The Interactive Celestial Sphere
Explore four challenging essential coordinate systems in astronomy in 3D and 2D, visualizing celestial motion from an Earth-fixed and space-fixed perspective.
Key Features
Controls and Menus
- Navigation: Orbit the 3D view with Right Click+ Drag. Zoom in and out by scrolling
- Headers: Click headers to expand. Colored headers have at least one active item. Some items may relate to multiple categories
- Checkboxes: toggle items on and off
- Rotate Earth: view the Earth’s daily rotation from a fixed point in space
- Rotate Sphere: view the apparent daily rotation of the Celestial Sphere including stars, the equinoxes, and the Sun as if you were an observer at a fixed location
- 2D Equator View: a top-down projection of the celestial sphere at the Equator, ideal for studying time systems
- Observer: Move around the Earth in 3D (click Observer- Observer)
- Star: Change declination in 3D (Star - Move Star), or move it along its apparent daily path manually in 3D
- Greenwich Meridian: Shift with the Longitude slider
- Equinoxes: Shift the vernal equinox in 3D along the Equator
- Sun: Move the Sun along the Ecliptic in 3D and view the annual motion of the Sun (Ecliptic System – Annual Motion of Sun)
Definitions and Notes
Earth and Celestial Sphere
The Earth is approximated by a sphere with a defined Center point in this model. The Celestial Sphere is an infinitely large sphere used to describe the positions of celestial objects. The spin axis of the Earth passes through the North and South Poles, and if it were extended, it would pass through the North Celestial Pole (NCP) and the South Celestial Pole (SCP). The Equatorial Plane is perpendicular to the line passing from the SCP to the NCP. The Celestial Equator is the great circle where the Equatorial Plane intersects the Celestial Sphere. A great circle is any circle on the Celestial Sphere with a circumference equal to the circumference of the Celestial Sphere whose Centre coincides with the Earth’s Centre. A Meridian is a plane or circle that passes through a specific place on the Earth's surface and the SCP and the NCP. Variations in the Earth’s spin axis were not included in this model. The Greenwich Meridian passes through Greenwich, which is an arbitrary 0 point on the Earth’s surface for longitude measurements.
Animations and Views
If we view the Earth from a fixed point in space, it will appear that the Earth is rotating counterclockwise (Rotate Earth), resulting in any Earth or observer-based features rotating like the Horizon System. In contrast, if we consider the Earth as fixed as if we were an observer
on the Earth, the Celestial Sphere would appear to move clockwise around the Observer (Rotate Sphere), resulting in any features not fixed to the Earth appearing to rotate like the Right Ascension System, the Equinoxes, the Star, and the Sun. The Earth or the Celestial Sphere completes one full revolution per day.
To view a top-down projection of the Celestial Sphere at the Equator, frequently used for studying time systems, use the 2D Equator View. Think of this view as a slice of the Celestial Sphere at the Equator.
Observer
The Observer represents the point on Earth from which measurements are taken. The Person provides a graphical representation of the Observer’s location on the Earth. The orientation of the person in the
model is arbitrary. The observer’s Latitude is the angle from the Equator to the Center of the Earth to the Observer. The magnitude of the latitude is shown in the model, even though latitude is often expressed with direction, which results in a negative (or Southern) latitude in the Southern Hemisphere. The observer’s Longitude is the angle East from the Greenwich Meridian along the Equator to the Observer’s Celestial Meridian. In the model, the Greenwich Meridian can be moved with the Longitude slider to allow for easy changes to the Observer’s longitude. However, in reality, the Greenwich point is fixed on the Earth, and the observer would need to move to change longitude.
Star
The Star represents any celestial object of interest. The Star’s daily apparent Path for an Observer with a fixed location on the Earth would follow a small circle around the Celestial Sphere in the opposite direction to the Earth’s rotation, so the Star would appear to rotate clockwise (Rotate Sphere). Depending on the star, the declination of the star on the Celestial Sphere will be different and can be changed in this model with the Move Star point, which moves the Star along the SCP to NCP line.
Horizon System
Measurements by an Observer on the Earth are taken in the Horizon System. Assuming a spherical Earth of even density, a Plumb Line passes through the Observer and the Center of the Earth, resulting in the Nadir point directly below the Observer and the Zenith point directly above the Observer, both on the Celestial Sphere. The Celestial Meridian of the Observer is the great circle that passes through the NCP, SCP, Zenith, and Nadir points. The Horizon Plane is a tangent plane to the Earth at the Observer’s location. Assuming the Observer is on flat ground, anything on the Observer’s side of the Horizon Plane shows what an Observer would be able to see from their location. Since the Earth is infinitely small compared to the Celestial Sphere, the Horizon Plane was drawn at the Center of the Earth rather than passing through the Observer. The Celestial Horizon is the intersection of the Horizon Plane with the Celestial Sphere (a great circle).
If the Observer looks directly North (N), East (E), South (S), or West (W), they will see those points on the Horizon on the Celestial sphere. The Prime Vertical is the great circle that is perpendicular to the Horizon Circle and passes through the East and West Points. Common angular measurements to stars by observers include Azimuths, Altitudes, and Zenith Distances. The Azimuth is the angle measured clockwise from the North Point along the Horizon plane to the Star. The Altitude is the angle up from the Celestial Horizon to the Star. The Zenith Distance is the angle down from the Zenith to the Star (90° minus the altitude). Almucantars are any small circles that are parallel to the Horizon Circle.
