celestial sphere
Definition: An imaginary sphere centered on the observer onto which directions to celestial objects are projected.
Why it matters here: It turns a three-dimensional universe with mostly unknown distances into a two-dimensional map of observable directions.
Relationships: Altitude and azimuth locate points on the local celestial sphere; daily apparent rotation traces arcs on it as Earth rotates.
Boundary or common confusion: It is a geometric model, not a physical shell, and it does not by itself encode an object's distance.
horizon
Definition: The great circle separating the visible half of the sky from directions blocked by the ground for a particular observer.
Why it matters here: Rise, set, and target visibility are defined relative to this local boundary.
Relationships: Altitude is measured upward from the horizon, while azimuth is measured around it; both depend on location and time.
Boundary or common confusion: A real skyline may sit above the ideal astronomical horizon because of terrain, buildings, trees, or atmospheric refraction.
zenith
Definition: The point on the celestial sphere directly above an observer.
Why it matters here: Objects near the zenith are viewed through less atmosphere than objects near the horizon.
Relationships: The zenith has altitude \(90^\circ\); its position among the stars changes continuously as Earth rotates.
Boundary or common confusion: Zenith is observer-specific: two separated observers generally have different zenith directions.
\[ h_{\rm zenith}=90^\circ \]
meridian
Definition: The great circle passing through north, the zenith, and south on an observer's sky.
Why it matters here: A target crossing the meridian is usually at its greatest altitude for that day and is often best placed for observation.
Relationships: Meridian crossing connects local sky geometry to hour angle and local sidereal time.
Boundary or common confusion: Crossing the meridian does not guarantee visibility if the target culminates below the horizon or daylight is present.
altitude
Definition: The angular height of an object above the local horizon.
Why it matters here: Altitude determines whether a target is visible and strongly affects atmospheric extinction and image quality.
Relationships: It ranges from \(0^\circ\) at the ideal horizon to \(90^\circ\) at the zenith and is paired with azimuth.
Boundary or common confusion: Altitude changes with time and observer location, so it is not a permanent coordinate of a star.
azimuth
Definition: The compass direction of an object measured around the local horizon, conventionally from north through east.
Why it matters here: Together with altitude it gives an immediately usable pointing direction for naked-eye or telescope observations.
Relationships: Azimuth is the horizontal coordinate in the altitude-azimuth system and changes as a celestial object follows its daily arc.
Boundary or common confusion: Conventions can differ in other fields, so the zero direction and direction of increase must be stated.
angular size
Definition: The angle an object spans at the observer, rather than its physical diameter.
Why it matters here: Astronomers can measure angular size directly even when physical size or distance is unknown.
Relationships: For small angles, physical size \(D\), distance \(d\), and angular size \(\theta\) satisfy \(D\approx d\theta\) when \(\theta\) is in radians.
Boundary or common confusion: Large angular size does not necessarily mean large physical size; a nearby small object can appear larger than a distant giant object.
\[ D \approx d\theta\quad(\theta\ {\rm in\ radians}) \]