Two models to explain Moon phases
Oftentimes in science, more than one “model” or explanation for a natural phenomenon can be
imagined. In these cases, scientists devise testable predictions of the various models. Then
scientists conduct experiments or observations of nature to see which predictions are most
closely borne out. The model whose predictions are best borne out in nature is then considered
most likely to be correct. (Of course, it is possible that none of the imagined models is correct.
In this case, scientists must scratch their heads and think of yet new models.)
For example, consider the cause of phases of the Moon. When most people are asked about
phases of the Moon, they offer one of two explanations or “models”.
1. Moon phases are caused by the shadow of the Earth on the Moon – According to this
model, the Earth casts its shadow on the Moon. At different times, the Earth’s shadow
covers more or less of the Moon, thus accounting for the different phases of the Moon.
2. Moon phases are caused by different angles between the Moon, Earth and Sun –
According to this model, the angle between the Moon and Sun changes over time. As a
result, we see different fractions of the Moon’s illuminated hemisphere at different times,
thus accounting for the different phases of the Moon.
Recall that a model in science is a conceptual description of some phenomenon in nature. (For
example, we talked about the “celestial sphere” model in class, even though we know that this
particular model is not literally correct.) In this inquiry project, you will be asked to develop
testable predictions for each of the two Moon phase models above. Then you will be asked to
gather data, as described below, and test your predictions to determine which model best fits
your predictions. In so doing, you will be learning about how science works.
• An example of a model and a testable prediction – Suppose this project were about
seasons. Then your model might be as follows: “The Earth goes around the Sun in an
elongated orbit, causing the distance between the Earth and Sun to vary significantly during
the year. This yearly variation in Earth-Sun distance causes seasonal variations in
temperature on the Earth.” A testable prediction might be as follows: “Everywhere on
Earth, temperatures should be highest on about the same date of the year, namely the date
when the Earth is closest to the Sun. Therefore, summer should take place all over the Earth
at around the same time of year.” Note that this particular model is false. Nonetheless, if the
project were about seasons, you could gather temperature data throughout the year for
various locations on Earth (Northern and Southern Hemispheres), compare these data with
your prediction, and infer that the model is false. Then you would try to create another
model about seasons for which the testable predictions were verified by the data.
AST Inquiry Project
Ready? Please follow steps 1-5 below. Don’t worry if everything is not 100% clear to you,
especially when you first read these steps. Things are rarely 100% clear in science, especially at
the beginning of an investigation.
1. Develop testable predictions for the moon phase models
Think about testable predictions for Moon phases, based on the two Moon phase models listed
above. By comparing your predictions with naked eye Moon observations and, especially, with
web data on Moon phases, you can argue which model above is correct. Of course, you may
already know which model is correct. If so, good for you! Nonetheless, you are asked in this
inquiry project to clearly demonstrate why you think one Moon phase model is correct and the
other is incorrect.
To help you develop testable hypotheses for both models, recall that the Moon orbits the Earth in
about one month’s time. Then consider these questions:
• If Moon phases are caused by the shadow of the Earth on the Moon (model 1), where do you
predict the Moon should lie in its orbit when the Moon is new? (It might help you to make a
simple drawing of the Earth, the Moon’s orbit about the Earth, and the Sun off to one side.
Your drawing need not be to scale.) What will be the angle between the Sun and the Moon
in the sky at new Moon? Note that new Moon is the phase in which all of the Moon’s face is
dark in our Earthly sky. So in model 1, the Moon must be entirely in the shadow of the Earth.
• If Moon phases are caused by the shadow of the Earth on the Moon (model 1), is the Moon
full for most of the lunar month, for part (say, about half) of the lunar month, or for only a
small fraction of the lunar month (say, a day)?
• If Moon phases are caused by different angles between the Moon and Sun (model 2), then
how should the illuminated fraction of the Moon’s face be related to the angle between the
Sun and the Moon in the sky? For example, when half of the Moon’s illuminated
hemisphere is visible from Earth (“half moon” in popular language), what should the angle
be between the Sun and Moon in the sky?
