9853

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 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. Additional information is shown in tooltips, when mousing over Sun or star.

SNAPSHOTS

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

DETAILS

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 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.
    • 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.









 
RELATED RESOURCES
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 © 2014 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+