Dr. Fred’s Five Rules for the Apparent Motion of the Stars
Purpose of this document: This document lays out five “rules” that pertain to the
apparent motion of the stars as seen from any latitude in the northern hemisphere on the
Earth. These rules describe and quantify the apparent motion of the stars. You should
practice applying them to various locations on the Earth. The first exam and the final
comprehensive exam will provide you an opportunity to demonstrate your understanding
and facility applying these rules.
1) An observer looking north will see the stars appear to circle counter clockwise around
Polaris (the NCP really) once every 23h 56m 4.09s. Polaris appears above the
northern horizon. This altitude of Polaris equals the observer’s latitude. A large
portion of the circular path of these stars appears above the horizon, thus these stars
appear above the horizon for more than 12 hours.
a) Formula: Altitude of Polaris = Observer’s latitude
b) Example: An observer in Charlotte, N.C. (latitude = 35) will see Polaris appear
35 altitude above the northern horizon.
c) Example: The apparent motion of the stars looking north as seen from Charlotte,
N.C. appears below:
Meridian
60 Altitude
50 Altitude
40 Altitude
Circumpolar
Region
Polaris
30 Altitude
Stars cycle around Polaris
once every 23h 56m 4.09s
Northern stars are above the
horizon for more than 12
hours
20 Altitude
10 Altitude
North
d) Exercise: Draw the apparent motion of the stars looking north as seen from
Orlando, FL (latitude = 28) [Draw in Polaris and several other hypothetical
stars and create an illustration similar to the one above.]
60 Altitude
50 Altitude
40 Altitude
30 Altitude
20 Altitude
10 Altitude
North
2) An observer looking north will see that some stars never dip below the horizon during
their diurnal cycle around Polaris (the NCP really) because they appear closer to
Polaris (the NCP really) than Polaris is to the horizon. These stars are called
circumpolar stars. Circumpolar stars never rise or stet, but are always above the
horizon – even in the daytime. The circumpolar region extends in declination from
+90 (the NCP) down to (90- observers latitude).
a) Formula: Lowest declination circumpolar star = 90- Observers latitude
b) Example: An observer in Charlotte, N.C. (latitude = 35) will observe that the
lowest declination circumpolar star has a declination of 55.
c) Exercise: Is the circumpolar region smaller or larger in area as seen by an
observer in Orlando, FL (latitude = 28) compared to that as seen by an observer
in Charlotte, N.C.? Justify your answer.
3) An observer looking towards the east (or west) will see that stars appear to rise (or
set). The celestial equator will intersect the horizon at exactly east and west for all
observers. Stars near the celestial equator appear to rise in the east and set in the west
at a slant angle relative to the vertical equal to the observer’s latitude. All stars near
the celestial equator appear above the horizon for about 12 hours (except for
observers at 90 latitude).
a) Formula: Slant angle (relative to the vertical) = Observer’s latitude
b) Example: The apparent motion of the stars looking east and west as seen by an
observer in Charlotte, N.C. appears below.
Stars cycle
around the
celestial
sphere once
every 23h
56m 4.09s
Celestial
Equator
35
35
35
East
Celestial
Equator
35
35
35
35
Stars near
the celestial
equator are
above the
horizon for
about 12
hours
West
c) Exercise: Draw the apparent motion of the stars looking east and west as seen
from Orlando, FL (latitude = 28). Will these stars rise and set at an angle closer
to the vertical or farther from the vertical compared to Charlotte, N.C.?
East
West
4) An observer looking south will see that stars appear to move in a clockwise circular
motion about some point hidden below the horizon (the SCP). Only a small portion
of the circular path of these stars appears above the horizon, thus these stars appear
above the horizon for less than 12 hours. The southernmost visible star has a
declination given by (the observer’s latitude - 90).
a) Formula: Declination of southernmost visible star = Observers latitude - 90.
b) Example: An observer in Charlotte, N.C. (latitude = 35) will observe that the
southernmost visible star has a declination of -55 degrees. No stars south of -55
degrees declination are ever visible from this location.
Meridian
Stars cycle around the South
Celestial Pole once every 23h
56m 4.09s
Southern stars are above the
horizon for less than 12 hours
Southern most
visible star
South
South Celestial
Pole
c) Exercise: Draw the apparent motion of the stars looking south as seen from a
high latitude near the North Pole
South
5) All visible stars (except the circumpolar stars) rise along the eastern half of the sky,
rise to a maximum altitude as they transit the meridian, and set along the western half
of the sky. All visible stars obtain a maximum altitude at transit given by 90 minus
the absolute value of the difference between the observer’s latitude and the
declination of the star.
a) Formula: Maximum altitude = 90 - observer’s latitude-declination of the star
b) Example: The star Vega has a declination of +38. Its maximum altitude as seen
from Charlotte, N.C. (latitude = 35) is 90 - 35-38 = 90 - 3 = 87
Deneb
Meridian
West
87
South
North
East
c) Example: The star Antares has a declination of -28. Its maximum altitude as
seen from Charlotte, N.C. (latitude = 35) is 90 - 35- (-28) = 90 - 63 = 27
Meridian
Antares
West
South
27
North
East
d) Exercise: Calculate the maximum altitude of Deneb and Antares as seen from
Orlando, FL (latitude = 28). Do these stars reach a higher or lower maximum
altitude as compared to that in Charlotte, N.C.?
Meridian
West
South
North
East