Re: [math-fun] Curve-fitting methods ?
Henry Baker <hbaker1@pipeline.com> wrote:
Keith F. Lynch wrote:
One of my projects for satisfying extreme skeptics is a way to construct a crude picture of the Earth from years of data on the brightness of the Earth-lit part of the crescent moon as seen from one's backyard. Of course the skeptic would have to trust my software, so there's little point in my writing such software unless I am the skeptic. Still, it's an interesting project.
I'll bite. Have you constructed this crude picture of Earth, or are you suggesting that it could be done?
The latter, as I thought would be clear from, "there's little point in my writing such software...." In addition to the software, I'd need hardware with which I could measure the brightnesses of the earthlit part of the moon, the sunlit part of the moon, and an equal area of the sky near the moon. I'd subtract out the brightness of the sky near the moon so I'm only paying attention to light from the moon. I'd look at the ratio of brightnesses of the sunlit and earthlit parts (as adjusted for lunar phase and for how the lunar albedo varies due to lunar topography) to compensate for absorption as the light approaches me through Earth's atmosphere. Ideally this would be done in full color, so as to get a full color image of Earth.
I would be interested in such a picture, as it is an analogy to the "1 pixel camera" discussed here previously.
Years ago, I saw images of Pluto based entirely on its brightness measured from Earth. The north-south resolution was almost nil, presumably because all the observations were made at nearly the same Pluto latitude. Since Pluto has a high obliquity, this can be corrected by watching it for a whole orbit, 248 years. I doubt anyone will bother, since today we have high resolution images from New Horizons, a Pluto flyby probe. Indeed, I can't find those old low-res images online, since nearly any request for Pluto images returns images from that space probe. We can do better with the moon, since its terrestrial latitude varies from about -30 to +30 degrees. And we only have to wait 19 years for the moon to be in every possible state relative to the sun and our planet, not 248. That should give enough data that averaging would remove the clouds from the image and let you clearly see the continents, oceans, ice caps, and major islands. I'm a fairly radical skeptic. I believe trusted authorities are often lying to us, are mistaken, or are repeating others' lies or innocent mistakes. (As I myself recently did here with a mistaken claim about smooth functions. Sorry.) So I prefer to observe, measure, calculate, reason out, and prove as many things for myself as possible. If anyone's curious why I believe this, please ask me off-list. Thanks.
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Keith F. Lynch