Wolfram Computation Meets Knowledge

Solar Eclipses from Past to Future, Earth to Jupiter

Eclipse splash graphic

You may have heard that on March 20 there was a solar eclipse. Depending on where you are geographically, a solar eclipse may or may not be visible. If it is visible, local media make a small hype of the event, telling people how and when to observe the event, what the weather conditions will be, and other relevant details. If the eclipse is not visible in your area, there is a high chance it will draw very little attention. But people on Wolfram Community come from all around the world, and all—novices and experienced users and developers—take part in these conversations. And it is a pleasure to witness how knowledge of the subject and of Wolfram technologies and data from different parts of the world are shared.

Five discussions arose recently on Wolfram Community that are related to the latest solar eclipse. They are arranged below in the order they appeared on Wolfram Community. The posts roughly reflect on anticipation, observation, and data analysis of the recent eclipse, as well as computations for future and extraterrestrial eclipses.

I will take almost everything here from the Wolfram Community discussions, summarizing important and interesting points, and sometimes changing the code or visuals slightly. For complete details, I encourage you to read the original posts.

First, before the total solar eclipse happened on March 20, 2015, Wolfram’s own Jeff Bryant and Francisco Rodríguez explained how to see where geographically the eclipse is totally or partially visible. Using GeoEntities, Francisco was able to also highlight with green the countries from which at least the partial solar eclipse would be visible:

Using GeoEntities to see where  geographical visibility is of March 20, 2015 eclipse

Map showing visibility of eclipse using GeoGraphics function

Jeff Bryant is in the US and Francisco Rodríguez is in Peru, so as you can see above, neither was able to see even the partial solar eclipse. The intense red area shows the visibility of the total eclipse, and the lighter red is the partial eclipse. I consoled them by telling them that quite soon—in the next decade—almost all countries in the world, including the US and Peru, will be able to observe at least a partial phase of a total solar eclipse:

Future global visibility of total and partial solar eclipses

Visual representation of future partial and total solar eclipses

Another great way to visualize chronological events is with a new Wolfram Language function, TimelinePlot. I’ve considered the last few years and the next few years, and have plotted the countries and territories (according to the ISO 3166-1 standard) where a total solar eclipse will be visible, as well as when:

TimelinePlot showing future total solar eclipses

Visual of TimelinePlot future total solar eclipses

The image above shows the incredible powers of computational infographics. You see right away that a spectacular total solar eclipse will span the US from coast to coast on August 21, 2017 (see a related discussion below). You can also see that Argentina and Chile will get lucky, viewing a total eclipse twice in a row. Most subtly and curiously, the recent solar eclipse is unique in the sense that it covered two territories almost completely: the Faroe Islands and Svalbard. This means any inhabitant of these territories could have seen the total eclipse from any geo location, cloudiness permitting. Usually it’s quite the opposite: the observational area of a total eclipse is much smaller than the territory area it spans, and most of the inhabitants would have to travel to observe the total eclipse (fortunately, no visas needed). The behavior of the Solar System is very complex. The NASA data on solar eclipses goes just several thousand years into the past and future, losing precision drastically due to the chaos phenomenon.

At the time of the eclipse, I was in Odesa, Ukraine, which was in the partial eclipse zone. I made a separate post showing my position relative to the eclipse zone and grabbing a few photos of the eclipse. Using the orthographic GeoProjection, it’s easy to show that the total eclipse zone did not really cover any majorly populated places, passing mostly above ocean water. The black line shows the boundary of the partial eclipse visibility, which covered many populated territories:

Using GeoProjection to show my position relative to eclipse zone

Visual showing location related to eclipse zone

The Faroe Islands were in the zone of the total solar eclipse, and above I show the shortest path, or geodesic, between the islands and my location. In a separate post (see further discussion below), Marco Thiel posted a link to mesmerizing footage of the total solar eclipse, shot from an airplane (to avoid any cloudiness) by a BBC crew while flying above the Faroe Islands (see related discussion below). Francisco actually showed in a comment how to compute the distance from Odesa to the partial eclipse border:

