A. INTRODUCTION

B. THE MOON

• All of the apparent motions in the sky discussed in Lecture 3 were produced by the motion of the Earth. By contrast, the phases of the Moon are produced by the motion of the Moon in its orbit around Earth.

• The Moon's sidereal orbital period with respect to the stars is 27.3 days. Moves eastward (against the stars) in its orbit as viewed from Earth, about 13 degrees per day (changing rise/set times by ~50 minutes/day).

• Because Earth moves in its orbit around the Sun, the Moon does not return to the same position with respect to the Sun (e.g. 180 degrees away from Sun) for 29.5 days. This is called its synodic period and defines (roughly) our standard "month." (See illustration here .)

• The Moon exhibits drastic changes in apparent shape throughout the month, from crescent to round and back. The shapes are called phases of the Moon. Lunar phases had considerable practical consequences in pre-industrial societies which had to rely on the Moon for nighttime illumination. The Moon's surface is actually very unreflective (see the image above comparing the Earth and Moon). Its reflectivity, or "albedo," is only about 10%. Nonetheless, it is close enough to us to produce a large amount of light, and it is the second brightest object in the sky after the Sun.

• The phases were understood as early as 500 BC by the Greeks. The key clue is that the phase of the Moon correlates with its angular distance from the Sun. For instance, the Moon is in its crescent phase when it is near the Sun in the sky but full when it is opposite the Sun. The Greeks realized this implies the Moon is a solid sphere, in orbit about the Earth, half of which is always illuminated by the Sun. The situation is shown in this Java demonstration.
  

• In the figure above you are looking down on the Earth's North Pole. The Earth spins counterclockwise (in 24 hours), and the Moon orbits counterclockwise (in 27 days). The fraction of the Moon's sunlit hemisphere which we can see from Earth determines the lunar phase at any time. We see a "full," "crescent," or dark ("new") Moon depending on the angle between the Sun and Moon as viewed from Earth. An alternative version of the diagram above, with photographs of the Moon's appearance at each phase, is available here.
  • The diagram shows that a first quarter Moon is 90^o away (east) of the Sun and that a full Moon is 180^o away from the Sun. The Moon will be in a crescent phase when is it less than 90^o away from the Sun and a gibbous phase when between 90^o and 180^o away.

• You can also use the figure above to determine when the Moon in a given phase will rise, transit, or set. Use the concept of the horizon plane, and note that the positions A, B, C, and D correspond to places where observers experience noon, sunset, midnight, and sunrise, respectively.
  • Drawing a horizon plane at B, for instance, allows you to infer that a first quarter Moon will transit at sunset; a full Moon rises at sunset; and a waning gibbous Moon is not visible at sunset (below the horizon and not yet risen).

• This time lapse movie (472K) composed of still photographs of the Moon during a 29.5 day cycle vividly illustrates the relationship between shadowing and phases. The changes in the apparent size of the Moon and the slight "rocking" motion (known as libration) are caused by the fact that the lunar orbit is significantly non-circular in shape.

• The Moon repeats its phases after its synodic period of 29.5 days. This means the phases are almost, but not quite, synchronous with our calendrical months (of 28, 30, or 31 days). The phase of the moon on a given day of the month therefore shifts systematically throughout the year and from one year to the next.

1. Tides. The gravity of the Moon combined with the Sun is responsible for the tides in the ocean. We will not discuss tides further in the course.

2. Precession
   The gravity of the Moon & Sun act on the "bulge" at Earth's equator, causing a gradual cyclical change in the direction of the Earth's spin axis called precession. Projected on the celestial sphere, the poles slowly trace out large circles at a rate of 0.5 degree per century. It takes 26,000 years for the poles to complete one cycle. See figure below. Though subtle, precession was first detected in 150 BC by the Greek astronomer Hipparchus.
   

   
   

   Polaris is a convenient "North Pole star" now, lying about 1 degree from the true North Celestial Pole. However, it will not be as useful in a few 1000 years. Vega will be close to the pole 14,000 years from now, but most of the time there is NO useful pole star. This animation shows the pole position as a function of date (Note: the point labeled "zenith" in the drawing is actually the "North Pole".)
   Precession changes the location of the equinoxes as well as the celestial poles. The vernal equinox moves from one constellation of the Zodiac to the next in about 2000 years. Thus, precession changes the RA,DEC coordinates of all astronomical objects. The maximum annual change is about 10 seconds of time in RA and 20 seconds of arc in DEC. (See the table in Norton's Star Atlas.) Because of precession, all listings of RA,DEC must have the "epoch"---i.e. the date for which they are valid---specified. Most listings will now give epoch 2000 coordinates, though some still use 1950.

