Moon Apogee and Perigee LabName ____________
Determining the Moon’s Orbit from its apparent size
Background information:
As the moon orbits, we see different amounts of the day (lit) side of the moon. We
call these changing faces of the moon ‘phases’. A full
cycle of phases takes 27.33 days, or slightly less than
one month (moonth). These phases include: new moon,
waxing crescent, first quarter, waxing gibbous, full
moon, waning gibbous, last quarter, waning crescent and
new moons. The age of a moon phases is equal to the
amount of days past the most recent new moon. For
example, a 3 day moon is the thin, crescent shaped phase
that is visible 3 days after a new moon. As the moon
orbits around the Earth, we see it in a slightly different position each day. The moon’s
position is measured, in degrees, along the ecliptic- so it is called “ecliptic longitude”.
In addition to the changing phases, the moon changes in other, less noticeable ways.
As the moon orbits around the Earth in a slightly elliptical orbit, there are times when it
will be closest to the Earth (called Perigee) and times when it will be furthest from Earth
(called Apogee). As the moon gets closer to the Earth, it will appear slightly larger and
as it moves further away, it will appear slightly smaller. Obviously, the moon is not
getting larger and smaller; it is just appearing larger
and smaller because it is closer and further from us.
This is called the moons apparent diameter. In this
lab, you will measure the apparent diameter of the
moon throughout one month in order to determine
the date of apogee and perigee.
Perigee
Apogee
To complicate matters a little more, the moon doesn’t orbit along the same apparent
path as the sun. Its orbit is tipped about 5 degrees from the ecliptic (recall that the
ecliptic is the apparent path of the sun in our sky). This means that, in one month, there
will be times when the moon appears below the ecliptic (below the sun’s path) and there
will be times when the moon appears above the ecliptic. The moon’s position is
measured, in degrees, above and below the ecliptic- so it is called “ecliptic latitude”.
When the moon crosses the ecliptic (the ecliptic latitude is = 0), lunar and solar eclipses
can occur. These positions are known as nodes.
Lab procedures:
1. Measure each moon image for a full month of phases. (Tip: Measure from the top to the
bottom of each image NOT right to left. You may have to estimate for the first day. Try
doing the other dates first.)
Table 1 (Copy the same data into Table 2)
Date
Age of
Ecliptic
Ecliptic
Moon (past Longitude
Latitude
new)
(degrees)
(degrees)
2/18/1999
3 days
358.06
-3.21
2/20/1999
5 days
26.5
-4.64
2/22/1999
7 days
54.81
-5.1
2/24/1999
9 days
82.78
-4.48
2/26/1999
11 days
110.33
-2.93
2/28/1999
13 days
137.34
-0.77
3/2/1999
15 days
163.58
+1.56
3/4/1999
17 days
188.8
+3.56
3/6/1999
19 days
212.98
+4.81
3/8/1999
21 days
236.49
+5.06
3/10/1999
23 days
260.06
+4.25
3/12/1999
25 days
284.56
+2.54
* 1999 was NOT a leap year
Measured Apparent Diameter
(in centimeters)
2. Draw 2 graphs (or plot them in Excel)
a) Date vs Measured Apparent Diameter
b) Date vs Ecliptic Latitude
3. Describe what is happening to the moons’ apparent diameter over the course of a month.
___________________________________________________________________________
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4. Describe what is happening to the moons’ ecliptic latitude over the course of a month.
___________________________________________________________________________
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5. Based on the measured diameters, which date do you think the moon is closest to the earth
(perigee) ? _______________________ Which date do you think is apogee? ___________
6. Based on your second graph, on what date does the moon appear to cross the ecliptic?
_________________
7. If lunar eclipses can only occur during full moons, could a lunar eclipse have occurred
during this month? _____________________ When? _____________________
8. If lunar eclipses can only occur during full moons when the lunar latitude is = 0, could a
lunar eclipse have occurred during this month? __________________ When ?________
9. Using the formula: dD = constant (where d represents the apparent diameter, and D
represents the distance to the moon)
d
D
Determine the constant value on the date of Perigee. On this date, ___________ the moon is
at perigee and is at a distance of 368,653 km from Earth.
constant = dD
= (measured diameter on ______) x (368,653 km) =
Determine the constant value on Apogee. On this date, _________ the moon is at apogee and
is at a distance of 404,751 km from Earth.
constant = dD
= (measured diameter on _______ ) x (404,751 km) =
Average these two values together
to get the constant. Use this number in formula below
constant =
Use this value in the formula below to determine the actual distance to the moon on all other
dates. Enter your results into Table 2.
D= constant / d
Table 2
Write your CONSTANT here => _____________
Date
Ecliptic Longitude
(degrees)
2/18/1999
2/20/1999
2/22/1999
2/24/1999
2/26/1999
2/28/1999
3/2/1999
3/4/1999
3/6/1999
3/8/1999
3/10/1999
3/12/1999
358.06
26.5
54.81
82.78
110.33
137.34
163.58
188.8
212.98
236.49
260.06
284.56
Measured Apparent
Diameter
(in centimeters)
Distance to Moon
(in kilometers)
Average Distance
10. How does your calculated average distance to the moon compare to the accepted average
distance value of 384,400 km? __________________________
Percentage error = ( Difference in value / Accepted Value ) x 100
11. Using the circular graph paper provided, you can now plot the position of the moon
throughout the month. Start by drawing a line from the center to the right of the circle. This
will represent 0 degrees. The circle is divided into 15 degree ‘pie’ pieces. You may need to
use a compass! Plot the position of the moon on the circular graph paper. This graph will
represent the elliptical orbit of the moon. Make each bold circular grid line equal to 50,000
km and make each minor grid line equal to 25,000 km. (Your outer grid line should be
450,000).
12. Describe the appearance of the moon’s elliptical orbit. Does it have a large or small
eccentricity?
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___________________________________________________________________________
___________________________________________________________________________
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Want more math? Try this Math Extension!
Calculate the eccentricity of the moon’s ellipse.
Procedure:
Mark the dates of Apogee and Perigee on your graph paper.
Determine the average circle size in the circular graph you created.
Cut out a circular piece of paper with the diameter of the average circle size.
Place this circle over the graph paper and adjust it so that it fits the data points as best as
possible.
Mark the center of this paper circle on the circular graph paper. This dot represents one
foci of the moons orbit.
Measure the distance from the center of the circular graph paper to the dot representing
the center of the paper circle.
Measure the distance ( c ) between these two dots.
Determine the length of the semi major axis ( a ) by measuring the distance from apogee
to the foci dot you just drew.
Use the formula e = c / a to determine the eccentricity of the moons orbit.
How does your value for e compare with the accepted value of 0.055? ___________