How can I extract the coordinates from an existing LROC image to search for that area in the LRO Image Search Tool?
What coordinates should I enter in this example?
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The LROC data specification has information on how the images are labeled.
The LROC derived products are compatible with the recommendations of the LRO Data Working Group  and draft recommendations and mapping conventions identified by the LGCWG (the Lunar Geodesy and Cartography Working Group) . The coordinate system used is the mean Earth/polar axis system, and using planetocentric latitude and east positive longitude direction. The planetocentric latitude is the angle from the equator to a point on the surface of an oblate planet. The longitude increases from west to east (left to right on an Equirectangular projection).
The MAXIMUM_LATITUDE element specifies the northernmost latitude of the map.
So longitude increases going East, negative longitudes are West. Positive latitudes are North, negative latitudes are South.
LRO images are pretty big, so the long/lat figures you enter in the Search box depend on what feature of an image you want. If it's the whole image, use the Center long/lat figures.
If you're looking for a specific region within the image, try to estimate the long/lat of that feature by measuring the image.