• Eclipses are shadow effects. There are two types: lunar eclipses and solar eclipses. Both can be dramatic and beautiful events, for properly situated observers on Earth.
  
• Eclipses occur when the shadow of the Earth strikes the Moon (a lunar eclipse) or the shadow of the Moon strikes the Earth (a solar eclipse for observers in the shadow path). A multi-exposure image of a solar eclipse is shown above. A lunar eclipse is shown at the right (click for enlargement).
  

  
  

• The figure above shows the shadow configuration for a solar eclipse (not to scale). Anyone along the path where the tip of the Moon's shadow strikes the Earth will experience a total solar eclipse. The shadow moves rapidly across the Earth because the Moon moves rapidly in its orbit.

• You can also see that if the Moon moves into the Earth's shadow on the other side of its orbit, it will suffer a lunar eclipse. Referring to this figure and the one above which shows the phases, we can see that see that:
  • A solar eclipse can only occur near New Moon and

  • A lunar eclipse can only occur near Full Moon

• Eclipses can be total or partial, depending on whether the core or periphery of the shadow is involved. Because of the different sizes of the two shadows, a total lunar eclipse can last up to 90 minutes while a total solar eclipse lasts only up to 7 minutes. Lunar eclipses are easy to observe because they can be seen from any location on Earth where the Moon is above the horizon. Solar eclipses are observable only from within the path of the Moon's (rapidly moving) shadow on the Earth's surface.
  A total solar eclipse is interesting mainly because the Moon just barely covers the luminous surface of the Sun and you can see the surrounding solar atmosphere ("chromosphere" and "corona") which is usually hidden in the glare. The rapid fall of "night" coupled with the appearance of the corona are very dramatic for observers in the shadow path.
  As viewed from the Earth, the Sun and the Moon have nearly the same size, about 0.5 degree, (even though they are, of course, of vastly different intrinsic sizes). If the Sun appeared much larger than the Moon, there would never be total eclipses, and if the Moon appeared much larger than the Sun, eclipses would be less interesting aesthetically and scientifically---though they would last longer.

• The Moon, Earth, and Sun must be perfectly aligned for an eclipse to occur, meaning that the Moon must be almost exactly in the ecliptic plane during an eclipse (hence the name of the plane). Because the Moon's orbit is actually tilted 5^oout of the plane, eclipses follow a complicated pattern in time. For more information on eclipses, see Espenak's Eclipse Home Page.

  
  

• The Moon has no atmosphere, so there is no obscuration of its surface features. More importantly, these are not subject to weathering. The Moon's surface has been shaped over 4.5 billion years by the relentless impact of asteroids, meteoroids, and smaller interplanetary debris. Almost all of its geology is related to impacts.

• The numerous craters (up to 150 mi diameter) are the best indicators of impacts. Unlike on the Earth, almost none of these are related to volcanic activity. The mountains on the Moon (drawing at right), which range up to 25,000 feet, are also impact effects, not the products of plate tectonics as on Earth.

• The rounded, dark grey areas (part of the "man in the Moon" face) are called maria ("seas"), even though we now know they contain no water. They are the products of massive impacts by asteroidal bodies which were later filled in by dark lava. They have smooth surfaces except for a few craters. These regions are younger than the lighter grey, rougher "highland" regions. Ages can be estimated by the crater density (fewer craters implies younger regions).

• Click here for more illustrations and descriptions of lunar topography.

C. PLANETARY ORBITS

• The planets condensed out of the solid debris which surrounded the Sun as it formed. Their orbits consequently lie in almost the same (physical, 3D) plane. The picture above shows an oblique view of the planetary orbits to scale (though the planet sizes shown are not to scale). Here is an edge-on plot of the orbits showing the near-coincidence of the orbital planes.

• This means that all of the planets (except Pluto) will always be observed in a relatively narrow band in the sky, centered on the ecliptic. They therefore move through the Zodiacal constellations.

