DOCUMENT By: Robert Jaquin

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 declinationare 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 moveclockwise 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 anylocation.

[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 thecenter 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 thecenter of their circular motion is above the horizon and are thus above the horizon for less than 12 hours. ]