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Abstract
Photography of the celestial bodies (the Earth) onto tangent and tilted planes and its transformation to panoramic photographs from an external exposure station, if done mathematically, is useful for interpreting the photos taken by a camera mounted on a space vehicle located anywhere in space and pointed towards any part of the Earth.
The Earth is considered as a sphere. General formulas for vertical and tilted photographs have been established with will be used to find the panoramic coordinates in terms of geodetic coordinates for different points on the Earth.
Inverse formulas of coordinates for any point on the photo, and equations of the grid lines for the vertical and tilted photography are given. Special cases of vertical and tilted panoramic photographs and reduced formulas in case of polar and transverse photos of the sphere are derived.
A numerical example is given to check on the accuracy of the coordinate equations.
Formulas are derived also to find the scale distortions.