At my workplace there is a large aerial photo that is over 10 years old on the wall showing our company site and a partner company's site. A colleague of mine who is also an amateur pilot would like to take an updated photo to show a then-and-now depiction. To do this he wants to take the photo from the same location (coordinates and altitude), but the source of the original photo has gone in the mists of time so we are left with making the determination by mathematical means.
Conveniently, in the photo there is a landmark in the distance that is vertically aligned with the two sites so we can work in two dimensions. The scenario is pictured below.
P Plane (as in aeroplane/airplane) G Ground-point directly below plane A Our site B Partner's site C Landmark a/b/c Equivalent locations to A/B/C on the photo viewed from the perspective of P P | | | | | | | | G---------------------A---------------B----------------------------------C-----
The following values are known. (We are working in metric so I've provided some conversion factors if you require them.)
AB = 800 metres BC = 8750 metres ab = 290 millimetres bc = 415 millimetres 1 metre = 1000 millimetres 1 metre = 3.28084 feet 1 inch = 25.4 millimetres
The following assumptions are made.
The Earth is flat! There is no refraction. The viewpoint is with the naked eye.
Question: What is the location of "P", i.e. the values for GA and GP?
Although there is obviously a relationship between the mathematical plane of the photograph and that of the ground, I've been unable to figure out how to represent it.
Previous questions I found on here of a similar theme (below) were unanswered so I've tried to provide more information, especially by way of the pictorial representation.
And for the adventurous...
I'm willing to believe it's possible that the location of P has multiple solutions, i.e. it's defined by a curve. In this case the question would be, What is the function for the curve?
And probably related (but possibly a separate issue), it's likely the photo was taken using a telephoto lens from higher and further away. Again in this case the question would be, What is the function for the curve?