Lunar limb profile
- The Moon's silhouette departs from a circle by up to about 3 arcseconds, about 6 km at the Moon, which moves second and third contact by 2 to 3 seconds anywhere in the path and by tens of seconds near the edges 1 2.
- Watts' 1963 charts gave way to laser altimetry. Watts' datum is elliptical, offset from the centre of mass and libration-dependent, so it needs the Morrison and Appleby corrections of up to 0.4 arcseconds. Kaguya (SELENE) and LOLA heights are referenced to a 1737.4 km sphere centred on the centre of mass, so that correction disappears 3 4.
- A limb profile belongs to one observer at one instant. It is built by rotating the DEM point cloud into the observer's line of sight with the topocentric libration and keeping, in each position-angle bin, the point of largest angular radius 5 6.
- Corrected contact times are good to about 0.2 seconds with LOLA or Kaguya profiles, against 0.5 seconds with corrected Watts data and 2 to 3 seconds with none 7 8.
- Baily's beads are the same computation read at every position angle, and timing them at the path edge is how IOTA has measured the apparent solar radius since 1979 2 9.
What this topic covers
This topic covers the one input that separates a textbook eclipse prediction from one that matches a stopwatch: the shape of the Moon's silhouette. It traces the data from Watts' photographic charts through the laser-altimeter models of Kaguya (SELENE) and LRO, gives the geometry that turns a digital elevation model into a height-against-position-angle table for one observer at one instant, quotes the numbers each source reports for the effect on contact times and path edges, and describes how Baily's beads are predicted and how their timings are inverted for the solar radius.
Notes in this topic
- Limb profile methods: history, the DEM-to-limb geometry with formulas, the effect on contact times and path limits, the software, and a worked pipeline.
- Datasets: Watts, Kaguya, LOLA: every dataset with its resolution, reference sphere, frame, accuracy, file format and download location.
- Baily's beads: how bead events are defined and predicted, and how IOTA uses them to measure the solar radius.
What this topic changes for the pipeline
The pipeline gains a limb stage between local circumstances and the reported contacts, and a second limb stage inside the path-limit search. Both need the lunar orientation model and the observer vector in the Moon's body-fixed frame, which the Besselian stage does not otherwise compute, so the ephemeris layer must expose that frame. The path product changes shape as well: the umbra outline becomes a polygon that must be emitted as a polygon, and each limit line becomes a pair of lines, interior and exterior.
References
- 1primary Espenak, F. The Lunar Limb Profile and Eclipse Predictions. NASA Eclipse Web Site Read. Summary of Watts, the 0.4 arcsec systematic errors, the 2 to 3 second uncorrected error, the 0.5 second Watts-corrected agreement and the 0.2 second Kaguya/LRO level.
- 2peer-reviewed Herald, D. (1983). Correcting predictions of solar eclipse contact times for the effects of lunar limb irregularities. Journal of the British Astronomical Association 93, 241-246 Read in full from the ADS scan (page images). The displacement-curve method: h = 960 (M-1)(1-cos P), r = 0.97 M n arcsec per second, radial rate r cos(PA-N), the path-limit factor 1.863 km per arcsec times sqrt(sin^2 D / sin^2 a + cos^2 D), the limiting magnitudes for total and annular eclipses, and the error budget.
- 3peer-reviewed Morrison, L. V. and Appleby, G. M. (1981). Analysis of lunar occultations III. Systematic corrections to Watts' limb-profiles for the Moon. MNRAS 196, 1013-1020 Read in full from the ADS scan (OCR text). Source of the harmonic correction formula, the 1737.97 km datum radius, the +0.04 arcsec radius term, the -0.18 arcsec latitude shift, the -0.09 arcsec ellipticity, the +0.50 arcsec sin Q centre-of-figure term, and the 0.4 arcsec peak error.
- 4primary PDS Geosciences Node. LRO LOLA GDR label ldem_128.lbl (LRO-L-LOLA-4-GDR-V1.0, V3.0) Read. 128 pix/deg, 236.901 m/pix, A_AXIS_RADIUS 1737.4 km, OFFSET 1737400, SCALING_FACTOR 0.5, 16-bit, MEAN EARTH/POLAR AXIS OF DE421, data 2009-07-13 to 2016-11-29.
- 5peer-reviewed Wright, E. and Young, C. A. (2024). A Raster-oriented Method for Creating Eclipse Maps. The Astronomical Journal 168, 163 Read through the IOP HTML in several targeted passes (the PDF download returned a script page). Source of the DEM-to-limb-profile algorithm, the L = 18000 bin recommendation, the 0.01 deg libration refresh threshold, the totality test rho, the 49-sided umbra, the 696000 km solar radius, DE440 and the Moon ME frame, and the Herald 1983 history.
- 6primary NASA SVS 4517: Umbra Shapes (Wright, E., released 2016-12-13) Read from a Wayback Machine snapshot dated 2025-12-10 because the live host refused connections. Describes the point-cloud limb method, SLDEM2015, SRTM, DE421, the polygonal umbra, the up to 3 km elevation shift and the 18x exaggerated limb animation.
- 7company Espenak, F. Lunar Limb Profile and Eclipse Predictions. EclipseWise Read. Same text as the NASA page with the added statement that Kaguya and LRO data bring the accuracy to about 0.2 seconds.
- 8company Herald, D. (2016-11-20). Update to Occult and Observations Read (curl). States that a position-angle error of up to 0.2 deg in the traditional method corrupted the limb correction, and that with the LOLA lunar limb (Occult download #26) most occultation predictions are within 0.3 s of observation.
- 9peer-reviewed Fiala, A. D., Dunham, D. W. and Sofia, S. (1994). Variation of the solar diameter from solar eclipse observations, 1715-1991. Solar Physics 152, 97-104 Read pages 97-102 from the ADS scan. Describes the IOTA edge-observation method (Sofia, Dunham and Fiala 1979), its dependence on Watts data, and Table II of solar-radius corrections per eclipse relative to 959.63 arcsec.