How a ship navigates
Navigating a vessel in the three-dimensional void of space can be difficult. Plotting a course to an object requires accurate measurements of complex angles
between the object and the vessel. To make this easier, Starfleet uses a two-part plotting system, based on degrees of a circle. The first part of this plotting
system is called the "Bearing," which denotes the horizontal angle between the starship and the selected target object, from 000 degrees to 359 degrees,
clockwise. The second part of the system is called the "Mark," which denotes the vertical angle between the starship and the selected object, again in degrees
of a circle, from 000 to 359 degrees.
Bearing 000 is directly abow (ahead) of the vessel, Bearing 090 is directly to the vessel's starboard (right) side, Bearing 180 is
directly astern (behind) of the vessel, Bearing 270 is directly to the vessel's port (left) side.
The Mark is measured by the "positive pitch" or "nose up" angle between the starship and the object. If the object is at a "negative pitch" or "nose down" angle in relation to the starship, then the Mark angle would be closer
to 359 degrees, keeping in mind that mark 000 is directly abow (ahead) of the vessel, Mark 090 is directly above the vessel, Mark 180 is directly astern (behind) of
the vessel and Mark 270 is directly below the vessel.
Note that if an object is dead abow, dead astern, to port or to starboard of the vessel, the duplicate Mark coordinate
is not needed. Often, you will hear of an object Bearing 000, "dead ahead", or Bearing 180, "dead aft" or "dead astern," noting that the Mark coordinate is not
quoted in that case.
Bearing 045 is called "starboard bow," while Bearing 315 is called "port bow." Likewise, Bearing 135 is called "starboard stern" or
"starboard aft", while Bearing 225 is called "port stern" or "port aft."
Combining the Bearing and Mark angles provides a three-dimensional course plotting
solution between the starship and the object it is attempting to navigate toward. This plotting system is also used when the starship is attempting to target its
weapons on the object.
Example:
Image from MJ's Star Trek site