Daily & Annual Motions Key Ideas: Daily Motions Reflection of the Earth's Daily Rotation Circumpolar Stars Annual Motions Reflection of the Earth's Orbital Motion Ecliptic: The Path of the Sun Zodiacal Constellations Solstices & Equinoxes Daily Motions Objects in the sky appear to rise in the East and set in the West each day. This apparent daily motion is a reflection of the Earth's rotation about its axis. Earth rotates once a day (24 hours) The sense of rotation is Eastward Facing North, rotation is towards the Right. Apparent Paths The Apparent Paths of objects are parallel to the Celestial Equator. Their orientation depends on your latitude: At Equator: perpendicular to the horizon At Poles: parallel to the horizon Mid-Latitudes: Tilted by (90 Latitude)
Circumpolar Stars Any star closer than your latitude to your visible celestial pole (north or south) will always be above your local horizon. These are the Circumpolar Stars Ursa Major, Ursa Minor, & Draco are circumpolar constellations as seen from Columbus
(Click on the image to view it in color at full resolution [Size: 20Kb]) The opposite pole's circumpolar stars never rise above your horizon. Ursa Major never rises for latitudes south of about 40 S Summary of Daily Motions: Daily Motions of celestial objects reflect the Earth's daily rotation about its axis: Celestial objects to appear to rise in the East and set in the West. Apparent daily paths are parallel to the Celestial Equator. The inclinations of these paths relative to the horizon depends on the observer's latitude. Circumpolar objects are those always above or below the local horizon. Annual Motion of the Sun Over the course of a year, the Sun appears to move a little towards the East each day as seen with respect to the background stars. This daily eastward drift is <1 per day (there are 365 days in a year, but only 360 in a circle). This apparent motion is a reflection of the Earth's annual orbit around the Sun.
The Ecliptic The Ecliptic is the apparent path of the Sun relative to the stars. Great Circle projected onto the Celestial Sphere Tilted by approximately 23.5 from the Celestial Equator (Click on the image to view it in color at full resolution [Size: 22Kb]) This tilt is called the Obliquity of the Ecliptic The Obliquity of the Ecliptic varies between 21.2 and 24.5 with a roughly 41000 year period: Now (2007 Sept 26): it is 23 26' 17.826" In 2000 it was 23 26' 21.448" The Zodiac As the Sun moves along the Ecliptic as seen from Earth, it passes through 12 ancient constellations known as the Zodiac. Many date from Babylonian times. These are familiar from astrological lore: Aries, Pisces, Aquarius, Capricorn, Sagittarius, Scorpius, Libra, Virgo, Leo, Cancer, Gemini, and Taurus.
The Zodical Constellations can be used as a kind of an astronomical calendar: See which Zodiacal constellation is the highest (on your celestial meridian) at midnight. The Sun is in the opposite constellation. (Click on the image to view it in color at full resolution [Size: 21Kb], inspired by a drawing by Nick Strobel) A Note about the Zodiac: The amount of time the Sun spends in the region of a particular Zodiacal constellation does not, in fact, correspond to the calendar dates associated with the twelve "Sun Signs" in the newspaper and magazine astrology columns. This is no accident. As we will see later, the celestial equator slowly moves ("precesses") around the sky once every 26,000 years. This means that the celestial location of the Sun during a given month today has moved substantially since the common astrological traditions were codified by Ptolemy during the 2nd century AD. In fact, according to the constellation boundaries established by the IAU in 1888, at the present time the Sun actually passes through 13 constellations over the course of a year! In late November the Sun crosses over the northern part of Scorpius for about 5 days, after which it passes into the constellation of Ophiuchus until mid-december. Ophiuchus is, of course, not one of the traditional 12 constellations of the Zodiac. The amount of time the Sun spends in a constellation is also quite variable, and nowhere near the uniform time intervals suggested by traditional astrology. While both astronomy and astrology share common roots in the distant past, they bear no relation to each other today. Astrology as now practiced has strayed far from the reality clearly visible in the night sky.
