The Apparent Motion of the Stars
There are rules that can be derived from the celestial sphere model of the Universe that allow a person to predict the apparent
motion of the stars as seen from any location on. Those rules relate the latitude of the observer to the (1) altitude of Polaris, (2)
size of the circumpolar region, (3) direction of movement of stars rising along the eastern horizon, (4) southernmost visible part
of the sky, and the (5) minimum zenith angle of a star. Precession causes the position of the NCP, SCP and equinoxes to slowly
change over a very long time scale (26,000 years).
I would like you to be able to do the following tasks after completing this section.
 State the altitude of Polaris (or the North Celestial Pole) as seen from any location.
[Rule: The altitude f Polaris (NCP, really) equals the observer’s latitude.]
 Draw the apparent motion of the stars around Polaris (or the NCP) as seen from any location.
[Rule: The stars appear to move counterclockwise around Polaris (NCP, really) once every 23h 54m4.09s – the sidereal
day]
 Delimit the circumpolar region as seen from any location.
[Rule: The circumpolar region where stars never set below the horizon is a circular area of the sky centered on the visible
celestial pole and extending to the horizon. The declination of the circumpolar boundary is given by ±(90°-observer’s
latitude).]
 State and draw the slant path of rising/setting stars along the eastern/western horizon as seen from any location.
[Rule: The Celestial Equator (0° dec) intersects the horizon due East and West for all observers. All stars follow their
respective lines of declination and, near the celestial equator, the slant angle relative to the vertical of lines of declination
are equal to the observer’s latitude.]
 Draw the apparent motion of stars looking toward the south as seen from any location and identify the southernmost (when
viewing form the northern hemisphere) or northernmost (when viewing form the southern hemisphere) visible declination.
[Rule: The stars appear to move clockwise around the SCP once every 23h 54m4.09s – the sidereal day. The declination of
the southern/northern most visible star is given by ± (90°-observer’s latitude).]
 Derive the maximum altitude of a star given its declination and your latitude.
[Derivation: The simplest way to derive the maximum altitude of a star given its declination is to sketch a 2D celestial
sphere diagram and
1. Construct the line connecting the celestial poles from the given latitude labeling the declination of the poles ±90° dec.,
2. Construct the plane of the celestial equator (seen edge-on as a line) perpendicular to the line connecting the celestial
poles labeling the declination of the celestial equator 0° dec.,
3. Sketch in the correct location of the star in question using its given declination, and
4. Use right-angle geometry to determine the maximum altitude of the star. ]
 State the approximate times that stars of a given declination will appear above the horizon from any location.
[Rule: The time a star spends above the horizon depends on the fraction of its diurnal circle that is above the horizon. Stars
near the visible celestial pole have more than half their diurnal cycle above the horizon because the center of their circular
motion is above the horizon and are thus above the horizon for more than 12 hours. Stars near the celestial equator have
about half their diurnal circle above the horizon and are thus above the horizon for about 12 hours. Stars near the invisible
celestial pole have less than half their diurnal cycle above the horizon because the center of their circular motion is above
the horizon and are thus above the horizon for less than 12 hours. ]
Rio de Janeiro,
Brazil, 23° S
The altitude
of Polaris
and size of
the
circumpolar
region
The slant
path of stars
rising along
the eastern
horizon
The
apparent
motion of
stars
looking
south and
the
southernmo
st visible
star
The time
Deneb (38°
Dec) is
above the
horizon and
its
maximum
altitude.
The time
Antares
( -26° Dec) is
above the
horizon and
its
maximum
altitude
angle.
Equator,
0°
Miami,
25° N
Syracuse,
43° N
The altitude of Polaris is
43° above the northern
horizon. The
circumpolar region
extends 43° around
Polaris down to 47°
declination.
Stars rise slanting
toward the south (right
as you watch them) at an
angle of 43° from the
vertical)
Stars move from the east
to the west along
partially revealed semicircular paths whose
center is 43° below the
horizon. The
southernmost visible
star has a declination of
-47°.
Deneb is a northern
hemisphere stars but
near the circumpolar
region. It will be above
the horizon for more
than 12 hours but closer
to 24 hours. The
maximum altitude is
85°.
Antares is a southern
hemisphere star but it is
north of the southern
most visible star. It will
be visible for less than
12 hours. The
maximum altitude is
21°.
Location: ______________________________
Latitude: ____________________________
Looking North
Looking East
Looking South
Looking West
Z
S
N
Location: ______________________________
Looking North
Latitude: ____________________________
Looking East
Looking South
Looking West
Z
S
N
Location: ______________________________
Looking North
Latitude: ____________________________
Looking East
Looking South
Looking West
Z
S
N
Location: ______________________________
Looking North
Latitude: ____________________________
Looking East
Looking South
Looking West
Z
S
N
Location: ______________________________
Looking North
Latitude: ____________________________
Looking East
Looking South
Looking West
Z
S
N
Location: ______________________________
Looking North
Latitude: ____________________________
Looking East
Looking South
Looking West
Z
S
N