• If Moon phases are caused by different angles between the Moon and Sun (model 2), is the
Moon full for most of the lunar month, for part (say, about half) of the lunar month or for
only a small fraction of the lunar month?
To Do – Using the questions above and/or your own ideas, develop two testable predictions for
each of models 1 and 2. You should briefly explain your reasoning for each of these testable
hypotheses.
2. Make naked eye observations of Moon phases in the sky
• How many Moon phase observations to make – You are asked to observe the phase of the
Moon in the sky on at least four days over a roughly two week period. However, more
observations over a longer period are encouraged if your schedule and the weather permit.
• What information to record – For each Moon observation, you should record the following
information: (a) the date of your observation; (b) the time of your observation, Eastern
Standard Time, 24 hour clock; (c) the location of your observation (e.g. “outside The Ninety”,
or “outside my apartment on Woodland Avenue”); (d) the approximate per cent of the
Moon’s round disk that is illuminated (e.g. 10%, 50%, 100%, where 100% means full moon);
and (e) the elevation angle of the Moon above the level horizontal horizon in degrees. (See
measurement instructions immediately below.) Note that your Moon observations need not
all be made from the same location.
• How to measure the elevation angle of the Moon above the level horizon – Hold your fist
vertically at arm’s length so that the bottom of your fist is level with your eye. Do not extend
your thumb. Estimate how many fists fit between the level horizon and the Moon in the sky.
Each fist is about 10 degrees of angle. So if the Moon is about 2 fists above the level horizon,
the elevation is 20 degrees. Of course, this method of measuring Moon elevation is not
particularly accurate. Therefore, do not try to measure the Moon elevation to better accuracy
than a half a fist width (i.e. 5 degrees). Note – The level horizon extends horizontally away
from you into the distance. If you were on a ship at sea, the actual horizon would be the level
horizon. In practice, the level horizon is usually blocked in Lexington and elsewhere by
buildings and trees. Nonetheless, you can estimate the location of the level horizon by
placing the bottom of your fist level with your eye, as described above.
• A Microsoft Excel spreadsheet file to help you record information – To help you record
your information and include the information as a table in your report, you may wish to
download the Microsoft Excel spreadsheet file Moon Phases Data AST191 S17.xls. You can
record your observations in the Excel worksheet Observations of the Moon. Note the
comments in the top row of the worksheet. To download this file from Canvas, choose Files
in the menu on the left side of the course homepage. Click on the filename, then choose
Download.
• Useful Hints – Observations will be conveniently possible in the late afternoon and/or early
evening if you begin observing on about Thursday, March 30, weather permitting. (On that
date, avoid black cats while observing the Moon!) Observations of the Moon do not
necessarily have to be made at nighttime! The Moon is frequently visible in broad daylight.
For example, go outside on a clear day in the late afternoon in the approximate time frame
April 1-5, 2017. You will find the Moon visible rather high in the sky during the daytime.
3. Gather Moon phase data from a website
• Where to find Moon data on the internet – Information about the Moon is available at the
U.S. Naval Observatory website http://aa.usno.navy.mil/data/. Go to this site and choose
Complete Sun and Moon Data for One Day near the top of the webpage. Insert the requested
information into Form A – U.S. Cities or Towns on the webpage, and then click on Get data
to see the results for a specified location and date. Chose Lexington Kentucky as your
location. Important note – You can generate a table of moonrise & moonset times and a
separate table of sunrise & sunset times for all dates in 2017. To do so, go back to the
homepage designated above and click on Table of Sunrise/Sunset, Moonrise/Moonset…
Again specify Lexington, Kentucky. Then choose Type of table, then Compute Table.
