So they take high altitude pics of the earth and knit them together to create that image..
What, we don't have anything out there that can fit the entire planet in one shot?
The earth rotates which would refute your sun/earth dilemma. Take a video or time lapse to get it all in.
Not a mathfag. Just how far away would you have to be, with the correct lens, to fit the planet in the frame. Certainly not as far as the moon since we have those great tiny earth shots from Apollo and the moon surface itself.