Plot of asymmetric curve with vectors

I am trying to find a sloution for the following application.

I have a centre of gravity (CG) and want to revolve a tube (telescope) around it. CG is 480mm from the vertex that corresponds to a rotation angle of 90 DEG (vertical) and CG is 300mm from the vertex that corresponds to a rotation angle of 0 DEG (horizontal). I want to plot the curve that corresponds to the endpoints of the gravity vector for rotation angles increasing from 0 to 90 and radii increasing from 300mm to 480mm.

Then I want to find the closest fit Fibonacci spiral with the radius sequence 3, 5, 8 for that curve. How could this be accomplished?

I am just beginning to recover long lost math skills, so I would really appreciate any type of hint about where to start.

Perhaps the logarithmic spiral is a suitable curve.

$$a(\mathrm{e}^{bt}\cos t,\mathrm{e}^{bt}\sin t)$$

Solve[{({a*Exp[b*t] Cos[t], a*Exp[b*t] Sin[t]} /. t -> 0) == {300,
0}, ({a*Exp[b*t] Cos[t], a*Exp[b*t] Sin[t]} /.
t -> π/2) == {0, 480}}, {a, b}, Reals]
ParametricPlot[{a*Exp[b*t] Cos[t], a*Exp[b*t] Sin[t]} /. %, {t,
0, π/2}] • How can I plot the resultant curve of the vectors progressing from (300,0) through (0,480) centered at the CG? What I am after is to find the non-circular curve that is perpendicular for every angle of rotation. In practical terms, as I rotate the tube from 0 DEG to 90 DEG, the CG should move up vertically in a straight line. Sep 27 '20 at 19:22