- `theta = pi * t/(12hr)`
- `vec w = ( x_(w), y_(w) ) = R*( sin theta, -cos theta )`
- `vec s = ( x_(s), y_(s) ) = R*( theta, -1 )`
- `hat u = ( sin theta, -cos theta )`
- `hat e = ( cos theta, sin theta )`
- `vec Delta = vec s - vec w`
… `= ( x_(s) - x_(w), y_(s) - y_(w) )`
… `= ( R*theta - R*sin theta, -R + R*cos theta )`
- `vec delta = vec Delta / R = ( theta - sin theta, -1 + cos theta )`
- `vec A = vec delta * hat u`
… `= (theta - sin theta)*(sin theta) + (-1 + cos theta)*(-cos theta)`
… `= (theta * sin theta - sin^2 theta) + (cos theta - cos^2 theta)`
… `= theta * sin theta + cos theta - 1`
✓ checking: there should be no altitude at `theta = 0`: ✓
✓ `vec A(0) = 0 * sin 0 + cos 0 - 1 = 0*0 + 1 - 1 = 0` ✓
- `vec Q = vec delta * hat e`
… `= (theta - sin theta)*(cos theta) + (-1 + cos theta)*(sin theta)`
… `= (theta * cos theta - sin theta * cos theta) + (-sin theta + cos theta * sin theta)`
… `= theta * cos theta - sin theta`
✓ checking: there should be no eastward travel at `theta = 0`: ✓
✓ `vec Q(0) = 0 * cos 0 - sin 0 = 0*1 + 0 = 0` ✓