbits to estimate long-period Kepler elements and rates. Each of the Kepler elements is represented by an independent function of time. The long-period perturbing effects of the earth, sun, and solar radiation are explicitly modeled in this scheme. Kepler element variations estimated by this empirical processor are then ascribed to the non-central lunar gravitation features. Doppler data are reduced in this manner for as many orbits as are available. In the second step, the Kepler element rates are used as input to a second least-squares processor that estimates lunar gravity coefficients using the long-period Lagrange perturbation equations.

Ferrari, A. J.↗
NASA NTRS1972

S-band transponder experiment

The experiment which derives data from three lunar-orbiting objects, the command-service module (CSM), the lunar module (LM), and the subsatellite in the S-band is described. Each provides detailed information on the near-side lunar gravitational field. The primary emphasis is on the low-altitude (20 km) CSM data. The LM data cover a very short time span and are somewhat redundant with the CSM data. The resolution of the high-altitude (100 km) CSM data is not as great as that of the low altitude data. The low-altitude CSM and LM data coverage and the complementary coverage obtained during the Apollo 14 mission are presented. The experiment uses the same technique of gravity determination employed on the Lunar Orbiter, in the data of which the large anomalies called mascons were first observed. The data consist of variations in the spacecraft speed as measured by the Earth-based radio tracking system.

Sjogren, W. L.↗
NASA NTRS1975

A determination of the lunar moment of inertia

An estimate of the second zonal coefficient of the spherical-harmonic representation of the lunar gravitational field has been obtained from an analysis of particular orbital-element variations of the Explorer 35 and Explorer 49 spacecraft. Data from these spacecraft were used because the orbital configurations resulted in variations of the longitude of periapse and node which were, to first order, dependent only on the even zonal harmonics. The data time span for each satellite was extremely long: 2138 days for Explorer 35 and 230 days for Explorer 49. The value of the harmonic coefficient is determined and used to obtain a value of the lunar moment of inertia.

Gapcynski, J. P.↗
NASA NTRS1977

An improved value of the lunar moment of inertia

The lunar gravitational research reported on by Gapcynski et al., (1975) has been extended to include an additional 600 days of the time variation of ascending node for the Explorer 49 spacecraft. Analysis of these additional data resulted in an improved value of the second-degree zonal harmonic coefficient C(20) = (-2.0219 equal to 0.0091) times 10 to the minus 4. This value of C(20) used in conjunction with the parameters beta equal to libration (631.27 + or - 0.03) times 10 to the minus 6 and gamma to (227.7 + or - 0.7) times 10 to the minus 6 yields a more accurate definition of the lunar moment of inertia ratio equal to 0.391 + or - 0.002.

Blackshear, W. T.↗
NASA NTRS2006

Repeat Ground Track Lunar Orbits in the Full-Potential Plus Third-Body Problem

A high degree and order Lunar gravitational field is superimposed on the Earth-Moon Restricted Three Body model to capture the dominating forces on a spacecraft in the vicinity of the Moon. For the synchronously rotating Moon, periodic orbits in this model map repeat ground tracks and represent higher order solutions to the frozen orbit problem. The near-circular, stable or near-stable solutions are found over a wide range of defining characteristics making them suitable for long-lifetime parking applications such as science orbits, crew exploration vehicle parking orbits, and global coverage constellation orbits. A full ephemeris is considered for selected orbits to evaluate the validity of the time-invariant, simplified model. Of the most promising results are the low-altitude families of near-circular, inclined orbits that maintain long-term stability despite the highly non-spherical Lunar gravity. The method is systematic and enables rapid design and analysis of long-life orbits around any tidally-locked celestial body with an arbitrarily high degree and order spherical harmonic gravity field. .

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