Lunar Phases (1)
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Apr 3, 2024
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Lunar Phases
Earth’s only natural satellite, the moon, rotates one full time every 27.3 days with respect to the background stars. The moon completes one orbit around the Earth in the same amount of time, 27.3 days. Since the orbital period and rotational period are equal, synchronous rotation
, we always see the same ‘face’ of the moon. As the moon orbits the Earth, it exhibits 8 different phases due to the position of the moon and sun relative to the Earth (
See diagram below)
. The phases are defined based on the percentage of the moon’s surface that appears illuminated from the Earth’s surface and whether the illumination is increasing, waxing
,
or decreasing, waning
.
When the illumination is waxing, the right side of the moon’s
surface is illuminated, but when it is waning, the left side of the moon’s surface is illuminated. Since the Earth is orbiting the sun at the same time the moon orbits the Earth, it takes just a little bit longer than the orbital period, 29.5 days
, for the moon and sun to return to the same positions relative to the Earth for the same illumination to occur (i.e., full moon to full moon or new moon to new moon). This is called the synodic period
, or lunar phase period. There are four cardinal phases, the new moon phase
(0% illumination), the quarter phases
(50% illumination), and the full moon phase
(100% illumination), that occur for only a single instant. The new moon occurs when the moon is directly between the sun and the Earth. The full moon occurs when the Earth is directly between the sun and the moon. The quarter phases occur when the sun and the moon make a right angle with the Earth. The intermediary phases are crescent
, greater than 0% but less than 50% illumination, and gibbous
, greater than 50% but less than 100% illumination. The intermediary phases require the “waxing” or “waning” terms to fully describe them. In this ‘top-down’ view or the moon’s orbital path, the moon moves in a counterclockwise direction around the Earth. The side of the Earth and moon that are closest to the sun are illuminated, and the sides facing away from the sun are covered in darkness. From the surface of the Earth, we can only perceive the half of the moon that is closest to the Earth, leading to the images shown in the outermost ring of the diagram. Since the phases of the moon occur when the moon and sun are in specific locations relative to the Earth, it is easy to approximate the rise times and set times of the moon. If we assume it takes 24 hours
for the Earth to rotate, and assume the moon is at the celestial equator, then the moon will be in the sky
for 12 hours. If we make the same assumptions with the sun, it would spend 12 hours in the sky and would rise at 6 a.m. and set at 6 p.m. When the moon is in the new moon position, it rises with the sun at approximately 6 a.m. and sets with the sun at approximately 6 p.m. The midday positions, at the meridian, of these objects would occur halfway between the rise and set times. As you work your away around the positions shown in the diagram in a counterclockwise direction, the rise and set times increase by three hours. For example, the waxing crescent in the next position after the new moon would rise at 9 a.m. and set at 9 p.m.; the first quarter moon would rise at 12 p.m. and set at 12 a.m., etc. These values of course vary (based on whether or not we are in daylight savings time, our distance from the center of a time zone, the declination of the moon/sun, etc.) in the real world, but these approximations help us get an idea for where the moon will be in the sky at a given
time of day based on the phase it is currently in as you will discover in this week’s activity. Use the ‘
Lunar Phase Simulator
’ to help you determine the answers to the following questions.
1. The moon rotates one time every 27.3 days with respect to the background stars as it orbits the Earth.
Is there a permanent dark side of the moon? *Explain your reasoning.
Half of the moon is always dark, as only half of the moon is illuminated by the sun. As the moon rotates one side remains illuminated whilst the other is in shadow. Even when the moon look ‘half illuminated’ to us on Earth, we just aren’t seeing the other quarter that is illuminated. 2. How long, in days, does it take between subsequent full moon phases? Hint: this question is asking you about the synodic period
(lunar phase period) of the moon.
29.5 days. 3. Suppose the moon is in the full moon phase today. Identify the phase after:
a. One week (7 days after the full moon)
Third quarter
b. One month (30 days after the full moon)
full moon
4. List all phases in the correct order, starting from the new moon phase.
New moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, third quarter, waning crescent.
5. Identify the correct phase
a. 80% of the moon’s surface is illuminated from the right side
waxing gibbous
b. 25% of the moon’s surface is illuminated from the left side waning crescent
c. 70% of the moon’s surface is illuminated from the right side
waxing gibbous d. 50% of the moon’s surface is illuminated from the left side
third quarter 6. Identify the correct horizon (eastern or western).
a. Does the moon rise
in the east or the west?
