Celestial Sphere Basics

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 the 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.
103 stars are included. Among them are the 58 navigational stars. A star's name is shown as a tooltip when you mouse over it.
To use: select the Earth observer's latitude and time and check the objects you wish to view. Drag the mouse over the sphere to change your viewpoint, looking from outside the celestial sphere. Or, for better control, use the sliders at the bottom and right. Additional information is shown in tooltips, when you mouse over Sun and the two selected stars or their arcs.
  • Contributed by: Hans Milton


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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. Equatorial coordinates are shown when mousing over the arc from pole to the Sun or a star. Coordinate values are given in decimal notation. When an angle is given in the unit of hours it can be converted to degrees by multiplying by 15, that is, .
Horizontal coordinates shown in tooltips measure azimuth from North to East.
Hour angles shown in the tooltips are measured from the local meridian toward West. In the Northern Hemisphere, the zero hour angle is at local meridian South. In the Southern Hemisphere, the 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 is also shown in a tooltip when you mouse over the meridian arc.
Local sidereal time, hour angle and right ascension are related. Any two of the values determines the third: .
Two different time scales can be selected by radio buttons: solar and clock time. They correspond to Apparent Solar Time and Mean Solar Time, respectively. See [2]. In solar time, 24 hours is the interval between the Sun's successive appearances at the meridian. In clock time, 24 hours is the interval in which the celestial sphere rotates 361°. Solar and clock time coincide at equinoxes and solstices. To see the difference, select a day that is close to being halfway between an equinox and solstice.
Since this Demonstration uses a simplified model of the Earth's orbit, coordinate values differ from those given by an ephemeris table, but the difference is generally 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].
[1] G. V. Brummelen, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry, Princeton, NJ: Princeton University Press, 2009.
[2] Apparent and Mean Solar Time, https://en.wikipedia.org/wiki/Solar_time


    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2015 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+