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Astronomy Olympiad

Problems on Positional Astronomy


Conjunction, Opposition, Cardinal Points,

Alt-Az (Horizon System)


Altitude is the height of the object as measured from the horizon. Zenith Distance (z) & Altitude (h) are complimentary. Azimuth is measured from the north, going towards the east (NESW), in the plane of the horizon. Alt-Az changes with the earth’s rotation. Blind spots at zenith


Motions of the Sun

Daily motion of the sun – rise & set – causes it to change its Alt-Az throughout the day. Sun’s annual motion causes the background of the sun to change, thereby defining the zodiac. Seasons are a consequence of the annual motion of the sun. Apparent north-south shift of the rise point of the sun (Uttarayan-Dakshinayan) due to the fact that the ecliptic plane does not coincide with the equatorial plane of the earth.

Ecliptic System

The reference circle is the ecliptic. Point of origin is the vernal equinox. The coordinates are longitude (l) – measured along the ecliptic, from the g-point, to the east – and latitude (b) – measured from the ecliptic either towards N or S. The zodiac lies entirely along the ecliptic, therefore the zodiac boundaries are defined in the ecliptic system.

Equatorial System

Solar Motion




21st March



22nd June



23rd September



22nd December



The reference circle is the celestial equator. The reference point is the vernal equinox. The coordinates are Right Ascension (a) – measured from VE on the celestial equator towards the east; is expressed in units of time – and Declination (d) – is measured to the north or south of the equator.

This system is usually used in star maps. For stars these coordinates are fixed for all practical purposes. This system is connected with the calculation of time.

Concepts in Time

Hour angle is the angle measured in hours, minutes & seconds from the upper meridian.

How to find sidereal time:




Altitude is the



  1. Work out the Alt-Az of stars, sun & moon when they are rising or setting or at meridian transit, from the equator.
  2. Work out the Alt-Az f the Sun, Moon & Stars when they are rising, setting or transiting, when the observer is at arbitrary latitude.
  3. Alt-Az description of ground-based phenomena and calculation of their actual heights on the basis of the coordinates & motion
  4. Observing the zodiac and hence working out the exact motions of the Sun/earth as viewed from the solar north-pole at a far distance from the solar system. (top-view) Hence work out the constellations & apparent phenomena such as seasons.
  5. Calculate the position of the sun at sunrise, on the dates – 30 Jun, 18 Sep, 1 Mar.
  6. At what date & time will the sun be exactly overhead at 19.10N latitude?
  7. When will the Sun pass the zenith for an observer at 100S latitude?
  8. Compute the shift in declination of the sun in a day’s motion? Construct a formula for this quantity, valid for any time of the year.
  9. Derive transformations between the Horizontal & the Equatorial system.
  10. Derive transformation equations for the Horizontal & the Ecliptic system.
  11. Use sky-maps to determine the RA-Dec of a certain star which does not lie on the drawn grid. Hence work out the ecliptic coordinates.
  12. The equatorial coordinates of a star are given. Find its local coordinates for an observer at a latitude 25oS at 2:30 am on the 14th Sep, 2004.
  13. What will be the sun’s equatorial coordinates on the 30th July at 12:00 GMT? At the same time, what will be its local coordinates for an observer at longitude 820W & latitude 300N?

Copyright@Kedar Soni