There's also a very clear change in angle between those two photographs.
Yes, there is.
Their lens had a fixed focal length, and they were far from the mountain in the background (to say nothing of the earth in the sky above it). This means the picture distance between the earth and the top of the mountain could not be changed by moving the camera a few meters or pointing it in a different direction.
Sure enough, when you measure the distance between the earth and mountain top in the second picture and then measure the same distance above the mountain top in the first picture, you see that the earth was off the top edge of the frame.