NavList:

There is another way to do this, but not nearly as fast.

Take a shot.

Transfer the photo to a Windows computer then open with Paint.

Paint has an x,y coordinate indicator at the bottom.

Using that you can count pixels from horizon to body.

Knowing the pixel to angle ratio for your camera you can determine Ho.

To calibrate the camera shoot a number of bodies, or a single body repeatedly from a known position at known times so that you can determine the number of pixel per arc-min.  It may be that the result is not linear for the optics of your camera, but with a range of values you should be able to graph the results in Excel.  This would give you an "error card" similar to what a physical sextant would have.  I would assume the optical distortion was symetrical around the center of the focus field for the camera so always aim for the midpoint between horizon and body and the errors would be repeatable shot to shot and the error card more valid.  It may be that holding the camera in portrait or landscape orientation makes a difference.  

If your camera optically zooms you will want to zoom all the way out to maximize the pixel count and the precision of the result.

I expect there are phone camera apps that let you count pixels, but I don't know what they are.