East
b. Does the moon set
in the east or the west?
West
7. In general, knowing two of the three following things allows us to estimate the third:
a. Moon’s position in the sky
b. Time of day
c. Lunar phase
If we know the moon’s position in the sky
and the time of day
, we can estimate... (What is the activity called this week?)
Lunar phase.
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8. Look at the following pictures of the moon’s appearance and use the simulation to help you determine the moon’s phase. Phase: _________
Waxing Crescent
__________________
Phase: ______
Waxing Gibbous
_______________________
Phase: _________
Waning Crescent
____________________
Phase: __________
Waning Gibbous
____________________
What do you notice about the illumination with each waxing and waning phase? (Which side of the moon is illuminated when the moon is in its waxing phases? Which side is illuminated for the waning phases?)
For the waxing phases of the moon, the right side of the moon is illuminated, whilst in the waning phases, the left side of the moon is illuminated. Keep this in mind when you do your lunar observations for the observation project this semester! (Although, it’s possible that the moon may appear to rest at a slight tilt when you observe it in the sky.)
9. Use the ‘Lunar Phase Simulator’ to determine the approximate rise time, meridian crossing time, and set time for the moon in each of the phases. You can adjust time by days, hours, and minutes using the controls in the bottom-left panel – but, you can generally focus on adjusting the time by hours (see the examples given in the table below). The cardinal directions in blue, located above the table, indicate in which direction you would have to look to see the moon in the sky at specific times. For example, anytime the moon rises, it will rise in the east; every time the moon crosses the meridian, it will be located due south in the sky; every time the moon sets, it will set in the west.
*Make the assumption that the sun rises at ~6 am and sets at ~6 pm. Azimuth of Moon:
E 🡪
SE 🡪 S 🡪 SW 🡪 W
Phase
Rising Time
Meridian Crossing Time
Setting Time
New Moon
~6am
~12 pm
~6pm
Waxing Crescent
~9 am
3pm
9pm
First Quarter
12pm
6pm
12am
Waxing Gibbous
3pm
9pm
3am
Full Moon
6am
~12am
~6 am
Waning Gibbous
~9pm
3am
9am
Third Quarter
12am
6am
12pm
Waning Crescent
3am
9am
3pm
10. Use the data from question 9 to answer the following questions.
a. Approximately how many hours does it take for the moon to travel from the eastern horizon to the meridian? 6 hours
b. How many hours does it take for the moon to travel from the meridian to the western horizon?
6 hours
c. Approximately how many total hours is the moon above the horizon?
12 hours
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11. Use the information you learned in question 9 to try and predict the missing entry in each row of the
table below. Use the simulation to check your answers, and then record the correct answers. Time
Location
Phase
Noon
Rising
Eastern Horizon
First Quarter
3 pm
Southwest
First Quarter
12am
Western
Horizon
First Quarter
9 pm
Rising
Eastern Horizon
Waning Gibbous
3 am
Southwest
Third Quarter
Midnight
Southwest
Waxing Gibbous
12pm
Southeast
Waxing Crescent
12. The image below shows the Sun-Earth-Moon positions during a solar and lunar eclipse. During a solar eclipse
the moon casts a shadow onto the Earth. Observers in the darkest part of the shadow, the umbra,
will observe a total solar eclipse
where the entire disc of the sun is covered by the moon, and observers in the lighter part of the shadow, the penumbra
will observe a partial solar eclipse
where part
of the disc of the sun will still be visible. During a lunar eclipse
, the Earth casts a shadow onto the moon.
A total lunar eclipse
occurs when the whole moon is in the umbra, a partial lunar eclipse
occurs when any part of the moon enters the umbra, and a penumbral lunar eclipse
occurs when any part of the moon is located in the penumbra. Answer the following questions based on the diagram below. Eclipses don’t necessarily occur every time the sun, Earth, and moon are in these alignments because there is a 5
∘
tilt between Earth’s orbital plane and the moon’s orbital plane which can cause the shadows being cast to miss the necessary object for the eclipse to occur.
a. What is the approximate phase of the moon during a solar eclipse?
New moon
b. What is the approximate phase of the moon during a lunar eclipse?
Full moon
c. Based on what you see in the diagram, why do lunar eclipses happen more often than solar eclipses?
*What do you notice about the sizes of the shadows produced by each object?
Because during a lunar eclipse it is much easier for the moon to be in the Umbra. The Umbra is much larger, and the shadow cast by the Earth is much greater than the shadow that would be cast by the moon during a solar eclipse.
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