The eclipse limits of the umbral shadow path of a total solar eclipse are traditionally depicted as smooth lines on a map. Inspection of our eclipse maps (https://www.besselianelements.com/eclipse-maps/) reveals that we have represented those limits in a far more complex way as jagged lines, as shown in Figure 1.
Figure 1 Umbral shadow northern limit of the 2026/08/12 total solar eclipse near Elorrio (Spain). North is towards the top of the image and East towards the left side of the image.
Why limits and centreline are not smooth
The eclipse limit in Figure 1 is the combination of two lines encasing a narrow area. The eclipse is total south of the southernmost line and partial north of the northernmost line. In the area between the two lines the nature of the eclipse is uncertain.
To understand why the limit has been depicted in such a way, we need to explore how eclipse limits are computed. In the traditional eclipse computational method based on Besselian Elements, the Moon is considered as a smooth sphere, Earth is modelled as a smooth oblate ellipsoid, and the solar radius has a well determined value. Under these assumptions, the umbral shadow limits end up being smooth lines on a map.
The Moon’s surface is constellated by craters and mountains, and hence its limb, as seen from Earth, is not perfectly smooth. The Earth surface also has a complex orography, with mountains, valleys, depressions. The solar radius is not a perfectly known quantity, but our knowledge of it is affected by uncertainty.
To go beyond the simplifying assumptions of Bessel’s method, we need to account for these three additional factors. This is what has been done for the northern limit depicted in Figure 1: the complexity of the lunar limb has been included, the effect of terrain has been accounted for and the fact that the eclipse solar radius is known with a 0.05″ uncertainty has been considered.
We have done research to estimate the eclipse solar radius in the last ten (and plus) years. We have estimated the eclipse solar radius to be equal to 959.95″±\pm0.05″. The southernmost line in Figure 1 has been computed by using an eclipse solar radius equal to 959.90″, while the northernmost line an eclipse solar radius equal to 960.00″. The area in between these two lines is an acknowledgment that this uncertainty exists and that there cannot really be a clear-cut demarcation between the area where the eclipse is seen as total and the area where the eclipse is seen as partial. It is better to think about a narrow transition zone than a hard boundary.
The position of the lines is heavily affected by the lunar limb and the value of the eclipse solar radius. The jaggedness of the lines is heavily influenced by the terrain topography. Figure 2 depicts the centreline of the 2026/08/12 total solar eclipse when the eclipse leaves Spain and enters the Mediterranean Sea. On land, the centreline is not a smooth line as it warps around the terrain, but, over the sea, it becomes smooth as the surface becomes everywhere flat.
Figure 2 Centreline of the 2026/08/12 total solar eclipse when the eclipse leaves Spain and enters the Mediterranean Sea.
Umbra jumps
We notice that the transition between the jagged centreline and the smooth centreline seems to materialise itself as a slanted segment between the jagged centreline and the smooth centreline. This turns out to be an artifact. If we look at Figure 3a, we see that there is a spine of hills just at the back of the beach in the Parc Natural de la Serra d’Irta. The eclipse will become total here at around 20h30 local time with the Sun just 4 degrees above the horizon. At that time, the spine of hills will cast a shadow that will extend past the beach and into the sea, as Figure 3b shows. The centreline will come from the west, climb the western side of that spine of hills and then “jump” from the top ridge of the hills directly into the sea few kilometers away.
The centreline was computed at thousands of points that were then joined together. So, that slanted segment appears as a consequence of this joining procedure, even if the centreline technically does not exist there. To explore this phenomenon further, in our TSE20260812 eclipse, you can activate the layer showing the orographic shadows at totality time. Every time the centreline apparently seems to cross an area in the shade, it is in reality “jumping” from one location to another. The centreline will often be jagged in the areas in the light, but it will become a straight segment in areas in the shade.
Figure 3a Google Earth image of the Parc Natural de la Serra d’Irta, showing a spine of hills at the back of the beach. Figure 3b Map showing the location of the centreline (in blue) in the same area and the shadows (in light grey) cast by the hills at totality time.
Comparison with smooth lines maps
After examining how the eclipse centreline and limit lines are computed and displayed on our eclipse maps, we can compare them to the ones provided by other sources. We have chosen the Goggle Earth predictions by Xavier Jubier (http://xjubier.free.fr/en/site_pages/SolarEclipsesGoogleEarth.html) as they are a popular resource among eclipse chasers. Xavier’s predictions are smooth limb predictions, are plotted on the reference ellipsoid and use a more traditional solar radius equal to 959.63″.
Figure 4 shows the comparison between our prediction and Xavier’s prediction. We are obviously expecting discrepancies, as our prediction makes less approximations. The centreline is unaffected by the lunar limb or the choice of solar radius. We are then expecting the discrepancies to be caused by the terrain. If we look at the centreline in Gulf of Biscay and in the Mediterranean Sea, we can see that the lines are very close. Over Spain, we see our prediction departing from the smooth limb predictions: most of the country traversed by the centreline is mountainous and on high plateaux, so accounting for the terrain will create a jagged line and a shift south. Similar consideration can be made for the northern and southern limits, even if the comparison is not as straightforward. Xavier’s smooth limits also depend on the choice of mean lunar radius. Because our predictions account for the lunar limb, they are not influenced by this choice (i.e. the mean lunar radius is irrelevant).
Figure 4 Comparison of the centreline and limit lines between two sources: solid lines are the ones displayed on our TSE20260812 eclipse map and dashed lines are the ones provided by Xavier Jubier as a KML file.
We noticed that the online predictions Xavier offers on its main webpage (http://xjubier.free.fr/en/site_pages/SolarEclipsesGoogleMaps.html), so we have done comparisons putting side by side our predictions and Xavier’s predictions. In Figure 5, we can see that, at sea, the centreline of both predictions is basically identical. We are expecting this, as the centreline only depends on the position of the Moon’s and Sun’s centres (and the Earth’s orientation) and these quantities are usually very close in different eclipse data sources. Moreover, the difference between sea level and the reference ellipsoid (i.e. the geoid height), is less than 100m, hence, at sea, we should not see major discrepancies. Of course, when the centreline comes ashore, the effect of terrain starts playing a noticeable role.
Figure 5 Comparison of the centreline depicted on our TSE20260812 eclipse map and on the one provided by Xavier Jubier in his online Google Map eclipses predictions, for the location when the centreline comes ashore in Spain near the Gulf of Biscay.
Figure 6 shows a far more interesting comparison: it is again the northern limit near Elorrio (Spain). This time the discrepancies are noticeable. It is useful to use National Road 636 as an anchor point. The more detailed and accurate limit depicted on our maps is at times over 1km away from Xavier’s smooth limit.
Figure 6 Comparison of the northern limit depicted on our TSE20260812 eclipse map and on the one provided by Xavier Jubier in his online Google Map eclipses predictions, for locations near Elorrio (Spain).
Eclipse Countdown App
To provide accurate guidance for community straddling the northern and southern limit of a total solar eclipse, it is paramount to account for all those aspects (lunar limb, improved eclipse solar radius, orography) to give the most accurate depiction of the eclipse limits. Even if it is true that most eclipse chasers stay well clear from the eclipse limits, some daring one do get as close as possible to the limits. Moreover, not everyone travels towards the centreline on eclipse day, and some local people will be located on the limit lines (e.g. the northern suburbs of Madrid, like Fuencarral and Barajas).
Our eclipse app (https://www.besselianelements.com/eclipse-app/) is fully compatible with the more complex eclipse limits depicted on our eclipse maps. If you wish to have accurate eclipse prediction and an eclipse scheduler on eclipse day, get the app 🙂