Using GeoDistance to compute distance from Odesa to partial eclipse boarder

My photos, shot with a toy camera, were of course nothing like the BBC footage. Dense cloud coverage above Ukraine permitted only a few glimpses of the chipped-off Sun. Most images were very foggy, but ImageAdjust did a perfect job of removing the pall. A sample unedited photo is available for download in my Wolfram Community post:

Using ImageAdjust on solar eclipse photos

Solar eclipse images filtered with ImageAdjust

By the way, can you guess why you see the candy below? As I said in my post, the kids in my neighborhood in Ukraine observed the eclipse through the wrapper of this and other similar types of Ukrainian candy. The candy is cheap, and the wrap is opaque enough to keep eyes safe when the Sun brightens in the patches between the clouds. Do you remember using floppy disks? It was typical in the past to look at the Sun through floppy disk film. Many people may remember.

Candy wrappers used to see solar eclipses through

And this is where the conversation got picked up by our users. Sander Huisman, a physicist from the University of Twente in the Netherlands, asked a great question: “Wouldn’t it be cool if you could find your location just from the photos? We can calculate the coverage of the Sun for each of your photos, and inside the photo we can also find the time when it was taken. Using those two pieces of information, we should be able to identify the location of your photo, right?” I did not know how to go about such calculations, but Marco Thiel, an applied mathematician from the University of Aberdeen, UK, posted another discussion, Aftermath of the solar eclipse. Marco and Henrik Schachner, a physicist from the Radiation Therapy Center in Weilheim, Germany, tried to at least estimate the percentage of the Sun coverage using image processing and computational geometry functionality. This is the first part of the problem. If you have an idea of how to solve second part, finding a location from a photo timestamp and percentage of the Sun cover, please join the discussion and post on Wolfram Community. Marco and Henrik used photos from Aberdeen, which was very close to the total eclipse zone.

Estimating percentage of Sun coverage using image processing and computational geometry functionality

Even though he was so close, Marco did not have a chance to capture the partial eclipse due to high cloudiness. What irony and luck that the photos he used came from a US student from Cornell University, Tanvi Chheda, who spent a semester abroad at Marco’s university. She grabbed the shots with her iPad, but what wonderful images with the eclipse and birds. Thank you, Tanvi, for sharing them on Wolfram Community! Here is one:

Image of eclipse from Tanvi Chheda

Well, that’s the turbulent nature of Wolfram Community—something interesting is always happening, and happening quite fast. I’ll summarize the main subject of Marco’s post in a moment (see the original Community post for more images and eclipse coverage estimation), but as Marco wrote: “Even before today’s eclipse, there were reports warning that Europe might face large-scale blackouts because the power grids would be strained by a lack of solar power. This is why I decided to use Mathematica to analyze some data about the effects on the power grid in the UK. I also used data from the Netatmo Weather Station to analyze variations in the temperature in Europe due to the eclipse.”

Marco owns a Netatmo Weather Station, and had written about its usage in an earlier post. He used an API to get data from many stations throughout Europe, and also tapped into the public data from the power grid. One of his interesting findings was a strong correlation between the eclipse period and a sharp rise in the hydroelectric power production:

Correlation between eclipse period and hydroelectric power

For more observations, code, data, and analysis, I encourage you to read through the original post. There, Marco also touched on the subject of global warming and the relevance of high-resolution crowd-sourced data. To visualize the diversity of the discussion, I imported the whole text and used the new Wolfram Language function WordCloud:

Using WordCloud to show the diversity of a Community discussion

WordCloud showing diversity of topics in Community post

It’s nice that the Wolfram Language code, as well as the text, is getting parsed, and you can see the most frequently used functions. In the code above, there are three handy tricks. First is that the option WordOrientation has diverse settings for words’ directions. Second is that the option ScalingFunctions can give the layout a good visual appeal, and the simple power law I’ve chosen is often more flexible than the logarithmic one. The third trick is subtler. It is the choice of background color to be the “bottom” color of the ColorFunction used. Then not only do the sizes of the words stress their weights, but they also fade into the background.

