Wolfram Demonstrations Project

The celestial sphere is a model of the objects in the sky as viewed from an observer on Earth. The concept of the celestial sphere is often used in navigation and positional astronomy. The purpose of this Demonstration is to visualize the basic principles behind changes in the appearance of the celestial sphere as, it varies with the observer's latitude, time of year, and time of day.

A simplified model is used, in which the Earth moves in a circular orbit around the Sun. The speed of Earth in its orbit is assumed constant. At the observer's longitude, equinoxes occurs at noon on March 21 and September 21. Solstices occurs at noon on June 21 and December 21. For simplicity, the year is assumed to have 360 days, divided into 12 months of 30 days each.

To use: select the Earth observer's latitude and time and check the objects you wish to view. Click and drag the mouse over the sphere to change your viewpoint, looking from outside the celestial sphere. Or, for better control, use the "pan" sliders.

Contributed by: Hans Milton

Rotate and Zoom in 3D
Slider Zoom
Gamepad Controls
Automatic Animation

The obliquity of the ecliptic is set to 23.43929°.

Tooltips show the coordinates of the Sun and two other selected stars. To see horizontal coordinates, mouseover the Sun or the star. The hour angle and declination are shown when mousing over the arc to the Sun or the star. Coordinate values are given in decimal notation.

Horizontal coordinates shown in tooltips measure azimuth from North toward East.

Hour angles shown in tooltips are measured from local meridian toward West. In the Northern Hemisphere, zero hour angle is at local meridian South. In the Southern Hemisphere, zero hour angle is at local meridian North.

In the collection of stars, one star is included that has no real counterpart. Named FP of Aries, its location is First Point of Aries. Its hour angle gives local sidereal time.

Local sidereal time, hour angle and right ascension (all in hours) are related. Any two of the values determines the third. Example:

Since this Demonstration uses a simplified model of the Earth's orbit, coordinate values will differ from those given by an ephemeris table. But the difference will generally be small, for the purpose of locating a star in the sky.

For examples on the use of the celestial sphere in connection with spherical trigonometry, see [1].

Reference

[1] G. V. Brummelen, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry, Princeton, NJ: Princeton University Press, 2009.