Tag: spherical cap

The topographic Earth

By Phil Plait | October 18, 2011 1:30 pm

This is pretty nifty: a new elevation map of the Earth has just been released by NASA and Japan. It’s a "significantly improved" version of one that came out in 2009.

It uses Japan’s ASTER, the Advanced Spaceborne Thermal Emission and Reflection Radiometer, an instrument on board NASA’s Terra satellite. Terra is an Earth-observer, with detectors on board used to study various properties of our planet. ASTER looks both straight down and slightly behind the satellite’s track on the Earth is it passes. Over time stereo image pairs are created, and these can be used to create very high-resolution elevation maps (called topographic maps) of the surface of the Earth.

The new images are higher-res than before, and cover the Earth better to the tune of 260,000 more images. As an example of what can be done, they used it to make this map of the Grand Canyon:

[Click to enmesanate.]

One thing that struck me as funny when I read it: the coverage of ASTER’s observations goes from the Equator to as far north and south as 83° latitude… and they say that this is 99% of the Earth! That sounds odd, doesn’t it? You’d think the north and south poles of the Earth from 90° to 83° would be more than that, but in fact it’s true.

The portion of a sphere above a certain latitude line is called a cap, and the area of that cap depends on the latitude in question, and the radius of the sphere. I drew myself a diagram, fiddled with the numbers a bit, and found that the area of the Earth north of 83° compared to the surface area of the northern hemisphere is about 0.75%! So in fact, ASTER covered a bit more than 99% of the Earth’s surface, even if it never got past that 83°latitude.

Math! Surprising people since the time of Pythagoras.

Anyway, if you want to download the ASTER data yourself, you can: it’s public. Japan has a copy, and so does the USGS. I imagine it won’t be long before it’s integrated into Google Earth and all that too. Living in the future is pretty cool.

Image credit: NASA/GSFC/METI/ERSDAC/JAROS, and U.S./Japan ASTER Science Team


Related posts:

Staring down an active volcano’s throat
The Earth’s lumpy gravity
Satellite view of a volcanic pressure valve
Volcano study in red

CATEGORIZED UNDER: Cool stuff, NASA, Pretty pictures
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