*Motions are measured with respect to the stars, except for the diurnal motion, which is with respect to the local horizon.

• The motions may be complicated, but they are repeatable over periods of months to years. It was this cyclic nature that encouraged early astronomers to seek a deeper understanding of them. If the easily observable sky phenomena had been random in character, science might never have developed, and superstition might still prevail. The famous science fiction story "Nightfall" by Isaac Asimov describes what might befall a society whose planet was less fortunately situated than ours (such that darkness occurs only every 2000 years).

B. EXPLANATION OF MOTIONS

• Intrinsic motions of the objects themselves with respect to one another

• The motion of the observer, or the platform on which he/she is standing---in this case, the Earth

C. EFFECTS OF EARTH SHAPE AND SPIN

• Earth is a sphere.

• Night = shadow side (away from Sun). Half of Earth is always in shadow.

• Daylight = sunlight scattered by Earth's atmosphere. Daylight glare overwhelms the light of the planets and stars, so we cannot see them when the Sun is above the horizon.

• Earth spins on its axis with respect to the stars once in 23 hours, 56 minutes (one "sidereal day"). This causes the apparent diurnal rotation of sky. The universe is not moving around the Earth once per day.

• The spin is counterclockwise (eastward) as seen from above N pole; ==> apparent rotation of sky is westward

• Left-hand panel of diagram above shows Earth viewed from above its North Pole. The Earth rotates counterclockwise in this diagram, carrying observers with it. The positions where observers on the equator are experiencing sunrise, noon, sunset, and midnight are marked. Mean local times of day corresponding to these points are 6 AM, 12 noon, 6 PM, and 12 midnight, respectively.

• The right hand panel shows the local "horizon plane," which is the plane "tangent" to Earth at your location. You can see (in principle) objects above the plane but not below. Note that half of the entire celestial sphere is always above your horizon plane. However, the horizon plane (and visible hemisphere) is different at each location on Earth. The horizon plane sweeps across sky as Earth spins and determines the rising and setting of objects. Objects rise over the eastern horizon and set toward the western horizon.

• By combining the concept of the horizon plane with the definition of local time in the left-hand panel, you can visualize what parts of the sky are observable at any given time.

D. EFFECTS OF EARTH'S MOTION IN ORBIT

• Earth is a planet moving in orbit around the Sun

• Orbit is nearly circular (distance to Sun varies only 3%)

• Orbit lies in a plane called the "ecliptic" plane. Seen face-on, the orbit is technically an ellipse but deviates only slightly from a circle. Seen edge-on, the orbit is a thin line.

• Earth orbits Sun in 365.25 days (one year) moving at ~66,000 mph. Motion is counterclockwise as seen from above N. pole
  

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• Stars visible at night are those "opposite" the Sun. See figures above. The night side of Earth is that opposite the Sun. So, in May, the constellation Scorpio will be prominent in the night sky, while in November, it lies in the direction of the Sun and therefore is not visible because of the atmospheric glare.
  • Warning! this drawing, and most others you will see in this course and in astronomy texts, is grossly distorted and not to scale! In reality, the Earth's orbit is 100 times the diameter of the Sun; the Earth is 100 times smaller than the Sun; the stars are vastly distant from the Earth's orbit; and the stars in a given constellation are not necessarily near one another in space. We are viewing Earth's orbit here from an angle such that it looks highly elliptical, whereas it is nearly circular seen face-on. Obviously, no one could produce or sensibly view a figure like this drawn to actual scale.

• The Earth's motion around the Sun is counterclockwise in the drawings above. This produces an apparent eastward "motion" of the Sun as seen from the Earth against the stellar reference frame. In the drawings, the Sun in November would be seen in projection against Libra (if you could be outside the Earth's atmosphere), while in December, the Earth has moved such that the Sun is seen in projection against Scorpio. The average "motion" of the Sun against the stars is 1 degree per day eastward.
  • "Solar" vs. "sidereal" days: The daily motion of the Earth in its orbit means that the Earth must spin a little more than once on its axis to bring the Sun back to the point of local "noon" (i.e. halfway between rise and set). The extra amount is 4 minutes, on average. This accounts for the difference between the sidereal rotation period of the Earth (23 hours, 56 min) and the average difference between successive noons (24 hours, the "solar day"). [See illustration of effect of Earth's motion during one sidereal day here.]

• The Sun's location on the sky as seen from Earth is confined to the ecliptic path = the projection of the ecliptic plane on the celestial sphere.
  • The "Zodiac" is the set of constellations through which the ecliptic path passes. (See Lecture 1.) Those are the only constellations which have been illustrated in the drawings above. Of course, there are 76 other constellations not shown. You should know the names of the Zodiacal constellations.

