A determination of the parameters of the level surface of lunar gravity

The parameters of the best-fitting ellipsoid have been derived using the latest spherical harmonics of the Phobos topography (Duxbury, 1989) by solution of non-linear overdetermined inverse problem. The lengths of the equatorial axes of the ellipsoid have been determined (a = 12.9 km, b = 11.4 km). They are nearly the same as established by Duxbury (ibid.) on the basis of the linearized relationship between the squared lengths of ellipsoidal axes and the topography coefficients C,, and C,,. The length of the polar axis (c = 9.1 km) differs of about 20% from Duxbury's value. Supposing mass homogeneity of Phobos, the Stokes parameters of the external gravitational field have been derived up to those of the sixth degree and order. The large irregularities in the Phobos figure cause the values of the Duxbury's potential coefficients be fairly inaccurate except the harmonics CzO, C2, S,, and Ssl, i.e. linearized relationship between gravity and topography cannot be applied for Phobos. Finally, positions of the centre of figure and the directions of the principal axes of inertia have been established.

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The Phobos gravitational field modeled on the basis of its topography

Martinec

Pêĉ

Burša

1989

Earth Moon Planet

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Effect of topographic bias on geoid and reference ellipsoid of Venus, Mars, and the Moon

Ardalan

Karimi

2013

Celest Mech Dyn Astr

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Parameters of the best fitting lunar ellipsoid based on GRAIL’s selenoid model

Cziráki

Timár

2023

Acta Geod Geophys

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Since the Moon is less flattened than the Earth, most lunar GIS applications use a spherical datum. However, with the renaissance of lunar missions, it seems worthwhile to define an ellipsoid of revolution that better fits the selenoid. The main long-term benefit of this might be to make the lunar adaptation of methods already implemented in terrestrial GNSS and gravimetry easier and somewhat more accurate. In our work, we used the GRGM 1200A Lunar Geoid (Goossens et al. in A global degree and order 1200 model of the lunar gravity field using GRAIL mission data. In: Lunar and planetary science conference, Houston, TX, Abstract #1484, 2016; Lemoine et al. in Geophys Res Lett 41:3382–3389. http://dx.doi.org/10.1002/2014GL060027, 2014), a 660th degree and order potential surface, developed in the frame of the GRAIL project. Samples were taken from the potential surface along a mesh that represents equal area pieces of the surface, using a Fibonacci sphere. We tried Fibonacci spheres with several numbers of points and also separately examined the effect of rotating the network for a given number of points on the estimated parameters. We estimated the best-fitting rotation ellipsoid’s semi-major axis and flatness data by minimizing the selenoid undulation values at the network points, which were obtained for a = 1,737,576.6 m and f = 0.000305. This parameter pair is already obtained for a 10,000 point grid, while the case of reducing the points of the mesh to 3000 does not cause a deviation in the axis data of more than 10 cm. As expected, the absolute value of the selenoid undulations have decreased compared to the values taken with respect to the spherical basal surface, but significant extreme values still remained as well.

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A determination of the parameters of the level surface of lunar gravity

Cited by 3 publications

References 12 publications

The Phobos gravitational field modeled on the basis of its topography

The Phobos gravitational field modeled on the basis of its topography

Effect of topographic bias on geoid and reference ellipsoid of Venus, Mars, and the Moon

Parameters of the best fitting lunar ellipsoid based on GRAIL’s selenoid model

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