This interactive chart shows how the solar eclipse will occur on Aug. 21. (Aug. 22. 02:30 GMT)
UPDATED: GOES satellite images (provided courtesy of UW-Madison SSEC) are, day by day, projected onto the surface of the Earth. Will the shadow of the moon be clear as we are expecting?
The previous chart was based on the famous Kelper's law of planetary motion. In hindsight, the law, published in 1619, is a simple application to two planetary objects of Newton's laws of motion and universal gravitation. In reality, the universal gravitation works among all planets. The moon is affected by not only the earth but also the sun and even the jupiter. That's the reason the previous version failed to present the expected eclipse.
In this version, the positions of the moon and the earth are based on the NASA's HORIZON database. The NASA, as well as the other space agencies, no longer uses the Kepler's law but uses extensive computer simulations based on the Newton's laws and Einstein's theory of relativity. (It's time dilation, which kept Anne Hathaway ever young in the movie, Interstellar)
Having put the moon and the earth in the 3D space, Their shadows are drawn as a common tangent of the two balls. It's the simplest geometry.
3D graphics are sometimes very powerful. By just changing the viewpoint onto the surface of the earth, we can use it as a location simulator. The NASA published the prediction of the total solar eclipse area.
On Aug. 21 we will test how good at calculations NASA is and whether the school geometry is applicable in the outside of the earth.
The usual chart about the solar eclipse explains how it occurs very well. It gives us good visual definitions of two kinds of shadows, umbra and penumbra. The umbra is the region where the light is completely blocked by the astromonial body (the moon in this case). An observer in the umbra can see a total eclipse. The penumbra is the region in which only a part of the light is obscured and a partial eclipse is observed.
However, it might give us a wrong impression on the frequency of the solar eclipse.
Firstly, if the earth is fixed (does not rotate), the moon goes around the earth once a day, just as we observe it with a pre-Copernican mind. But if both the earth and the sun are fixed, as in the 2D chart above, it takes about 30 days for the moon to make a circle around the earth. That's why we call it month. The arrangement of sun-moon-earth occurs only once a month, not once a day.
Secondly, the sizes and distances of the three objects are deceptively distorted in the chart. If proportionally drawn, the coin-size sun on the front page of a broad sheet newspaper would need the period-size moon on page 4. The shadow made by the distant sun is minuscule.
Finally, the space is 3 dimentional. In most cases, the razar-thin shadow of the moon travels well above the north pole or below the south pole of the dot-size earth.
The interactive chart on top of this document are drawn proportionally to the actual size. The yellow sharp cone shows its umbra. The white grid indicates earth's equator plane. You can zoom in to the earth or zoom out to see the whole solar system. Remember, your slow drag/touch makes the viewpoint move faster than light.
I'm sorry for my poor English, if you call it English.
GOES images are projected onto the surface. Original images are provided by the courtesy of University of Wisconsin-Madison Space Science and Engineering Center.
Textures: the earth: Natural Earth, the moon: solarsystemscope