Solstices Solstices occur when the Sun is at its maximum northern and southern declination. The word Solstice is derived from the Latin words "sol sistere" = "sun" and "stand still". Solstices occur twice a year in June and December: Summer Solstice: Maximum northern declination of the Sun (June). Winter Solstice: Maximum southern declination of the Sun (December). These names are ambiguous, as while in June it is Summer in the Northern Hemisphere, it is Winter in the Southern Hemisphere (and similarly flipped during December). You may occasionally see these called the "June" and "December" Solstices, respectively, in an attempt to not have a "Northern" bias, but this alternative is not widely used. Equinoxes Equinoxes occur when the Sun crosses the Celestial Equator. Derives from the latin "equinoctis" = "equal night". Equinoxes occurs twice a year, during March and September. Vernal Equinox: Sun crosses the Celestial Equator moving North (occurs in March) Autumnal Equinox: Sun crosses the Celestial Equator moving South (occurs in September) Like with the Solstices, there is a similar North/South ambiguity in their related seasons. In this case, however, the use of the latinate names (Vernal instead of Spring), signifies that we are using a strict astronomical definition that is agreed upon worldwide.
Length of the Day The length of the day depends on the location of the Sun along the Ecliptic. (Click on the image to view it in color at full resolution [Size: 18Kb]) Vernal & Autumnal Equinoxes: Occur in March and September, respectively. The Sun rises due East and sets due West. Day and Night have equal lengths (12 hours each). Summer Solstice: Occurs in June The Sun rises in the Northeast, and sets in the Northwest Day is longer than Night in the Northern Hemisphere Day is shorter than Night in the Southern Hemisphere Winter Solstice: Occurs in December The Sun rises in the Southeast, and sets in the Southwest Day is shorter than Night in the Northern Hemisphere
Day is longer than Night in the Southern Hemisphere Summary of Annual Motions: Annual Motions reflect the Earth's orbit around the Sun: The Ecliptic: Sun's path relative to the stars. The Obliquity of the Ecliptic: 23.5 Constellations of the Zodiac along the Ecliptic. Equinoxes: Sun crosses the Celestial Equator. Solstices: Sun at maximum North & South declination. Length of the day depends on the location of the Sun along the Ecliptic. The Four Seasons Key Ideas: The Four Seasons Due to the tilt of the Earth's axis relative to the plane of its orbit. NOT due to changes in the distance of the Earth from the Sun!!! The tilt of the Earth's axis affects The amount of direct sunlight (Insolation) The length of the day Precession of the Equinoxes The Obliquity of the Ecliptic The Earth's rotation axis is tilted relative to the plane of its orbit around the Sun: Tilt is about 23.5 degrees from perpendicular relative to the Ecliptic Plane. The Earth's axis points towards the same direction in space as we orbit around the Sun: Currently points near Polaris.
Changes slowly with time (as we'll see below) The Equinoxes In March & September: Axis is at right angles to the Earth-Sun line. The Sun is seen on the Celestial Equator. Day and Night are equal length (12 hours). Vernal Equinox Occurs around March 21 Northern Spring & Southern Autumn. Autumnal Equinox Occurs around September 21 Northern Autumn & Southern Spring.
Winter Solstice Occurs around December 21: The Earth's northern axis is tilted away from the Sun. The Sun is at its maximum southern declination as seen in the sky Northern Hemisphere Winter: The Sun is low in the sky. The day is shorter than the night Southern Hemisphere Summer: The Sun is high in the sky. The day is longer than the night Summer Solstice Occurs around June 21: The Earth's northern axis is tilted towards from the Sun. The Sun is at its maximum northern declination as seen in the sky. Northern Hemisphere Summer: The Sun is high in the sky. The day is longer than the night Southern Hemisphere Winter: The Sun is low in the sky. The day is shorter than the night The picture below summarizes the direction of the Sun at the four seasons:
(Click on the image to view at full scale [Size: 43Kb]) Insolation What matters for solar heating is how directly the rays of the sun hit the ground: Sun directly overhead (at Zenith): Maximum concentration of sunlight on the ground Approximately 1000 Watts/meter 2 of heating. Sun 30 above the Horizon: Sunlight spreads out over 2 meter 2 Get only 500 Watts/meter 2 of heating.