Hour Angle System
The Hour Angle System is partially tied to the Observer and partially tied to the Celestial Sphere. The X-axis of the Hour Angle System (X HA) is where the Celestial Meridian intersects the Celestial Equator on the Observer’s side. The Hour Circle is the great circle that passes through the Star, NCP, and SCP. The Hour Angle (HA) is the angle measured clockwise along the Equator from the X-axis of the hour angle system to the Hour Circle of the Star on the Star’s side. The Declination of the Star is the angle from the Celestial Equator to the Star. The magnitude of the Declination is shown in the model, even though Declination is often expressed with direction, which results in a negative Declination in the Southern Hemisphere.
Right Ascension System
The Right Ascension System is a system based entirely on the Celestial Sphere and is not influenced by the Observer’s location, so it is frequently employed to catalogue the positions of stars. The Vernal and Autumnal Equinoxes are the points where the Sun’s annual apparent path (the Ecliptic) intersects the Celestial Equator. The Vernal Equinox serves as the X-axis of the Right Ascension System. The Equinoctial Colure is the great circle that passes through the Equinoxes, the SCP, and the NCP. The Right Ascension (RA) is the angle from the Equinoctial Colure on the Vernal Equinox side to the Hour Circle of the Star. The Right Ascension is fixed based on the Sun’s path, but a Right Ascension slider was put in the model to set the Right Ascension of a specific Star by shifting the Vernal Equinox.
Ecliptic System
The Ecliptic System is based on Earth’s orbit around the Sun. The Earth’s spin axis is tilted from the Earth’s orbit around the Sun by the Obliquity of the Ecliptic (approximately 23.44°). The obliquity of the Ecliptic is considered constant for this model, although in reality it changes slightly over time. The Ecliptic circle shows the path of the Sun throughout the year. Due to the Obliquity of the Ecliptic and the Earth’s orbit around the Sun, the Sun’s apparent motion moves North-South throughout the year in addition to the circular apparent motion of distant stars. The Summer Solstice occurs where the Sun reaches its maximum declination, while the Winter Solstice occurs where the Sun reaches its minimum declination. The solstices are 90° degrees from the location of the equinoxes on the Ecliptic. The North and South Ecliptic Poles (NEP, SEP) occur where the perpendicular line from the Ecliptic plane at the Center of the Earth intersects the Celestial Sphere. To view angles to the Sun, click the Use Sun as Star checkbox.
In this model, the Annual Motion of the Sun around the Ecliptic is approximated as moving at a constant rate around the Ecliptic. To see the full motion of the Sun, including daily and annual motion, turn on Rotate
Sphere and Annual Motion of the Sun together. The annual motion up and down of the Sun is sped up relative to the rotation of the Star for illustration purposes, since it should take approximately 365.25 circular motions of the Sun to complete one full revolution around the Ecliptic.
Star Positions
As the star follows its apparent path, it will pass through several points of interest that relate to the Observer and points on the Celestial Sphere. Equatorial Stars, stars with declination between 90° minus latitude and latitude minus 90°, Rise and Set when the star's apparent path crosses the Horizon Circle. Stars that do not Rise or Set are always visible or never visible and are called Circumpolar Stars. A Star with a declination between 0 and the Latitude of the Observer has Prime Vertical Crossings where its apparent path intersects the Prime Vertical of the Observer. A Star with a Declination greater than the Latitude of the Observer appears to pass through a point where the star only moves in the vertical direction (when the Parallactic Angle is 90°), which is called Eastern and Western Elongation, and is ideal for taking horizontal/azimuth measurements to stars. A Star appears to pass through Lower and Upper Culmination/Transit when the Star is only moving in the horizontal direction (when the star’s hour angle is 0 or 12 hours), and is ideal for taking vertical/altitude measurements to stars.
Additional Items and Views
The Astronomical Triangle, GST, and LST allow for conversions between the Horizon, HA, and RA coordinate systems with spherical trigonometry and time-based calculations. The Astronomical Triangle represents the spherical triangle between the NCP, the Star, and the Zenith. The sides of the Astronomical Triangle are 90°-Declination, 90°-Latitude and the Zenith Distance. The interior angle of the Astronomical Triangle at the NCP is equivalent to the Hour Angle if the Star is West of the Observer’s Celestial Meridian, or equivalent to 24 hours (360°) minus the Hour Angle if the Star is East of the Observer’s Celestial Meridian. The angle at the Star in the Astronomical Triangle is called the Parallactic Angle (P). The angle at the Zenith of the Astronomical Triangle is called the Azimuth and is equivalent to the Azimuth from the Horizon System or 360° minus the Azimuth from the Horizon System. GST, Greenwich Sidereal Time, is the angle between the Vernal Equinox and the Greenwich Meridian along the Equator. LST, Local Sidereal Time, is the angle between the Vernal Equinox and the Celestial Meridian of the Observer and is equivalent to the GST plus the Longitude of the Observer.
About the Model
This model was created by Samuel McNally for the Introduction to Global Navigation Satellite Systems course taught by Dr. Richard Langley. This model was submitted to the Computer Assisted Teaching Contest 9 for the International Photogrammetry and Remote Sensing Congress 2026. If you have any feature requests or bug reports, feel free to email me at samuel.mcnally5@gmail.com. Feel free to use this model and add it to your favorites page, but please do not post a copy of it publicly.