Stars, Constellations, and the Celestial Sphere

Constellation - a region of the sky with well-defined boundaries. Most star names are derived from the Arabic language. The brightest stars are also named by giving the relative brightness as a Greek letter (a being the brightest), followed by the possessive form of the Latin name of the constellation. h z e d a b Asterism - a group of stars with a recognized shape. Alioth = e Ursae Majoris Most constellation names are derived from the Latin language. g The Big Dipper The stars of the dipper asterism in Ursa Major are a notable exception to this rule. They are named in alphabetical order, beginning with a at the upper right edge of the bowl of the dipper. The brightest of these stars is actually e Ursae Majoris. The brightness of a star is usually expressed in terms of a quantity called magnitude, with smaller magnitudes corresponding to brighter stars. The distance is usually given in light years or parsecs (1 pc = 3.26 ly) The stars in a constellation are not all at the same distance. For example, we see the Big Dipper asterism (part of the constellation Ursa Major) as a projection (onto the plane of the sky) of a cluster of stars at various distances (100.7 ly, 78.2 ly, 80.9 ly, 81.4 ly, 83.6 ly, 79.4 ly, 123.6 ly).

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09/05/11 9:00 PM

Summer Triangle

Measures of Angle 360o = 360 degrees = all the way around a circle 1o =1/360th of a circle 1' = 1 arcminute = 1/60°→ 1o = 60' 1˝ = 1 arcsecond = 1/60' = 1/3600o → 1o = 3600˝ 10º ≈ apparent width of fist held at arm’s length 1°≈ apparent width of thumb at arm’s length Angular distance between two stars = the angle between lines from the observer’s eye to the stars. Angular size of an object = the angle between two lines from the observer’s eye to the two ends of the object. ½° ≈ angular diameter of the full Moon (or Sun). The angular distance between d and a in the Big Dipper is about the width of a fist held at arm’s length(10°). 90o d a

The Small Angle Formula

The Celestial Sphere NCP N S The green sphere represents Earth. The celestial sphere is an arbitrarily large imaginary sphere with Earth as its center. The plane determined by the equator intersects the celestial sphere in a great circle called the celestial equator. The point on the celestial sphere directly above Earth’s north pole is called the north celestial pole. NCP The vertical line through Earth’s center is its axis of rotation, which defines the north N and south S poles. N S The great circle half way between the north and south poles is the equator.

The horizon for an observer at O is the intersection of a plane tangent to Earth at O with the celestial sphere. Everything that the observer can see is above the tangent plane (represented by the green line in the figure). The angle between the celestial equator (yellow line) and the horizon (green line) is equal to 90° minus the latitude of the observer. For example, the latitude of an observer at the north pole is 90°; the tangent plane to this observer’s location is parallel to the equatorial plane. NCP The point directly above the observer is called the zenith and is labeled Z in the figure. Z O The stars are so far away that they appear to the naked eye to all be at the same distance. They look like they are embedded in the surface of the celestial sphere.

NCP NCP Z O Z Rotate the diagram so that the horizon has its more familiar orientation. O The Observer at O can see all of the sky above the horizon (green line). Actually, the size of Earth is negligible compared to the radius of the celestial sphere so we’ll replace the green disk by a point.

The altitude of the north celestial pole (denoted by f in the diagram) is equal to the latitude of the observer. Z NCP The great circle that passes through the north celestial pole and the zenith is called the local celestial meridian. q f The part of the celestial sphere above the horizon plane is visible to the observer, so the part of the sky visible to the observer depends on latitude. At the North Pole, for example, the stars neither rise nor set but move in circles parallel to the horizon. You can verify this by using a desktop planetariuim program. O At any given latitude (except at the Equator), there are some constellations that never go below the horizon. These constellations are called circumpolar. South Point North Point q = 90o - latitude f = latitude

Motions of Earth Relative to the most distant galaxies, Earth rotates once in 23.93 hours. It revolves around the Sun once in 365.25 days. The angle between the plane of Earth’s equator the plane of its orbit is 23½°. 23½° Rotation Axis Equatorial Plane Ecliptic Plane

Earth’s orbital motion and the angle between the ecliptic plane and the equatorial plane cause the seasons. June 20 December 20 December 20 June 20 Sunlight strikes Earth’s surface at a steeper angle in the summer than in the winter. The sunlight is more concentrated (spread out over a smaller area), so it heats up the ground faster and to a higher temperature.

The celestial equator (red line), the horizon (green line), and the ecliptic (orange line) are great circles on the celestial sphere. As Earth moves around the sun, the sun appears to move along the ecliptic on the celestial sphere. As Earth rotates once in 24 hours, the sun and other celestial objects seem to move once around the celestial sphere in circles parallel to the celestial equator (red line). Z Around June 20, the sun is at the position labeled SS (summer solstice) in the diagram. Its path during one day is indicated by the yellow dotted line. Celestial Equator NCP WS Ecliptic Around December 20, the sun is at the position labeled WS (winter solstice). Its path is indicated by the blue dotted line. Horizon SS Notice that the Sun is above the horizon for a shorter time on December 20. Consequently, the sunlight is heating the ground for a shorter time than on June 20. This is another reason why June 20 is warmer than December 20 in the northern hemisphere. This situation is reversed in the southern hemisphere. Around March 20 and September 20, the sun is on the celestial equator. Its path during the day is along the celestial equator in the diagram. These days, and the corresponding points in the sky are called the vernal equinox and the autumnal equinox, respectively.

Precession The motion of the spinning top in the figure is called precession. It is a result of the force of gravity that tends to tip the top over. Because Earth spins around an axis through its north and south poles and is not perfectly spherical, the gravitational forces of the Moon, Sun, and planets cause it to precess. The precession period is about 26,000 years. As a result, the position of the north celestial pole changes with a period of 26,000 years.

The Milankovitch Hypothesis Eccentricity of Earth’s orbit varies with a period of 100,000 years With a period of 26,000 years, precession of Earth’s axis of rotation changes the locations in its orbit where the seasons occur The inclination of Earth’s equator to its orbit varies between 22º and 24º with a period of 41,000 years. Ice ages occur with a period of about 250 million years. Within any given ice age, cycles of glaciation occur with a period of about 40,000 years. Oceanographic evidence shows ocean temperature variations that support the Milankovitch hypothesis. Nevertheless, this hypothes is not universally accepted by climatologists.

Celestial Equatorial Coordinates This coordinate system is defined by giving a reference line (the celestial equator) and a reference point (the vernal equinox). Celestial Equatorial Coordinates The direction toward any object in the sky can be given by specifying its celestial equatorial coordinates. The vernal equinox (green dot) is the point where the sun crosses the celestial equator on its way northward in the spring. The path of the sun on the celestial sphere is called the ecliptic (orange line). The celestial equator (red line) is the great circle halfway between the north and south celestial poles.

Declination lines are circles parallel to the celestial equator, analogous to latitude on Earth. The unit of declination is the degree. Lines of right ascension are semicircles from pole to pole, analogous to longitude on Earth. 75º The semicircle from pole to pole through the vernal equinox is defined to have a right ascension of 0 hours. The unit of right ascension is the hour of angle and is equal to the angle that Earth rotates through in 1 hour of time. Right ascension increases eastward. 60º Declinations south of the celestial equator are negative. 45º 30º 20h 15º 4h 21h 3h 22h 2h 1 hour = 15º. 23h 1h The celestial equatorial coordinates of an object tell you the direction in which to point a telescope in order to see the object through the telescope. 0h -15º -30º