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I've been reading about satellite observations (such as this one). The writer uses terms such as these to define the orbit:

1 41584U 16036A   16167.96105997 0.00000000  00000-0  00000+0 0    07 
2 41584   7.5055 353.7008 0046333  41.2140 319.1375  1.00195548    05 

rms 0.004 deg      from 9 obs June 14.70 - June 16.79  (2.09 day arc) 

What does each variable refer to, and what's the easiest way to view these on a map (either online or in an app of some kind?)

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These are known as two-line elements (see also nasa.gov, satobs.org). On both lines, the first field after the line number is a NORAD ID, which you can use to query a database such as N2YO. The second line gives geocentric orbital elements for the epoch given in the first line. The last line looks like an error estimate by observation analysis software.

The first convenient visualization service I found was Orbital Predictor, where I naively pasted the above TLE data with a name less appropriate than "Mentor 7" or "2016-036A."

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