Download HW #3 Solutions

Astronomy Assignment #3: The Apparent Motion of the Moon and Planets
__Solutions___
Your Name
Text Problems: Answer the following Review Questions from Nick Strobel’s AstronomyNotes: Chapter 3:
Astronomy Without a Telescope
1. How does the Moon move with respect to the stars?
On a diurnal timescale the Moon appears to move westward with the stars as if it were attached to the
celestial sphere. However, this is not exactly true because the Moon actually falls behind the stars about
12 each day. Thus on a longer monthly times scale the moon appears to race eastward through the stars
always staying near the ecliptic in a band 8 either side of the ecliptic called the zodiac taking 27.3
days to complete once cycle around the ecliptic (the lunar sidereal period).
2. How does the fact that we always see one side of the Moon prove that the Moon rotates once every
orbital period?
If the Moon did not rotate on its axis, then we would see its entire surface as it revolved around the
Earth. See figure below left where Captain Kirk’s head orbits the Earth and does not rotate. From Earth
we would see his front, top, back and bottom of his head. However, since we only see the same area of
the Moon as it revolves around the Earth it must be rotating at just the right rate to keep the same area
facing the Earth no matter what side of the Earth the Moon is on. This is illustrated in the figure below
right where Captain Kirk’s head is orbiting the Earth and rotating so we only get to see his face.


3. In a particular year the Moon is in the constellation Aries on June 1st. What date will it be in Aries the
next time?
If the Moon is in Aries on June 1st, then it will return to the same position against the stars in one lunar
sidereal period of 27.3 days. So the Moon would again be in Aries on June 28/29.
4. Why does the Moon have phases?
The Moon has phases because the Sun-Earth-Moon angle changes as the Moon orbits the Earth.
Sunlight illuminates half the lunar surface at all times. However, depending on where the Moon is on it
s orbit in relation to the Sun-Earth direction, we may be able to see all of the illuminated half of the
Moon, none of the illuminated half, or some fraction of the illuminated half of the Moon. We can only
see that side of the Moon that faces the Earth which may or may not be some or all of the side that is
illuminated by the Sun.
5. Why are New Moon phases longer than a sidereal period (27.3
days) apart from each other?
The time between New Moon phases (the lunar synodic period,
29½ days) is longer than the lunar sidereal period of 27.3 days
because as the Moon orbits the Earth once in 27.3 days, the
Earth has moved in its orbit around the Sun. See figure. Thus
the Moon has to revolve a bit more around the Earth to be realigned with the Sun. For those of you that like the numbers it
goes like this.
27.3 d
 26.9 around the Sun in its orbit.
365.241 d
2. So after one lunar sidereal period of 27.3 days, the Moon is misaligned from the Sun by 26.9.
26.9
 2.04 d .
3. Thus the Moon must revolve around the Earth an additional 27.3 d 
360
4. Finally after one lunar sidereal period (27.3 days) and an additional 2 days, the Moon is again
realigned with the Sun for a total of ~29½ days between consecutive identical lunar phases.
1. The Earth moves 360 
6. If the Moon was full 7 nights ago, what time of day (night) should you look for the Moon to be up high
in the sky in the south today? Explain your answer.
If the Moon was full 7 nights ago, then it will be a 3rd
Quarter Moon tonight. The 3rd Quarter Moon is in
quadrature 6 hr or RA or 90 west of the Sun. The Sun,
then, is 90 east of the 3rd Quarter Moon. The 3rd
Quarter Moon will be highest in the southern sky when
it transits the meridian. So when the 3rd Quarter Moon
is transiting the meridian due south, the Sun will be 90
east on or near the eastern horizon and the time of day,
then, will be around dawn (~6:00 a.m.). See the figure
from the UNL Lunar Phase Simulator.
7. What are the real angular separations for New and
Gibbous phase?
2
This is a slightly oddly worded question. However, I believe out textbook author is asking us to state
the Elongation angle (i.e. Sun-Earth-Moon angle) of Moon when it is New and Gibbous.
When the Moon is in the New Moon phase, it is in conjunction with the Sun and has an elongation angle
near zero. So the real angular separation of the New Moon and the Sun is near zero degrees.
When the Moon is in the Gibbous phase is between quadrature (1st or 3rd Quarter) and opposition (Full
Moon). So the elongation angle of the Moon must be greater than 90 but less than 180. The true
angular separation of the Gibbous Moon and the Sun is greater than 90 but less than 180.
8. About how much difference in time is there between moonset and sunset at first quarter phase? Does the
Moon set before or after the Sun at that phase?
When the Moon is in the 1st Quarter it is in quadrature with the Sun and the Moon and Sun appear to be
90 apart in the sky with the Sun being more westerly. Thus, when the Sun sets first (because it is west
of the Moon at 1st Quarter), the Moon will set 6 hours later.
9. About how much difference in time is there between moonset and sunset at new phase?
When the Moon is in the New Phase it is in conjunction with the Sun and the Moon and Sun appear to
be “joined together” in the sky. Thus when the Sun sets, so will the Moon set. There is no difference in
time between Moon set and Sun set at New Moon.
10. About when will the Waxing Crescent Moon be on the meridian? Explain your answer.
The Waxing Crescent Moon occurs when the Moon is 3h of RA or 45 east of the Sun. If the Moon is
45 east of the Sun then the Sun must be 45 west of the Moon. So if the Waxing Crescent Moon is
crossing the Meridian (i.e. due south), then the Sun, which is 45 to the west of the Moon, must be half
way to the western horizon, near 3 p.m..
