Does NASA have picture of our own solar system from outside our solar system?
And would this photo that does not exist yet dispel the urban legend of a second earth that's always is behind the sun, hidden from our Earth? The special case of 1:1 orbital resonance of two earths sharing the same orbit shold have been disproven by now. NASA has a whole bunch of spacecrafts that should end this urban myth - so why does this urban myth still persist?
Without being the authority, I believe that such photos were taken by probes sent to photograph gas giants in the outer solar system. I think from any distance it would be difficult to discern in any such photograph the inner planets of Mercury, Venus, Earth and Mars against the backdrop of a sun that would appear as a bright star. Interesting question, hopefully within my lifetime we will get to see more.
There is Voyager which has nearly left the outskirts of our solar system it i is nearing the Ort cloud I think however at that distance any photos taken certainly with our technology would not be able to see the Earth, there is a camera which orbits the Sun photographing it constantly, both sides and there is no planet on the far side of the Sun.
If I could answer those questions kind of backwards. First of all, urban myths and legends will always exist because people just want to believe. Second, your right about there not being another earth on the other side of the sun. That myth was dispelled when we got powerful enough telescopes to see that far. The path that the earth follows around the sun is not a perfect circle it's an ellipse, at some point we would be able to see it. And about that picture of our solar system, you displayed such a picture yourself, there are many such pictures all done by artists but none of them are real because we don't have the technology for that. And lets face it, any picture that would be a true representation with every celestial body in our solar system distinguishable from every other celestial body in our solar system and built to scale, would have to be as big as a city. Maybe bigger.
The current record is held by Voyager 1 I believe, it took a very famous photo of the Earth from about 6 billion kilometers away, after it had passed the orbit of Pluto. It is called the "pale blue dot"
http://en.wikipedia.org/wiki/Pale_blue_dot
It photographed the other planets too and these were stitched together to create the following image:
http://en.wikipedia.org/wiki/File:Family_portrait_(Voyager_1).png
Odd theories about 1:1 orbital resonance Earth's aside, that photo is extremely profound. Carl Sagan said it best:
"all of human history has happened on that tiny pixel, which is our only home"
The Wikipedia page has the rest of the passage (from his book), it is something everyone should read I think.
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