Modeling of the Eros gravity field as an ellipsoidal harmonic expansion from the NEAR Doppler tracking data

Abstract

[1] The gravity field for asteroid 433 Eros has been determined in terms of ellipsoidal harmonic functions by processing the Doppler tracking data of the NEAR spacecraft while it was in orbit about the asteroid. Using the same set of NEAR spacecraft Doppler tracking data, comparative descriptions of the Eros gravity field are provided for both the ellipsoidal and the traditional spherical harmonic models. It is shown that for elongated bodies, like the asteroid Eros, the ellipsoidal harmonics model permits a better representation of the gravity signature than does the spherical harmonics model. Eros has a nearly uniform density but there are negative gravity anomalies near the ends of Eros and positive gravity anomalies near the Psyche crater and the Himeros depression.

A Global Solution for the Gravity Field, Rotation, Landmarks, and Ephemeris of Eros

“…Since Eros is much closer to the shape of a triaxial ellipsoid, fewer coefficients are needed to represent the gravity field of Eros and less noise or "aliasing" is observed in the coefficients. Whereas both the spherical harmonics and ellipsoidal harmonics give nearly the same results through roughly degree 6 or 7, the ellipsoidal solution remains much smoother to higher degrees (Garmier et al 2002). However, the ellipsoidal coefficients are limited in numerical stability to about degree 12 (which is sufficient for the NEAR data of Eros).…”

“…However, the ellipsoidal coefficients are limited in numerical stability to about degree 12 (which is sufficient for the NEAR data of Eros). As mentioned above, both expansions result in the same scientific conclusions on the internal structure of Eros (Miller et al 2002, Garmier et al 2002. We solve for the ellipsoidal representation to degree and order 12 (167 parameters including the GM).…”

“…This solution has been archived in the Planetary Data System (PDS) as JPL gravity solution NEAR15A (or file JGE15A01.SHA). The ellipsoidal gravity solution for Eros is also based on the same complete data set and has been previously presented by Garmier et al (2002). It provides similar scientific conclusions on the homogeneity of Eros as to the spherical harmonics.…”

The Jacobi constant for a cometary orbiter

“…Since they in general do not vanish with increasing degree, the gravitational expansion (1) converges, roughly speaking, outside r ∼ r c (Garmier & Barriot 2001). The upper row in Table 1 corresponds, in this case, to so-called short-axis rotational mode (SAM) of the nucleus, while the lower represents the case of rotation around the nucleus' long axis (LAM).…”

Using Chebyshev polynomial interpolation to improve the computational efficiency of gravity models near an irregularly-shaped asteroid

“…Among them, spherical harmonics method is based on series expansion (Kaula 1966;Lundberg and Schutz 1988;Hu et al 2015), which may not converge inside the so-called Brillouin sphere (Brillouin 1933). Though ellipsoidal harmonics expansion has larger convergence region (Romain and Jean-Pierre 2001;Garmier et al 2002), the computation of ellipsoidal harmonics are not so straightforward and it does not fundamentally resolve the convergence problem. Recently, Takahashi and Scheeres (2014) proposed to use interior spherical harmonic expansion to extend the convergence region within the interior Brillouin sphere.…”