A time diagram is a diagram on the plane of the celestial equator that shows the celestial equator as a circle with celestial meridians and hour circles as radial lines. It is used to solve time problems and other problems involving arcs of the celestial equator or angles at the pole by showing the relationships between quantities like hour angles, longitude, and units of time. On the diagram, the Greenwich meridian is at the top with east longitudes to the right and west longitudes to the left as viewed from the south pole.

2. A time diagram is a diagram on the plane of
the celestial equator or equinoctial in which
the celestial equator appears as a circle, and
celestial meridians and hour circles as radial
lines. It is used to facilitate solution of time
problems and other problems involving arcs
of the celestial equator or angles at the pole,
by indicating relations between various
quantities involved. Conventionally, the
relationships are given as viewed from a point
over the south pole ( Ps ) westward direction
being counterclockwise.

3. TIME DIAGRAM
A DIAGRAM ON A PLANE OF CELESTIAL
EQUATOR AS SEEN FROM THE SOUTH
POLE.

4. Time diagram

5. HOW ARE HOUR ANGLES( HA ) AND UNITS OF TIME
MEASURED?
Longitude – ( measured from going G going E or W, 000⁰- 180⁰
As view from the south pole, if the Greenwich G is on top, to the
right are east longitudes and to the left, are west longitudes. By
conventions, the diagram is oriented so that M is at the top.
Therefore G will move either left or right of M depending on the
given longitude. Ex.
G
West East
g
M
G G
E W
g g
m

7. GHA – measured from G counterclockwise to the
body.
G
g

9. • M –UPPER BRANCH OF LOCAL MERIDIAN.
• m –LOWER “ “ “ “
• G –UPPER “ “ GREENWICH “
• g –LOWER “ “ “ “
• G – M –LONGITUDE OF OBSERVER (E/W)

10. • MERIDIAN ANGLE (t) – ANGULAR
DISTANCE MEASURED FROM FIXED
MERIDIAN UP TO THE BODY, EASTWARD
OR WESTWARD FROM 0° - 180°, NAMED
E/W DEPENDING IF IT IS RISING OR
SETTING.
• IF LHA < 180° / LHA = t NAMED “W”
• IF LHA > 180°/360° - LHA = t NAMED “E”

11. • GHA) – ANGULAR DISTANCE MEASURED
FROM GREENWICH MERIDIAN “G” UP TO
THE BODY FROM 0° - 360° COUNTER
CLOCKWISE. (WESTWARD)
• LHA – ANGULAR DISTANCE MEASURED
FROM LOCAL MERIDIAN “M” UP TO THE
BODY FROM 0° - 360° COUNTER
CLOCKWISE. (WESTWARD)

12. • SHA – ANGULAR DISTANCE MEASURED FROM
THE 1ST. POINT OF ARIES UP TO THE
BODY,FROM 0° - 360° COUNTER CLOCKWISE.
(WESTWARD)
• RA – ANGULAR DISTANCE MEASURED FROM
THE 1ST. POINTOF ARIES UP TO THE BODY,FROM
0° - 360° CLOCKWISE.
(EASTWARD)
SHA + RA = 360°
360° - SHA = RA
360° - RA = SHA

13. Example computation

14. Video show