(Click on the image to view at full scale [Size: 14Kb]) The Earth-Sun Distance The Earth's orbit is slightly elliptical, so that the Earth is closer to the Sun at some times, and farther away at others. Aphelion (greatest distance): Earth is 152.1 Million kilometers from the Sun Occurs in July (e.g., 2007 July 7) Perihelion (closest approach): Earth is 147.1 Million kilometers from the Sun Occurs in January (e.g., 2008 Jan 3) The difference in distances is about 5 Million kilometers. While this seems like a lot (it is about 13 times the mean Earth-Moon distance), overall it makes only a ~7% difference in the total amount of solar radiation hitting the Earth.
Summer vs. Winter in Columbus June 21 (Summer Solstice) December 21 (Winter Solstice) Sun's altitude at noon: 73.5 Sun's altitude at noon: 26.5 Insolation: 960 W/m 2 Insolation: 450 W/m 2 Average high/low temperature: 80/58 F Average high/low temperature: 39/25 F Length of the Day: 15 h Length of the Day: 9 h Distance from the Sun: 152 Million km Distance from the Sun: 147 Million km Hottest & Coldest Months: Hottest Month: July (average high/low 84/63 F) Coldest Month: January (average high/low 34/18 F) Distance Doesn't Matter The Earth is 5 Million kilometers closer to the Sun in January than in July, yet January is the coldest month in the North! As seen from Columbus: 7% more total solar radiation in January than July Insolation January is <50% what it is in July Differences in seasonal insolation beat variations in solar radiation due to differences in the Earth-Sun distance every time. Seasonal temperature variations have nothing to do with changes in the distance of the Earth from the Sun.
Precession of the Equinoxes The Earth's rotation axis slowly wobbles or precesses about the Ecliptic Pole. (Click on the image to view at full scale [Size: 10Kb]) Slow westward drift of the rotation axis Takes ~26,000 years to complete 1 circuit Amounts to ~50"/year, or 1 degree in 72 years. Discovered by Hipparchus of Nicaea (c. 150BC), but may have been known to the Babylonians. Caused by tidal torques from the Moon & Sun. The Age of Aquarius Precession causes the Equinoxes & Solstices to drift westward over time. Vernal Equinox: Now in Pisces, will enter Aquarius in 2597 AD ("The Age of Aquarius") 1 AD: in Aries ("First Point of Aries")
Summer Solstice: Now leaving Gemini & entering Taurus 1 AD: in Cancer ("Tropic of Cancer") The "North Star" Precession also changes which star is the northern pole star, if any, over time. 2000 AD: Polaris is 0.75 degrees from the North Celestial Pole. Gets closest to the NCP in 2099. 2700 BC: NCP was near the star Thuban in Draco. Thuban was the pole star of the Old Kingdom of Egypt.
The Phases of the Moon Key Ideas: The Moon always keeps the same face towards the Earth. Rotation and Revolution are synchronous. Phases of the Moon: Fraction of the sunlit side visible to us. Lunar Sidereal & Synodic Periods: Lunar Sidereal Period: 27.3 days Lunar Synodic Period: 29.5 days Our Nearest Celestial Neighbor The Moon is a natural satellite of the Earth. Its orbit around the Earth is elliptical: ~0.15% out of circular. Tilted by 5 from the Ecliptic. Mean Distance: 384,400 km Perigee (Closest Approach): 363,300 km Apogee (Maximum Distance): 405,500 km Appears ~11% larger at Perigee than at Apogee Synchronous Rotation The Moon's rotation period is equal to its orbital period: The Moon completes 1 rotation about its axis in the same time as it completes 1 orbit around the Earth. As a consequence, the Moon always keeps the same face towards the Earth. Near Side: hemisphere facing towards the Earth
Far Side: hemisphere facing away from the Earth The synchronization of the Moon's rotation and orbit is caused by strong tidal forces from the Earth that effectively "locks" the Moon's orientation relative to the Earth. [Note: The degree of synchronization is not perfect for two reasons. First, the Moon's orbit is elliptical rather than circular, so that the Moon's orbital speed is faster at perigee and slower at apogee. This mismatch in the exact orbital and rotation rates results in an apparent east-west "rocking" motion of the Moon by about 7.9 degress over the course of a month. The second is that the axis of the moon's rotation is tilted by about 7 degrees relative to its orbital plane (like the Earth's 23.5 degrees). This leads to an additional north-south nodding motion over the course of a month. The combined rocking and nodding motion motion is called "libration". You can see libration in the lunation movie below.] Phases of the Moon The Moon produces no visible light of its own It shines only by reflected sunlight Surface is very dark, only ~7% reflective During the month, we see a complete cycle of Phases: The sunward hemisphere is fully lit. The opposite hemisphere is dark. The phase of the Moon depends on the fraction of the sunlit hemisphere visible to us.
