Sequential Grazing Occultations during Solar Transits |
| During Earth-based transits of Mercury and Venus across the face of the Sun it is usually the case that the Earth and Moon can also be occulted by the transiting planet as seen from the surface of the Sun – albeit a largely theoretical possibility for any intrepid observer but an interesting computational problem to consider, nonetheless. |
| A question then arises about whether any of these events might involve grazing occultations of both the Earth and Moon? In particular external grazing occultations in which the limbs of the Earth and Moon are momentarily touched by the limb of the occulting planet. A zero magnitude and zero duration occultation, one might say. The aim is to find out if any such sequential events exist in reality. |
| The images shown below contain plots of the occultation paths on the surface of the Sun for some past and future transits of Mercury and Venus (follow the image links to see full-sized versions). Each path consists of an outer pair of "penumbral" limit lines; an inner pair of "umbral" limit lines; and a single central line running down the middle of the path. The penumbral lines indicate where you need to stand to see an external grazing occultation, while on the umbral lines you would see an internal grazing occultation resulting in complete, but momentary, disappearance of the occulted body. Standing on the central line gives you a perfectly aligned view of the occultation. |
| A sequential external grazing occultation is possible only if there is an intersection of the penumbral limit line on one path with the penumbral limit line on the other path – the intersection point is then the place to be on the Sun to see the event. Of course other special events are possible if there are intersections of any other path lines and these will also be considered below. But in general any spatial overlap of the paths would at least indictate that sequential partial occultations of the Earth and Moon are a possibility. |
| Occultation data are given for transits of Mercury in 2003, 2006, 2016, 2019, 2032, 2039, and for transits of Venus in 1874, 1882, 2004, 2012, 2117, 2125. Also included at the end are data for transits of Earth as seen from Mars in 1984 and 2084. Of these transits, consisting of a total of 140 individual path lines, only four special occultation events were found. Unfortunately none of these events consisted of an exact sequential external grazing occultation of the Earth and Moon. Each of the four special events are described below together with links to videos showing the view of each event from the surface of the Sun. The videos were recorded from my PlanetView application – an interactive 3D planetary geometry viewer. |
| Please note that the video files cannot be streamed from this server, so you must download each file completely before attempting to play it ("Save linked content as..." or your browser equivalent). All videos are H.264-encoded MP4 files, 900x600@30fps, format profile: High 4:4:4 Predictive@L4.2. Not all video players can decode this high-profile pixel format. Recommended MP4 players are MPC-BE and VLC. |
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| No path line intersections | Earth's central line intersects Moon's southern umbral line at λ = 8.828498°, φ = –26.877114° Animation of occultation events |
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| No path line intersections | Earth's northern penumbral line intersects Moon's southern umbral line at λ = 48.366124°, φ = +8.689206° Animation of occultation events |
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| No path line intersections | No path line intersections |
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| No path line intersections | No path line intersections |
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| Earth's southern penumbral line intersects Moon's northern umbral line at λ = 215.956037°, φ = –44.835377° Animation of occultation events |
No path line intersections |
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| Earth's central line intersects Moon's northern penumbral line at λ = 230.936664°, φ = +47.256128° Animation of occultation events |
No path line intersections |
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| No path line intersections Moon's inner path is antumbral, not umbral |
No path line intersections Moon's inner path is antumbral, not umbral |
| The JPL ephemeris DE430 was used to obtain solar and planetary positions. Body orientations were obtained from the IAU(2009) models, except for the Earth & Moon which use IAU2006B and DE430/ME orientations, respectively. The following body radii were employed: Sun - 696000 km, Mercury - 2439.7 km, Venus - 6051.8 km, Earth - 6367.445 km (mean), Moon - 1738.091 km, and Mars - 3386.195 km (mean). |
| First published 25 May 2016 |
All media files copyright (C) 2016 John Irwin