From the TimelinePlot infographics above, you can see that a total eclipse will span the US from northwest to southeast on August 21, 2017. I made yet another Wolfram Community post showcasing some computations with this eclipse. You should take a look at the original for all the details, but here is an image of all US counties that will be spanned during the total eclipse. Each county is colored according to the history of cloud cover above it from 2000 to 2015. This serves as an estimate for the probability of clear visibility of the eclipse. The colder the colors, the higher the chance of clear skies. That’s very approximate, though, especially taking into account the unreliability of weather stations. GeoEntities is a very nice function that selects only those geographical objects that intersect with the polygon of the total eclipse. Below is quite a cool graphic that I think only the Wolfram Language can build in a few lines of code:

Computing 2017 eclipse path and historical cloud coverage for areas

Map of historical cloud coverage and 2017 solar eclipse path

And now that we’ve looked into the past and the future of the total solar eclipses, is there anything left to ponder? As it turns out, yes—the extraterrestrial solar eclipses! We live in unique times and on a unique planet with the angular diameter of its only Moon and its only Sun pretty much identical. I mentioned above a documentary where a BBC crew shot a video of the total solar eclipse from an airplane above the Faroe Islands. Quoting the show host, Liz Bonnin, right from the airplane: “There is no other planet in the Solar System that experiences the eclipse like this one… even though the Sun is 400 times bigger than the Moon, at this moment in our Solar System’s history, the Moon happens to be 400 times closer to the Earth than the Sun, and so they appear the same size…”

So can we verify that our planet is unique? In a recent Wolfram Community post, Jeff Bryant addressed this question. He made some computations using PlanetData and PlanetaryMoonData to investigate the solar eclipses on other planets. The main goal is to compare the angular diameter of the Sun to the angular diameter of the Moon in question, when observed from the surface of the planet in question. He used the semimajor axis of the Moon’s orbit as an estimate of the Moon’s distance from its host planet. Please see the complete code in the original post. Here I mention the final results. For Earth, we have an almost perfect ratio of 1, meaning that the Moon exactly covers the Sun in a total eclipse:

Angular diameter of the Sun compared to the angular diameter of the Moon on Earth

Now here is Mars’ data. The largest Moon, Phobos, is only .6 the diameter of the Sun viewed from the surface of Mars, so it can’t completely cover the Sun:

Angular diameter on Sun compared to the Moons on Mars

With human missions to Mars becoming more realistic, would you not be curious how a solar eclipse looks over there? Here are some spectacular shots captured by NASA’s Mars rover Curiosity of Phobos, passing right in front of the Sun:

NASA's Mars rover Curiosity of Phobos

NASA/JPL-Caltech/Malin Space Science Systems/Texas A&M Univ.

These are the sharpest images of a solar eclipse ever taken from Mars. As you can see, Phobos covers the Sun only partially (60%, according to our calculations), as seen from the surface of Mars. Such a solar eclipse is called a ring, or annular, type. Jupiter’s data seems more promising:

Angular diameter of the Sun compared to the Moons of Jupiter

Jupiter’s Moon Amalthea is the closest with a ratio of 0.9, yet even if its orbit allows a perfect 90% of Sun cover, the spectacular Earth-eclipse coronas are probably not visible. During a total Earth solar eclipse, the solar corona can be seen by the naked eye:

Amalthea total solar eclipse
Image Courtesy of Luc Viatour

Do you have a few ideas of your own to share or a few questions to ask? Join Wolfram Community—we would love to see your contributions!

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  1. Very well done Vitaliy. Thanks for collecting all posts and adding so nicely to them. I really like the idea of using the wrap of that candy to observe the eclipse. We improvised a small “camera obscura”. Thanks for posting.

  2. Yes, Sander, I was really enjoying yours and other members’ responses. I just had to write about it, thank you all !