• The observed motions of the planets in the sky are limited by orbital geometry and are a combination of the intrinsic motion of the planets and the motion of the Earth.
  

  
  

• See the illustration above. All planets move in the same direction around the Sun (counterclockwise as seen from above the Earth's North Pole).
  Right panel: As viewed from the Earth, the two planets inside the Earth's orbit ("inferior" planets) will never appear at large angles from the Sun. Mercury and Venus always stay within 27^o and 48^o, respectively, of the Sun.
  Left panel: The planets outside Earth's orbit ("superior" planets), starting with Mars, can be seen at up to 180^o from the Sun. At that point they transit at midnight and are said to be at "opposition" with respect to the Sun. As the figure shows, planets at opposition are also nearest the Earth then and are therefore brightest.

• The planetarium simulation in the image below shows the concentration of the planetary orbits, as seen from Earth, to the ecliptic.
  Time lapse exposure of a planetarium simulation
  of several years of planetary motions as seen from Earth.

  
  

• The loops in the trajectories in the image above are caused by the Earth's annual motion around the Sun. Planetary motions are generally eastward, with the "retrograde loop" caused by the Earth's motion superposed. The retrograde motion for a superior planet is greatest at opposition. Here is an animation showing how retrograde motion is produced.

D. OBSERVING THE PLANETS

• MERCURY: Hard to observe only because it is always near the Sun and never very far from the horizon at night. Surface features are too subtle to be detected in a small telescope. Like Venus, shows phases.

• VENUS: Dazzling white in the sky. Can be astonishingly bright and is the source of more UFO reports than any other astronomical object. [Reality check: Watch for 5 minutes; is the "UFO" stationary with respect to the stars? Is it within about 40^o of the western or eastern horizon? Is it in a Zodiacal constellation? If yes, then it's probably Venus.]
  • Venus is the planet nearest Earth and has the orbital period most closely matching Earth's. Consequently, it can "linger" near the horizon before sunrise or after sunset, undergoing a complex set of motions over several month's time. See our Starry Night demonstration.

  • Unfortunately, Venus is shrouded in dense clouds (made of sulfuric acid droplets!), and you cannot observe its surface. However, it shows pronounced phases, like the Moon's (see illustration here), as it orbits the Sun. Neither Venus nor Mercury have satellites.

  
• MARS: Undergoes large changes in distance, and consequently brightness, from Earth. Brightest at opposition (once every 2.1 years), but because of its relatively elliptical orbit, its distance at opposition can vary by a factor of two (see diagram). Click here for a Java animation of the relative motion of Earth and Mars. At opposition, it can be brighter than Jupiter. In August 2003, Mars will be closer to the Earth than at any time in the last 16 years.
  • Mars' atmosphere is primarily CO₂ and is transparent. Its color is conspicuously red-pink (hence its association with the God of War), caused by iron oxide compounds = rust on its surface. Its surface has been explored with ever increasing resolution by Earthbound telescopes, orbiting spacecraft, and lander spacecraft. Use the links below to reach the large and beautiful set of spacecraft images of Mars. The image at the right was taken from Earth orbit by the Hubble Space Telescope.
    
  • Mars is distant enough that even at opposition telescopes on Earth yield relatively poor resolution (especially since they must contend with seeing), and this led to a long and controversial history over whether or not there was evidence for "canals" or other artificial features on its surface. (More details given here.)

  • However, under good conditions with an 8-in telescope, you can easily see the polar caps (some water but mainly frozen CO₂) and contrasting red and grey markings on the surface. Monitoring these features over several months will reveal slow changes, including growth or shrinking of the caps with the seasons and effects of dust storms on the surface, especially in the Martian spring.

• JUPITER: A very bright, yellowish object, normally the fourth brightest in the sky (after the Sun, Moon, and Venus). Celestial motion is much slower than any of the planets already discussed.
  
  • Unlike the four terrestrial planets, Jupiter, Saturn, Uranus, and Neptune are gas giants and have no sharp boundary between interior and atmosphere. The banded structures in Jupiter's atmosphere, called "belts" (dark) and "zones" (light), are cloud layers, and an 8-in telescope often reveals beautiful details. The red spot is an oval-shaped, perpetual cyclone in the atmosphere, about 3 times the diameter of Earth (seen near the right hand limb in the picture at right). Because Jupiter rotates in only 10 hours, you get to see a variety of features in just a few hours.

