Moon & Eclipses
Outline
1. Lunar Facts
* Distance/diameter relative to Earth
* Orbit: period = 27.3 days
* Far side, near side
2. Motion of the Moon
* Daily: east to west
* Monthly: eastward relative to stars
* Orbit plane tipped relative to Earth's orbit (ecliptic) plane; line of nodes
* Lunar rotation: rotation period = orbit period
3. The Lunar Phase Cycle
* New, crescent, gibbous, full phases
* Understanding the phase cycle
> Results from viewing (from Earth) different fractions of half-illuminated moon
* Phase (synodic) period = 29.5 days
* Phase visibility: When do different phases appear in the sky?
4. Eclipses
* Shadows
> Umbra, penumbra
* Lunar Eclipses
> Moon in Earth's shadow
> Full Moon, Moon along nodal line
> Maximum duration of totality ~ 100 min
> Illumination of Moon due to refraction, scattering of sunlight in Earth's atmosphere
* Solar Eclipses
> Earth in Moon's shadow
> New Moon, Moon along nodal line
> Zone of totality (~100 mi wide)
> Maximum duration ~ 7.5 min
* Annular Eclipses
> Moon's orbit not a circle
> Moon's umbra does not reach Earth
> Ring (annulus) of sun viewed
* How often do eclipses occur?
> Solar: twice per year, somewhere
> At given location: solar total once per 360 yrs
> Lunar: twice per year, somewhere
Diagram
Questions
1. The Moon circles Earth with orbit period 27.3 days. From Earth, we view this as the Moon circling (eastward) on the celestial sphere once every 27.3 days.
a) So, how many degrees/day does this amount to?
b) The Moon's angular diameter is 0.5o. How many of its own diameters does the Moon move (relative to the stars) in one hour?
c) Suppose the Moon's orbit period were 51 days instead of 27.3 days. How would this change alter the Moon's angular speed in our sky?
2. Why does the Moon exhibit phases?
3. What is the line of nodes, and how is related to lunar and solar eclipses?
4. What is the difference between the umbra and penumbra of a shadow?
5. What type of eclipse - lunar or solar - do you think most people have seen? Why?
6. How is an annular eclipse of the Sun different from a total eclipse of the Sun? What causes this difference?
7. What is the phase of the Moon if it (a) rises at 3 am? (b) sets at 9 pm? At what time (c) does the full moon set? (d) the first quarter moon rise?
8. At what time does the waxing crescent moon set?
9. You spot the Moon in the sky at 4 pm. What is its phase?
10. What is the phase of the Moon if, on March 21, the Moon is located at (a) the vernal equinox? (b) the summer solstice?
11. During a lunar eclipse, does the Moon enter Earth's shadow from the east or the west? Explain your answer. [See FIG 3 above]
12. Describe how a lunar eclipse would look (viewed from Earth, of course) if Earth had no atmosphere.
13. Prob. #3, pg. 49.
14. Prob. #4, pg. 49.
Answers
1. a) 360o/27.3 days = 13.2o/day
b) 13.2o/24 hr = 0.55o, so the Moon moves about 1 lunar diameter per hour (!)
c) The angular speed (the number of degrees moved per day) would be smaller.
2. The moon is always exactly one-half illuminated by the Sun (as is Earth). But as the Moon orbits Earth, we view only part of the illuminated half
3. The line of nodes is the line of intersection between Earth's orbit plane (the Ecliptic Plane) and the Moon's orbit plane. It's only when the Sun lies on this line at Full moon or new moon that we have an eclipse.
4. The umbra is the dark, inner shadow. If you find yourself in the umbra, the source of light (e.g., the Sun) is completely blocked, as in a total solar eclipse. On the other hand, within the penumbra, the source of light will be partly visible (as when the Sun is partially eclipsed).
5. Lunar eclipses are routinely observed by many more people than solar eclipses because a lunar eclipse is visible to all people on the dark (nighttime) side of Earth. This could represent half the Earth's population. On the other hand, solar eclipses are visible only to people located along a narrow path (the path of the shadow) on Earth.
6. During an annular eclipse, the disk of the Moon does not quite cover the disk of the Sun - leaving a ring ('annulus') of unobscured solar surface still in view. During a total solar eclipse, the entire Sun's disk is covered by the Moon. Annular eclipses occur when the Moon is far enough from Earth so that its shadow cone does not quite reach Earth's surface.
7. a) The waning crescent Moon rises at 3 am. b) The waxing crescent Moon sets at 9 pm. c) The full Moon sets at sunrise. d) The first quarter moon rises at noon.
8. The waxing crescent moon sets at 9 pm.
9. It could be any phase from waxing crescent to waxing gibbous.
10. a) The Moon's phase is new. b) The Moon's phase is first quarter.
11. The Moon enters Earth's shadow from the west, as the Moon moves eastward relative to the stars.
12. The Moon would look quite black (i.e., it would be invisible) as the atmosphere brightens and reddens the Moon due to refraction and selective scattering of sunlight.
13. a) At full Moon, Earth would appear to be in new phase. It would be daylight where you lived on the Moon (in fact, it would be approximately noon where you live).
b) You would not see Earth rise and set; the Earth would be stationary in your sky (relative to your horizon) as you would be located on the side of the Moon (the near side) that always faces Earth. (If you always face Earth, how can it disappear from your sky, as it would do were it to set?)
c) Solar eclipse: It would be nighttime for you, about midnight. You might be able to observe the Moon's shadow cone intercepting Earth, but Earth would change very little in brightness in your sky as the eclipse progressed. Lunar eclipse: It would start out as daytime for you (about noon), but as the Moon entered Earth's shadow, the sun would slowly be eclipsed by Earth. It is unlikely that you would see much of the Sun's corona as Earth's angular diameter viewed from the Moon is much larger than the Moon's angular diameter viewed from Earth. You might see a faint reddish glow around the disk of Earth as light from the Sun is refracted (and scattered) by Earth's atmosphere.
14. At twice it's present distance from Earth, the Moon's angular diameter would be only 0.25o, instead of its present 0.5o. This small angular size would never completely cover the Sun's disk (which would remain at 0.5o), so total eclipses of the Sun would never occur. Annular eclipses would continue to occur, because during an annular eclipse, only the central part of the Sun's disk is covered by the Moon, and this is still possible for the Moon's reduced angular diameter. Total lunar eclipses are still possible because Earth's shadow is long enough to intersect the Moon, even at twice the current distance of Moon from Earth.