ASTR 1230 (Whittle) Lecture Notes


4. MOTIONS IN THE SKY
& COORDINATE SYSTEMS


Star trails around South Celestial Pole in 10 hour exposure.


This lecture supplement covers the the origins of the motions of naked eye objects in the sky and the coordinate systems used by astronomers to locate astronomical targets. You should review this material in conjunction with Appendices A and B in the Manual, but you are not required to know it in detail.


A. MOTIONS OF BRIGHT OBJECTS

Cyclical motions of bright objects in sky were the main historical stimulus for the study of astronomy. We first describe these motions as they might have been seen by ancient astronomers but then explain them from a modern perspective.

The table below lists celestial motions which are easily detectable by someone on the Earth without telescopes. We call these "apparent" motions, because they can be produced by motions of the observer as well as by the objects themselves.


OBJECT PERIOD MOTION*
ALL Daily ("diurnal") Rotation Westward
SUN Annual (365 d) (i) 1 degree/day Eastward
(ii) North/South
MOON Monthly (29 d) (i) Eastward, N/S
(ii) Phase change
PLANETS Months-Years Generally Eastward, but complex
Most of these motions are so slow that if you aren't a practicing amateur astronomer, you probably aren't aware of them. The best way to visualize them is in a planetarium or with a good computer sky simulation program. We will use Starry Night to illustrate them in class.


B. EXPLANATION OF MOTIONS

In the rest of this lecture, we explain the diurnal motion and the Sun's motion from a modern scientific perspective.

The apparent motions of celestial objects can be produced by two entirely different effects: The apparent motions we discuss in this lecture are all in the second category:

We observe the universe from a spherical,
tilted, spinning, moving platform.

It is difficult for most people to visualize this situation. You instinctively feel yourself to be at rest on a flat Earth, but your instinct here is seriously misleading.


C. EFFECTS OF EARTH SHAPE AND SPIN

Day/Night; Horizon Plane


D. EFFECTS OF EARTH'S MOTION IN ORBIT


E. EFFECTS OF TILT OF EARTH'S AXIS

North/South Motions of Solar System Objects

The Seasons


F. ASTRONOMICAL COORDINATE SYSTEMS

Astronomers locate objects in the sky by using a set of coordinate systems. Each coordinate system is tied to a particular reference frame---for instance, the local reference frame of a given observer at a given latitude on Earth's surface at a given time of night.

But we already know from the discussion above that the local reference frames for different observers are different and that their orientation in space is constantly changing as Earth rotates. So, some more universal reference frame is needed to tie all these local frames together.

The universal frame used for astronomical observations from Earth is based on the concept of the celestial sphere. As illustrated below, the celestial sphere is a geometric construct on which to display the angular positions of astronomical objects.

In the next section, we describe the "RA and DEC" coordinates used to locate objects on the celestial sphere. The subsequent section describes coordinates useful in the local reference frame of a particular observer.

Professional astronomers using big telescopes usually need to know the positions of their targets to about 1 arc-second accuracy. So, they use the full formalism of the system described below.

In this class, we usually do not need high accuracy to locate targets. The most important questions you need to answer in planning observations are:

You can usually answer these questions satisfactorily by using your Sky Wheels. However, it is useful to know the background on the basic coordinate systems described next.


G. RIGHT ASCENSION AND DECLINATION


Local Reference Frame for an Observer on
Earth's Surface. (Green shows the horizon plane.)

H. THE LOCAL REFERENCE FRAME

The local reference frame of any Earth-bound observer is determined by that person's instantaneous horizon plane. The diagram above shows the local reference frame and its main reference points.

Two angles also suffice to locate any object in the local reference frame of an observer. Engineers would use an azimuth and altitude system, but conversion to these angles from RA and DEC requires the use of spherical trigonometry. With telescopes which have equatorial mounts, astronomers can use a simpler system based on DEC and "Hour Angle."


Visibility of Astronomical Objects: Declination

It is important to know how to determine when astronomical objects are well placed for observation from your particular location on Earth at a given date and time. The "DEC-HA" method is the quickest way to do this:

Visibility of Astronomical Objects: Hour Angle

Sidereal Time

Altitude & Meridian Slice


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Last modified September 2008 by rwo


Star trail image copyright © David Malin/Anglo Australian Observatory. Zodiac and axis tilt drawings copyright © by Nick Strobel. Equinox, RA, & Dec, drawings copyright © 1974,5 by Edmund Scientific Corp. Text copyright © 1998-2008 Robert W. O'Connell. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 1230 at the University of Virginia.