• What information to record from the website – Gather data for every other day over a
period of a month (that is, data for about 15 different days, spanning a total period of about
30 days). If your last name begins with “A”, begin gathering web data for April 1, 2017. (So
you will gather data for April 1, 3, 5…) If your last name begins with “B”, begin gathering
web data for April 2, 2017. (So you will gather data for April 2, 4, 6…) And so on. If your
last name begins with Z, begin gathering web data for April 26, 2017. (So you will gather
data for April 26, 28, 30…) For each day that you choose, record the following information
in a table: (a) date; (b) time of moonrise for that day, Eastern Standard Time (EST), 24 hour
clock; (c) phase of the Moon, e.g. waxing crescent; (d) per cent of the Moon’s visible disk
illuminated, and (e) time of sunrise. If you wish, you may record your data in the
spreadsheet file Moon Phases Data AST 191 S17.xls, worksheet Moon data from website.
Note the comments in the top row of the worksheet. When entering times of moonrise and
times of sunrise, take the information from the tables of moonrise/moonset and sunrise/sunset
described in the bulleted item immediately above. For some dates (e.g. April 16, 2017), the
moon does not rise in the 24 hour period of that day. For these dates, leave your moonrise
entry in the table blank.
4. Analyze and interpret your data for Moon phases
• Connections among the data you have gathered – Consider the data you have gathered
from the internet about time of moonrise, time of sunrise, phase of the Moon and the per cent
of the Moon’s visible disk illuminated. What connections can you find among these data?
Consider, for example, the differences in times between sunrise and moonrise for the 15 or so
days. (You should calculate the differences in these times. Take, for example, the time of
moonrise minus the time of sunrise.) How are these time differences related to other data
about Moon phases? If you are reasonably familiar with Microsoft Excel, you may want to
make a graph or two of the moonrise – sunrise time differences versus other data on Moon
phases.
• Comparison of the data with the Moon phase models and your testable predictions –
How well are your testable predictions for the two Moon phase models borne out by the data
you have gathered (data from observations of Moon phases in the sky and, especially, data
from the internet)? Which Moon phase model is more consistent with your predictions and
why? If you had more time to complete this project, what additional data might you have
used to further test your model’s predictions?
5. Write your report and submit to Canvas by Monday, April 24, 2017
• What to put in your report – Your report should consist of each of the four sections
outlined below. The credit to be assigned to each section is also listed. The instructor
envisions that reports on this project would typically be about 5-6 pages long, including
tables. However, grades for the report will be based solely upon how well you follow the
instructions for the project and carry out the requested data analysis, not upon the length of
the report. If you submit a shorter but thoughtful report that covers the important elements of
this project, you will receive full credit. Of course, there is no penalty for submitting a
somewhat longer report.
• How to submit your Inquiry Project report to Canvas – Your report must be submitted to
the course Canvas site in the format of a single pdf file. If you do not know how to create a
single pdf file, please consult on-line help or ask a friend. To submit your report, choose
Assignments in the Canvas menu on the left side of the course homepage. Then choose the
Inquiry Project assignment. Click on Submit Assignment, upload your pdf file, and then
click on Submit Assignment again.
Report sections (12% total credit)
1. Testable predictions for the two models (4%) – You should think of at least two testable
predictions for each model of Moon phases described earlier in this document. Briefly
explain your reasoning for the predictions.
2. Information about your observations of actual Moon phases in the sky (2%) – This
information can be provided in table form, extracted, if you like, from the Excel spreadsheet
file you may have used to record your information. You should include a brief text
describing your table.
3. Data from the website on moonrise, sunrise, etc. for every other day over a period of a
month (2%) – These data, too, should be given in table form, extracted, if you like, from the
Excel spreadsheet file you may have used to record your information. Again, include a brief
text describing your table.
4. Analysis of the data (4%) – Discuss the questions outlined above in the section above
Analyze and interpret data for Moon phases.
Possible bonus credit!
Students who follow the instructions above with reasonable attention are quite likely to receive
full credit for this project. However, students who show evidence of additional effort in data
collection and, especially, in data analysis and interpretation are eligible for up to 3% of bonus
credit