  • Jupiter has a satellite system, consisting of 28 known moons, mostly small. The four largest of these (Io, Europa, Ganymeade, Callisto) were discovered by Galileo and are known as the Galilean satellites. They are easy to see in a small telescope, and their relatively rapid orbital motions around Jupiter can be readily tracked. NASA's Voyager and Galileo missions revealed astonishing differences in surface constitution among the four. In small telescopes, unfortunately, no surface details are apparent.

• SATURN: Famous as the ringed planet, though all four gas giants actually have rings. Its cloud layers are deeper within its atmosphere than are Jupiter's, so it typically shows only faint surface banding. The rings are orbiting chunks of rock and ice and lie exactly in the equatorial plane of the planet. They are spectacular in small scopes, and a fair amount of substructure, especially the dark "Cassini Division" seen in the image at the top of this page, is visible. Spacecraft reveal hundreds of ringlets. Six of Saturn's 22 satellites would be visible in an 8-in telescope. The largest, Titan, is the only moon to have its own atmosphere.

• URANUS and NEPTUNE: All of the above planets were known to naked eye astronomers. The other three are products of the telescopic age. Uranus and Neptune are distant enough that they show only small blue-green disks in an 8-in telescope, without further details being visible (they have very low contrast atmospheres even seen close up). You will need a finding chart to locate them. Their satellites are too faint for detection in the 8-in scopes.

E. INTERPLANETARY MATTER

• COMETS: are chunks of ice which evaporate when they get within several Astronomical Units of the Sun (one AU = the distance between Sun and Earth), producing a gaseous coma and sometimes a tail. The Solar System contains billions of comet nuclei, but most are beyond the orbit of Neptune. Most have very elongated orbits and reach small distances from the Sun only infrequently. Some, however, are gravitationally deflected by Jupiter into orbits with shorter periods (< 100 years); these are called "periodic" comets. Most are faint. Halley's is an exception as a bright periodic comet. The most spectacular comets, like Hale-Bopp (at right) are usually first-time visitors to the inner Solar System. Click here for more information on Hale-Bopp. There are always several faint comets available to observe in the sky; but bright ones are rare: once a decade or so.

• METEORS: are the incandescent trails of tiny pieces of rocky or icy debris burning up at high altitudes in the Earth's atmosphere. Up to about 10 per hour can be seen on dark nights at any time of the year. Debris left behind by comets can produce concentrated meteor showers with much higher rates, up to 1000's of meteors per hour in rare instances. The Leonid shower (Nov. 17-18) was good in 1998 and 1999. Click here for plans for observing this semester's shower.

• ASTEROIDS: Also called "minor planets," asteroids are large rocky or metallic chunks ranging from less than a few meters to hundreds of kilometers in diameter. They move in their own orbits around the Sun. Most orbits are concentrated between Mars and Jupiter, but many cross the Earth's orbit. Ceres, 1000 km in diameters, was the first discovered (1801). There are now over 38,000 known(!)
  • Here is a snapshot plot of the location of asteroids in the inner Solar System.

  • Many asteroids are detectable with an 8-in telescope, but you need finding charts. Their signature is a fairly rapid motion with respect to the background stars.

  • Here is a video (266 kb) of the asteroid Eros taken by amateur astronomer Gordon Garradd.

• Consult Chapter IV of Norton's Star Atlas for additional information on Solar System observations, as needed. You are not required to know all the material there.

• Finish Lab 2 and move on to work on Lab 3.

• A set of sample questions & problems concerning the material covered in the lectures was handed out in class and is available on the course webpage. These are not to be handed in and will not be graded, but you should work through them in preparation for the Midterm Exam.

Lunar Phase Now
Lunar Info for Amateur Astronomers
Guide to Lunar Observing (A. Cidadao)
Espenak's Eclipse Home Page: everything you could possibly want to know about eclipses.
Information on the Planets ("The Nine Planets")
Information on the Planets ("Views of the Solar System")
Mars Open Directory
Mars in Literature, Film, etc
Java Simulator of Comet & Asteroid Orbits (UMd)
JPL Asteroid Home Page
Sky & Telescope Comet Page
JPL Comet Home Observation Page
Information on the Leonid Meteor Shower
Local Plans for Observing the 2002 Leonid Shower