1. If the Moon is in the first-quarter phase on September 14, what date in October
will the Moon be in full phase?
The Moon revolves around Earth every 29.5 solar days, and the full phase of the Moon
occurs 7 3/8 days after first-quarter phase. This means the next full moon will still
be in the month of September and we must wait one more cycle for a full moon in the month
of October. Thus, the Moon must progress through 1.25 cycles and 29.5 plus 7 3/8, or 37 days,
must pass. There are 30 days in September, so 16 days remain of this month, leaving 21 more
days needed for a total of 37 days. The first full moon in October will, therefore, occur on
October 21st.
It is often quite helpful to use a diagram similar to the one shown in the textbook for
Example 17.1 of the textbook to solve problems like number 2 below. This diagram helps
you visualize the various angles involved and gives you a better feel for the relative
position of the observer, the Moon, and the Sun. You can refer to this diagram as presented
in the textbook and change the angles to suit the current problem, or you can draw a new one
that will indicate the exact relationships involved. In either case you should carefully look
over this example in the textbook to see how it applies to problems of this type.
2. On December 21, the Moon is in full phase and has a declination of 28.5° What is the
altitude of the Moon at this time as seen by an observer on the meridian from 40°?
The angle between 28.5° and 40° is 11.5° This is equivalent to the zenith
angle. To obtain the altitude, subtract the zenith angle from 90° because the zenith
angle plus the altitude must always equal 90° Therefore, 90° minus 11.5° gives
78.5° for the altitude, which in this case will be the elevation of the Moon above the
southern horizon.
3. With reference to problem 2, what is the altitude of the next last-quarter moon when
observed on the meridian from 40°? Assume the date remains December 21 so that the
declination of the Sun is still 23.5°
The last-quarter moon is 90°, or one quarter cycle, east of the full moon. Since the
Moon is always within 5° of the ecliptic plane, the last-quarter moon must have a
declination of 0° latitude plus or minus 5° This means the zenith angle will
be 40° +/- 5°, and the altitude will be 50° +/- 5°
4. On September 21 the Moon is in new phase and has a declination of 5° What
is the declination of the next first-quarter moon? (Assume the Sun remains at 0°
latitude during this phase change even though it will actually change its declination by
about 2° during this 7-day period.)
A first-quarter moon is 90° east of the Sun and will be one quarter cycle from
the new moon. Thus, the first-quarter moon will have a declination of 28.5° S.
The declination will be exactly 28.5° S since the orbital plane of the Moon is
5° above the ecliptic plane at the equator.
5. With reference to problem 4, what will be the declination of the next full moon?
Assume the Sun still remains at 0° latitude.
The full moon is 180° east of the Sun. Since the new moon had a declination of
5° on September 21, the full moon will be 180° away from the Sun on the other
side of Earth at 5° S. Note that 5° is the angle above the Earth-Sun plane
on one side of the Moon's orbit and below on the other side, so one half cycle after
September 21st the Moon will be 5° of the equator.
6. With reference to problem 5, what is the declination of the next last-quarter moon?
Assume the Sun still remains at 0° latitude.
The last-quarter moon is 270° east of the Sun. Since the new moon has a declination
of 5°, the orbital plane of the Moon and the ecliptic plane must intersect at the
28.5° and at the 28.5° parallels. Thus, the declination of the last-quarter
moon will be exactly 28.5°
7. A high tide is occurring at Charleston, S.C., which is at a longitude of 80° What other
longitude is having high tide at this time?
The two high tides occur on opposite sides of Earth and so are separated by 180°
Traveling 180° around Earth from 80° in either direction gets us to 100°
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