E. EFFECTS OF TILT OF EARTH'S AXIS

• The polar rotation axis of the Earth is not perpendicular to its orbital plane. It is tilted by 23.5 degrees. See figure below (again, exaggerated for clarity):
  

  
  

• The rotation axis is fixed in direction with respect to the stars, not with respect to the Sun. This means that, as Earth orbits the Sun, the axis continues to point in the same direction in 3D space.

• This implies that the Sun, as viewed from the Earth, will appear to move north and south of the celestial equator through the year by a maximum of + or - 23.5 degrees. In the drawing above, if the North Pole is at the top, the Sun will be seen at its most southerly position. The total amplitude of the swing = 2 x 23.5 = 47 degrees.

• Equivalently, the ecliptic path is inclined 23.5 degrees to the celestial equator. The following diagram shows the ecliptic and the equator on the celestial sphere (see Lecture 1 for the definition of the celestial sphere).
  

  
  

• The ecliptic crosses the celestial equator at two points called equinoxes.
  • When the Sun is at an equinox, night and day are each 12 hours long at all latitudes. The "Vernal Equinox" occurs around March 21, while the "Autumnal Equinox" occurs around September 21.

  • The Sun is at its greatest distance from the equator (23.5 degrees) at the solstices ("sun stationary," approx. June 21, Dec 21). At these times, one hemisphere experiences its longest day, the other its shortest.

• The Sun's N/S distance determines the hours of daylight and the angle at which sunlight strikes Earth's surface. It thus determines "insolation," or the amount of sunlight incident on a unit area of the Earth's surface during 24 hours. This differential heating is responsible for the seasons. The "official" beginning dates of spring, summer, autumn, and winter correspond to the Vernal Equinox, Summer Solstice, Autumnal Equinox, and Winter Solstice, respectively.
  • The change in the geographic shadow distribution caused by the tilt is quite dramatic (even though the shadow always covers exactly one hemisphere of the Earth). Here are two images of the way the shadow is distributed at about 2 PM Eastern time on August 1 (left) and December 1 (right). The Earth's surface moves eastward through the shadow. You can immediately tell from the image which latitudes are receiving more sunlight in a 24 hour period. Click on the thumbnails for an expanded view.

    
    
    

  • Therefore, seasons are caused by tilt, not distance to the Sun. If the seasons were a distance effect, winter, for instance, would occur simultaneously in both the southern and northern hemispheres; but instead, the seasons differ by 6 months in the two hemispheres. The Earth is actually nearest the Sun in January, one of the coldest months in the northern hemisphere.

F. ASTRONOMICAL COORDINATE SYSTEMS

• The astronomical coordinate system is similar to the terrestrial two-angle coordinate system for finding places on the Earth's surface. The terrestrial angular coordinates are latitude, for measuring north-south distances, and longitude, for measuring east-west distances.

• The celestial Equatorial Coordinate System is very similar. It uses two angles to measure positions on the celestial sphere. Declination is analogous to latitude, while Right Ascension is analogous to longitude.
  

  
  

• As seen in the figure above, declination (abbreviated DEC or Greek "delta") is measured (in degrees) north or south of the celestial equator. The North and South celestial poles have DECs of +90 and -90 degrees, respectively. The equator has DEC 0.

  
  

  

  
  

• Right Ascension (RA or Greek "alpha") is measured as shown in the figure above. Lines of constant RA are great circles (also called "hour circles") drawn through the celestial poles. The zero point of RA is the vernal equinox, and RA increases eastward. (This is an arbitrary designation, just like the zero point of the longitude system is arbitrarily chosen to be Greenwich, England.)

• Rather than measuring in degrees, RA is measured in time units of hours, minutes, and seconds up to one sidereal day. Therefore, RA values run from 0 hours to 23^h59^m59^s. For a star on the equator, one hour of RA corresponds to 15 degrees of arc. But because of the convergence of the lines of constant RA toward the pole (see figure above), at other declinations one hour of RA corresponds to fewer than 15 degrees of arc. (Beware confusion between "minutes" and "seconds" of time and those of arc!).

• The figure above shows how the declination of an astronomical object controls its visibility with respect to your horizon. The shaded plane is the horizon. Star tracks are shown on the celestial sphere. The orientation of the sphere for your location is the same at all times of the year (though the Sun moves to different locations along it and thus changes the part of it which is visible at night).
  • As the Earth rotates on its axis during the course of a night, the stars appear to rise in the east, move along the heavy lines of constant declination, and set in the west. A star is farthest from the horizon when it crosses your meridian (see Lecture 1). At this time it is said to transit.

  • The figure above helps you visualize how long in each 24 hour period stars at different DECs are above your horizon. Some DECs (like +60 degrees here) are always above your horizon. Stars here are called circumpolar stars; they never set. By contrast, stars at -30 degrees DEC are above the horizon only for short periods. There are some stars farther south which are never above your horizon.

