In navigation, the heading was used to describe directions in space. Headings were programmed in at the ship's helm control using a combination of two 360-degree directions on planes that are at right angles to one another, separated by the word "mark". (TNG: "Datalore")
The given heading can be used to determine the course or direction that a starship was actually moving. (TNG: "Unification II") The course itself could be used to measure distance traveled. (TNG: "In Theory") Starships traveling at warp speeds usually traveled in a straight line to the destination coordinates. (VOY: "Drive") While sometimes, a course could also be a more elaborate flight path, that included changes in heading and parabolic trajectories. (VOY: "Alice"; Star Trek II: The Wrath of Khan) If a course was not set before engaging the warp drive, it was possible that one "could warp [them]selves into oblivion by crashing into a planet." (DS9: "Melora")
A more precise measuring angle system, beyond the 360-degree system, was sometimes used with headings such as 883-mark-41 or 902-mark-5. (TOS: "The Paradise Syndrome", "Day of the Dove", "Requiem for Methuselah"; TAS: "The Practical Joker"; TNG: "Lonely Among Us", "Symbiosis"; VOY: "Workforce")
In June of 2151, Captain Jonathan Archer ordered a course correction as he picked a Vulcan monastery at P'Jem as a destination following his studies of the Vulcan star charts. Later, while being held hostage by the Andorian Imperial Guard at the sanctuary he lied to Thy'lek Shran when telling him that this planet was along their course and the landing party just came to visit the monastery. (ENT: "The Andorian Incident")
Examples of headings
- Heading from the Bajoran system to the Klingon Empire was 327-mark-215. (DS9: "Sons of Mogh")
- Heading from Deep Space 9 to the Cardassian Empire was 269-mark-032. (DS9: "The Way of the Warrior")
- Heading from the Federation-Tzenkethi border to the Tzenkethi planet M'kemas III was 015-mark-47. (DS9: "The Adversary")
- Heading from Outpost 4 to the Romulan Neutral Zone was 111-mark-14. (TOS: "Balance of Terror")
- Heading from the Romulan Neutral Zone to Vulcan was 143-mark-012. (TNG: "Unification II")
- Heading from Starbase 234 to the Klingon-Romulan border was 118-mark-357. (TNG: "Redemption II")
- Heading from Starbase 375 to the Cardassian border was 054-mark-093. (DS9: "A Time to Stand")
- Heading from Starbase 55 to coordinates 002/3845 was 223-mark-85. (TNG: "Conspiracy")
- Heading from Tarsas III to Bynaus was 233-mark-45. (TNG: "11001001")
- Heading from the Vulcan system to the Laurentian system was 151-mark-3. (Star Trek)
- Heading from Ivor Prime to Earth was 0-mark-215. (Star Trek: First Contact)
- In 2371, USS Voyager was holding a course 351-mark-10 on its voyage back to Earth from the Delta Quadrant. (VOY: "Time and Again")
- In the more precise measuring angle system, heading from the Klingon-Federation border away from the Milky Way Galaxy was 902-mark-5. (TOS: "Day of the Dove")
The first use of headings in degrees occurred in Star Trek: The Original Series episode "Balance of Terror". The meaning of headings as two 360-degree angles was established in "Datalore". The system of degrees was further explained in reference books, such as Star Trek: The Next Generation Technical Manual (pp. 36, 37).
The first 360-degree figure is a direction in an imaginary plane similar to the galactic plane, but between the ship and the center of the galaxy. What ever the location of the ship in the galaxy is, heading 000-mark-0 is always a direct course to the center of the galaxy. Heading 180-mark-0 is a direct heading away from it. A heading from Earth directly to the Beta Quadrant would be 090-mark-0 and further into the Alpha Quadrant 270-mark-0.
As explained in "Datalore", the second 360-degree figure is the elevation angle at a right angle to the previous plane. A heading of 360-mark-90 would be a heading directly upwards away from the plane, where as 360-mark-270 a heading directly downwards.