As I understand to compute vector of gravity not saficient to compute normal to elipsoid, but we need to computer normal to geoid (by definition geoid is a surface to which the force of gravity is everywhere perpendicular).
So I have some questions:
How to compute normal to geoid?
What is the maximum discrepancy of angle between elipsoid normal and geoid normal?
About practical application of gravity normal:
I have some tall object that stand on Earth (like Leaning Tower of Pisa) and I can obtain GPS coordinates of it top and bottom points by using photos taken from air and applying photogrammetry methods. Then from GPS coordinates of top and bottom of object I can get vector in ECEF coordinates and find angle betwen this vector and gravity vector.
Also my question:
If difference in angle between ellipsoid normal and geoid normal("deflection of the vertical") is about 100 seconds of arc (0,0277778 degree) is it safe to use ellipsoid normal for this practical application?
I'm trying to understand if normal to ellipsoid is sufficient for practical application. In real life object is mounted by using spirit level and on this picture we can see that theoretically I need normal to geoid, but if deflection of vertical small enough I can use normal to ellipsoid as approximation.
I'm trying to estimate the error of angle measure, I have some error in calculating of GPS positions of my object top and bottom points say epsilon_1, also I have some error in calculating gravity vector because of I'm using normal to elispoid say epsilon_2 and I'm trying to understand how epsilon_1 and epsilon_2 affects resulting angle between object vector and gravity vector. So I need to derive the formula that will give me measurement error of angle using measurement error of GPS points and gravity vector(epsilon_1 and epsilon_2).