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Re: Oblateness calculation given observer's latitude
From: Peter Monta
Date: 2018 Feb 5, 09:03 -0800
From: Peter Monta
Date: 2018 Feb 5, 09:03 -0800
Frank writes:
> And you'll always get values in the lowest lying members of the sequence (like J2) in a lumpy body like the Moon, even if it's not by itself much use in describing the Moon's shape.
There's some discussion in this Clementine paper:
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19980018849.pdf
Figure 10 seems to show that the ellipsoid is real but weak. The polar and equatorial radii differ by 2 km, and the detailed topography accounts for the remaining 2 km rms (figure 8). The ellipticity seems reasonably robust to model order. Figure 11 shows the center-of-figure offsets.
It seems doubtful that the ellipsoid is of much use as a simple intermediate step prior to accounting for the detailed topography. Taking out only half the error, the ellipsoid is not exactly covering itself in glory.
> [ long-wavelength gravity terms, pear shape, J3 ]
> That early space age description is a mathematical artifact with little physical meaning.
Long-wavelength terms do have a disproportionate impact on orbits, though. High-order tidal terms peter out very rapidly, but the low-order ones more slowly, so they dominate for high orbits. Ultimately it's only the dipole that matters (and then, if you're really far out, the monopole). So a satellite sees a pear-shaped Earth in a physically meaningful way, but humans have to squint. (Well, J3 is on the same order as the low-order tesseral terms, so it's the overall "low-order lumpiness", not a distinct pear.)
I'm still waiting for the super-sextant that I can wave in the general direction of the Moon, from a moving platform, and get arcsecond offsets to the stars. Then there will be a cry for better lunar models in the reduction software.
Cheers,
Peter
> And you'll always get values in the lowest lying members of the sequence (like J2) in a lumpy body like the Moon, even if it's not by itself much use in describing the Moon's shape.
There's some discussion in this Clementine paper:
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19980018849.pdf
Figure 10 seems to show that the ellipsoid is real but weak. The polar and equatorial radii differ by 2 km, and the detailed topography accounts for the remaining 2 km rms (figure 8). The ellipticity seems reasonably robust to model order. Figure 11 shows the center-of-figure offsets.
It seems doubtful that the ellipsoid is of much use as a simple intermediate step prior to accounting for the detailed topography. Taking out only half the error, the ellipsoid is not exactly covering itself in glory.
> [ long-wavelength gravity terms, pear shape, J3 ]
> That early space age description is a mathematical artifact with little physical meaning.
Long-wavelength terms do have a disproportionate impact on orbits, though. High-order tidal terms peter out very rapidly, but the low-order ones more slowly, so they dominate for high orbits. Ultimately it's only the dipole that matters (and then, if you're really far out, the monopole). So a satellite sees a pear-shaped Earth in a physically meaningful way, but humans have to squint. (Well, J3 is on the same order as the low-order tesseral terms, so it's the overall "low-order lumpiness", not a distinct pear.)
I'm still waiting for the super-sextant that I can wave in the general direction of the Moon, from a moving platform, and get arcsecond offsets to the stars. Then there will be a cry for better lunar models in the reduction software.
Cheers,
Peter