Graphical depiction of the phases (click to see full-size) [Lunation Movie. This movie shows one month of lunar phases. Note how the moon appears larger at perigee and smaller at apogee. Also note the apparent nodding and rocking motions due to "librations" as mentioned above.] New Moon & Full Moon New Moon: Moon and Sun are on the same side of the sky. Near side is in total darkness. Moon and Sun rise together. Full Moon: Moon is opposite the Sun in the sky. The near side is fully illuminated. Moon rises as the Sun is setting.
Quarter Moon Quarter Moons occur when the Earth, Moon, & Sun are at right angles: Half of the near side is illuminated Half of the far side is illuminated First Quarter: Quarter Moon between New Moon and Full Moon. Last Quarter: Quarter Moon between Full Moon and New Moon. Sometimes also called "Third Quarter" With New Moon and Full Moon, they help to divide the Lunar Month into quarters. Waxing & Waning Waxing: increasing illumination Waxing Crescent: just after New Moon Waxing Gibbous: just before Full Moon Waning: decreasing illumination Waning Gibbous: just after Full Moon Waning Crescent: just before New Moon Moonrise, Moonset... You don't see all moon phases at all times Never see a crescent moon at midnight. Never see the last quarter moon at sunset. Never see a full moon during the day. Times of rising and setting depend on the details of the Earth-Sun-Moon configuration as viewed from the surface of the rotating Earth.
Moonrise and Moonset during Full Moon: (Click on the image to view at full scale [Size: 28Kb]) Full Moon rises as the Sun sets. The Full Moon is in mid-sky at Midnight. Full Moon sets as the Sun rises. Full Moon cannot be seen during the day. Other examples were given in class (Better, work out the approximate moonrise and moonset times for the current phase of the Moon, and then go outside and see if your predictions are correct!) The View from the Moon Question: What would an astronaut on the Lunar near side see during one month? Answer: See the Earth neither rise nor set, but stay nearly fixed at the same position in the sky. See the Earth rotate on its axis once every 24 h. See the Earth go through phases. Lunar Sidereal Period The Lunar Sidereal Period is the time it takes the Moon to complete one orbit around the Earth with respect to the stars. Moon's Sidereal period = 27.3 days
Also called the "Sidereal Month" The Sidereal Period of the moon is measured watching its motions against the background stars: The Moon on 1999 Oct 2: Last Quarter Moon in Gemini 27.3 days later on 1999 Oct 29: Waning Gibbous Moon in Gemini Note: The background constellation is the same 27 days later (Gemini), but the Moon is in a different, earlier phase (Waning Gibbous, which comes before Last Quarter phase). Lunar Synodic Period The Lunar Synodic Period is the time between successive New Moons. Moon's Synodic period = 29.5 days Also called the "Synodic Month" This is the month used by Lunar Calendars:
The Islamic calendar starts and ends on the New Moon, signaled by the first appearance of the Waxing Crescent moon. Why are they different? While the Moon orbits the Earth, the Earth orbits the Sun. Start at New Moon: Sun-Moon-Earth aligned. It takes the Moon 27.3 days to complete 1 orbit around Earth with respect to the stars. In the meantime, the Earth has moved through 27.3 days of its orbit (about 27deg along its orbit). The Moon & Earth must move together for an extra 2.2 days to re-align with the Sun. (Click on the image to view at full scale [Size: 9Kb]) A Note on Terminology: Sidereal is derived from the Latin word for star (sidus). A Sidereal Period denotes the time it takes for an object (for example, the Moon) to return to the same place as seen with respect to the stars. Synodic is derived from the Greek word synodos, meaning a "coming together" (e.g., a Church "Synod"). The Synodic Period of the Moon is therefore the time between the apparent coming together of the Sun and Moon on the same side of the sky at successive New Moons.
