If Ho is less than Hc, what direction is the distance away from the GP?

When Ho (Observed altitude) is less than Hc (Calculated altitude), this indicates that your actual position is further away from the geographic position (GP) of the celestial body being observed. In celestial navigation, the angle of elevation helps determine the horizontal distance to the point directly below the celestial object—essentially, the GP.

If you observe that your altitude is lower than what is calculated, it suggests that you are standing further away from the GP than if they were equal. The concept behind this is rooted in the geometry of sighting: if you are closer to the celestial body, you would have a higher observed altitude. Since your observed reading is less, it clearly indicates that you must move in the direction that will decrease that distance, which is moving away from the GP.