A view of the Moon's shadow during the July 2, 2019 total solar eclipse showing the umbra (black oval), penumbra (concentric shaded ovals), and path of totality (red). Images of the Sun show its appearance in a number of locations, each oriented to the local horizon.
On Tuesday, July 2, 2019, the Moon will pass in front of the Sun, casting its shadow across South America and the southern Pacific Ocean.
The Moon's shadow can be divided into areas called the umbra and the penumbra. Within the penumbra, the Sun is only partially blocked, and observers experience a partial eclipse. The much smaller umbra lies at the very center of the shadow cone, and anyone there sees the Moon entirely cover the Sun in a total solar eclipse.
In the animation, the umbra is the small black oval. The red streak behind this oval is the path of totality. Anyone within this path will see a total eclipse when the umbra passes over them. The much larger shaded bullseye pattern represents the penumbra. Steps in the shading denote different percentages of Sun coverage (obscuration), at levels of 90%, 75%, 50% and 25%. The images of the Sun show its appearance at a number of locations during the eclipse, each oriented to the local horizon.
The numbers in the lower left corner give the latitude and longitude of the center of the umbra as it moves eastward, along with the altitude of the Sun above the horizon at that point. Also shown is the duration of totality: for anyone standing at the center point, this is how long the total solar eclipse will last.
You might think that calculating the circumstances of an eclipse would be, if not easy, then at least precise. If you do the math correctly, you’d expect to get exactly the same answers as everyone else. But the universe is more subtle than that. The Earth is neither smooth nor perfectly spherical, nor does it rotate at a perfectly constant, predictable speed. The Moon isn’t smooth, either, which means that the shadow it casts isn’t a simple circle. And our knowledge of the size of the Sun is uncertain by a factor of about 0.2%, enough to affect the duration of totality by several seconds.
Everyone who performs these calculations will make certain choices to simplify the math or to precisely define an imperfectly known number. The choices often depend on the goals and the computing resources of the calculator, and as you'd expect, the results will differ slightly. You can get quite good results with a relatively simple approach, but it sometimes takes an enormous effort to get only slightly better answers.
The following table lists some of the constants and data used for this animation.