Synodic periods always require you to combine two Sidereal periods. In this case, we are combining the orbit of the Moon around the Earth (the Moon's Sidereal Period), and the Earth's orbit around the Sun (the Earth's Sidereal Period) together to compute the Synodic Period. Eclipses of the Sun & Moon Key Ideas: Lunar Eclipses Moon passes through the Earth's shadow Total, Partial, & Penumbral lunar eclipses Solar Eclipses Earth passes through the Moon's shadow Total, Partial, & Annular solar eclipses The Eclipse Year How often do eclipses occur? Umbra and Penumbra Because the Sun appears as a disk ~1/2 across, Sun shadows are fuzzy rather than sharp. This means shadows cast by the Earth & Moon are two-part shadows: (Click on the image to view at full scale [Size: 10Kb]) Umbra: Inner core of total darkness The disc of the Sun is completely blocked.
Penumbra: Outer, partial shadow Sun's disc is only partly blocked, with a bit peeking over the edge. Lunar Eclipses Lunar Eclipses occur when the Moon passes through the shadow of the Earth. They only occur during Full Moon when the Earth is between the Moon and the Sun. The Earth's umbra is ~1.4 Million km long: About 3.7x the mean Earth-Moon distance. Umbra's width is 9000 km at the distance of the Moon, or ~2.6x the Moon's diameter. The Earth's umbra is not totally dark because of light scattered by the Earth's transparent atmosphere. This gives the fully eclipsed Moon a slightly ruddy appearance (think about how the Sun looks reddish at sunset or sunrise). Three Types of Lunar Eclipses (Click on the image to view at full scale [Size: 10Kb]) Total Lunar Eclipse: Entire Moon is within the Earth's umbra. Can spend up to 1 h 40 m in the umbra
Whole show can last ~6 hours Partial Lunar Eclipse: Only part of the Moon enters the umbra. Penumbral Eclipse: Moon misses the umbra completely, only passes through the penumbral shadow. Because the Moon can be completely immersed in the Earth's umbra during a total lunar eclipse, these eclipses can be seen from the entire night-time hemisphere. This is in contrast to total solar eclipses as we'll see below. Solar Eclipses Solar Eclipses occur when the Earth passes through the shadow of the Moon. Solar Eclipses only occur during New Moon, when the Moon is between the Earth and the Sun. The Moon's umbra is only 380,000 km long: Just long enough for the tip to touch the Earth. But not large enough to cover the entire Earth. Solar Eclipses can be seen only where the shadow passes overhead. Types of Solar Eclipses (Click on the image to view at full scale [Size: 10Kb]) Total Solar Eclipse:
The observer is inside the Moon's umbra. The Moon completely covers the Sun. Partial Solar Eclipse: The observer is inside the Moon's penumbra. Only see part of the Sun covered by the Moon. Annular Eclipse: The Moon is at or near apogee, and so is too small to cover the Sun. The Moon's umbra does not touch the Earth, so observer's in the shadow path see the Sun as a ring ("annulus"). Total Solar Eclipses Total Solar Eclipses are localized and short: The Moon's umbral shadow is at most 267 km across on the Earth. Totality lasts at most about 7.5 minutes, with the shadow sweeping rapidly west-to-east. Only observers in the umbra see a total solar eclipse. Observers in the penumbra see a partial solar eclipse. Everyone else sees nothing. While we often sketch the penumbra as uniform, in reality the penumbra shades gradually from the completely dark umbra out towards the edges. The reason is simple: as you move outwards away from the edge of the umbra, you will see an increasing fraction of the Sun peeking out from behind the Moon. There is a very nice Mir image of the 1999 Aug 11 eclipse shadow showing what I mean. Why are eclipses rare? If the Moon's orbit were exactly aligned with the Ecliptic, we would see A solar eclipse every New Moon A lunar eclipse every Full Moon But, this clearly does not happen. Why?
The moon's orbit is tilted ~5 from the Ecliptic. Where the moon's orbit crosses the Ecliptic defines the "Line of Nodes" Eclipses only occur when the line of nodes and the Sun line up during Full Moon or New Moon. (Click on the image to view at full scale [Size: 9Kb]) Eclipse Year The Line of Nodes align with the Sun every 346.6 days. This is called the "Eclipse Year". But, it must be a Full or New Moon when the nodes line up to have an eclipse. This happens only very rarely. From a given location on the Earth you see a Total Lunar Eclipse every 3 years (or so). a Total Solar Eclipse every 360 years.