• Knowing DEC alone is not sufficient. The celestial sphere rotates continuously about the axis through its poles and therefore continuously changes the location of an astronomical object in your local coordinate system. An object's DEC may always be the same, but its east-west position changes during the night. To locate an astronomical object in the sky, you need to know one additional quantity besides DEC: the distance of its hour circle from your local meridian.
  

  
  

• The Hour Angle or HA is defined to be the angle measured along the equator between the hour circle of a star and your meridian. In the diagram above, the hour angle is denoted "H." It is quoted in time units (hours, minutes, and seconds), and is numerically equal to the time elapsed since the last transit of the star.
  Objects to the west of the meridian have positive HA, while objects to the east have negative HA. A star with HA = 2 crossed the meridian (i.e. reached transit) two hours ago, while a star with HA = -1 will be on the meridian in one hour. An HA of 23 hours is equivalent to HA = -1.

• To find the HA of a star we must know the current position of the zero point of RA, the vernal equinox. This is given by the sidereal time or ST. ST is defined to be the hour angle of the vernal equinox, and it is the fundamental measure of astronomical time of day. By this definition, ST is also equal to the RA of an object now on the meridian.

• At a given ST, the HA of a star with a given RA is:
  HA = ST - RA

• Sidereal time runs faster than the mean solar time that our watches use by 3 minutes and 56 seconds per day, a result of the Earth's orbital motion around the sun. This means that the sidereal time at a given standard time changes continuously by 2 hours per month (or 24 hours in a year). If the ST at 9 PM EST tonight is 6 hours, one month from now it will be 8 hours. A table listing the ST at 9 PM EST throughout the year is given in the Appendix to the 130 Manual.

• Using the HA/DEC system and an equatorially-mounted telescope, you can quickly locate objects in the sky if your know their RA, DEC, and the sidereal time. One problem: HA changes continuously, so when you predict HA, you need to allow time to set the telescope.

• You must know both HA and DEC to determine visibility (refer to the diagram at the start of this section). An object with HA = +6 hours (-6 hours) is just setting (rising) on the horizon if it lies on the celestial equator (with DEC = 0); it will be visible in the sky for almost 12 hours a night. Objects south of the equator will be visible for fewer hours. Objects north of the equator will be visible for more hours. Any object in the circumpolar region is above the horizon all the time (from HA = 0 to 24), but cannot be seen in the daytime because of scattered light from the Sun.

• The HA/DEC system is part of the celestial Equatorial Coordinate System defined with respect to the poles and equator. However, it is often useful also to know how to locate an object with respect to your horizon plane.

• Altitude is defined to be the angle between a star and your horizon plane. In general, you need to use trigonometry to find the altitude of an object with a given HA and DEC.
  

  
  

• However, when the star is on the meridian, there is a simple relation between its DEC, your latitude, and its altitude. This is illustrated in the figure above, which shows a geometric "slice" through your local meridian.
  • Based on the diagram, the altitude of a star above the southern horizon (SALT in the diagram above) is given by the following expression, where LAT is your latitude.
    SALT = DEC + (90^o - LAT)

  • LAT = 38^o at Charlottesville, so here SALT = DEC + 52^o.

  • Objects with DEC = LAT have altitudes of 90^o, i.e. they cross through your zenith. The celestial equator (DEC = 0) has SALT = (90^o - LAT).

• SALT is a useful concept for determining how high in the sky a planet or the Moon, for instance, can be on a given night.
  • As an example, the Moon orbits in a plane which is tilted 5^o from the plane of the ecliptic. Since the maximum DEC of the Sun (or the ecliptic) is +23.5^o, the maximum DEC of the Moon is +28.5^o. The maximum altitude of the Moon above the southern horizon is then:
    SALT = 28.5^o + (90^o - 38^o) = 80.5^o.

• Read Appendices A and B in the ASTR 130 Manual

• Consult reference material in Norton's Star Atlas, as needed

• A set of sample questions & problems concerning the material covered in the lectures will be available later this week. These will not be graded, but you should work through these in preparation for the Midterm Exam.

• You should complete the Constellation Quiz ASAP and move on this week to Labs 2 and 3.

Interactive Earth & Moon viewer (includes software & add'l links)
Astronomy Without a Telescope (introduction to naked-eye astronomy by Nick Strobel)

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Last modified 4 February 2001 by rwo

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Star trail image copyright © David Malin/Anglo Australian Observatory. Zodiac and axis tilt drawings copyright © by Nick Strobel. Other professional drawings copyright © 1974,5 by Edmund Scientific Corp. Other material copyright © 1998-2001 Robert W. O'Connell. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 130 at the University of Virginia.