11. The Moon is low in the western sky at sunrise, what is its phase? Explain!
Refer to the figure from the UNL Rotating Sky Module Paths of Stars. The star
on the eastern horizon represents the rising Sun. The star just above the
western horizon represents the Moon. As this figure illustrates the Moon will
be in a Waning Gibbous phase since it has passed through Full Moon (recall the
Moon is moving eastward through the stars from night-to-night. So a day or
two before the situation pictures in the figure the Moon would have been on the
western horizon as the Sun rose on the eastern horizon (i.e. Full Moon).
12. Why do we not have eclipses every month?
For an eclipse to occur, the Moon must be either New or Full and the Moon must be on (or crossing) the
ecliptic. Both these events happen twice a month: the New Moon and Full Moon each occur during the
course of a month and each month the Moon crosses the ecliptic twice in its slightly inclinded (5.2)
orbit around the Earth. However, these events (Moon Full or New and crossing the ecliptic) do not often
occur together. The 5.2 tilt of the Moon’s orbit around the Earth (this is why the Moon does not
3
exactly follow the ecliptic) prevents an eclipse every Full Moon and every New Moon. Only when the
Full or New Moon occurs as the Moon is crossing the ecliptic will eclipses occur.
13. How do the planets move with respect to the stars?
On a diurnal timescale the planets appear to move westward with the stars as if it were attached to the
celestial sphere. However, this is not exactly true because the planets generally fall behind the stars
some amount each day. Thus on a longer times scale the planets appears to drift eastward through the
stars always staying near the ecliptic in a band 8 either side of the ecliptic. This eastward drift
through the stars is known as direct or prograde motion. However, periodically and briefly the planets
stop there long-term direct motion eastward through the stars and appear to move westward through the
stars in what is called retrograde motion. The inferior planets of Mercury and Venus will retrogress only
when there are in inferior conjunction with the Sun. The superior planets Mars, Jupiter and Saturn will
retrogress only at opposition to the Sun.
14. What does the fact that all of the planets visible without a telescope move within 7° of the ecliptic imply
about the alignment of their orbital planes? What would an edge-on view of our solar system look like?
The fact that all of the planets visible without a telescope move within 7° of the ecliptic implies that the
orbital planes of the planets are very nearly coincident and that the Solar System must look very flat
from an outside edge-on view.
15. Why are Venus, and Mercury never seen at midnight while the other planets can be visible then?
Venus, and Mercury are never seen at midnight because they have maximum elongations of the Sun of
45 and 28 respectively. This means that Venus can never be see more than 3 hours after sunset or
before sun rise. For Mercury the time constraint is tighter being only 1h 52m after sunset or before sun
rise. These maximum times would apply only if the ecliptic were perpendicular to the horizon which
doesn’t happen at mid northern latitudes. So the actual window to see these planets is significantly
shorter than the times cited above.
You could also say the reason we cannot see Venus and Mercury at midnight is that they orbit closer to
the Sun that we do. Since to look up at the sky at midnight is essentially to look in the opposite
direction from the Sun, you could never see planets that orbited inside your orbit by looking out from
the Sun.
The other planets (Superior planets Mars, Jupiter and Saturn) can be seen at midnight because they have
no restrictions on their elongation angle. Expressed another way, since these planets orbit outside the
Earth’s orbit it is possible that they can be in opposition to the Sun and therefore be visible at midnight.
16. What phase would Venus be in when it is almost directly between us and the Sun? Where would it be in
its orbit if we see in a gibbous phase?
When Venus is almost directly between Earth and the Sun, near
inferior conjunction, it would appear in a relatively large thin
crescent phase. Venus would appear in a relatively small gibbous
4
phase when it was on the other side of the Sun from the Earth close to superior conjunction. See the
figure.
17. Are the planet motions random all over the sky
or are they restricted in some way?
Planet motions are not random all over the sky.
The planets are restricted to the zodiac - a strip
of sky 8 either side of the ecliptic ? See the
figure to the right that displays the zodiac and
the paths of the planets over a long time scale.
Instructor Assigned Topic:
Go to the University of Nebraska, Lincoln Solar System Models Lab (http://astro.unl.edu/naap/ssm/ssm.html)
and perform the following tasks:
1. Open the Basic Observations module
a. Read the module.
b. Answer the following questions
i. List the three pieces of evidence that the Ancient Greek Astronomers/Philosophers used
to assert that the Earth was a sphere.
1. The lower part of a ship disappears below the horizon first.
2. Different stars are visible to different observers and the path they take is different.
This implies that “up” is in a different direction as would be the case for those on
a spherical surface.
3. The shadows of the earth on the moon during a lunar eclipse are consistent with
the earth being a sphere.
ii. What is retrograde motion?
1. Retrograde motion is the apparent long-time scale motion that typically occurs
over a period of several weeks where a planet drifts westward through the stars in
contrast to its usual long-term direct motion eastward through the stars.
iii. What does the Greek word “planet” translate into English as?
1. The Greek word for planet is ἀστὴρ πλανήτης (astēr planētēs), meaning
"wandering star". (from wikipediea)
2. Open the Elongation module
a. Read the module.
b. Define the following planetary configuration terms
i. Elongation – the Sun-Earth-Planet angle, always less than 180
ii. Greatest Elongation (a.k.a. Maximum Elongation) – the term applies only to inferior
planets that appear “leashed: to the Sun. The Max. elongation angle is the largest value
the elongation angle can have for the particular planet; 45 for Venus and 28 for
Mercury.
iii. Inferior Conjunction – When the elongation angle of a planet is near-zero and the planet
is closer to the Earth than the Sun, applies only to inferior planets.
5
iv. Superior Conjunction – When the elongation angle of a planet is near-zero and the planet
is farther from the Earth than the Sun, applies to both inferior and superior planets.
v. Opposition – When the elongation is near 180 and the planet and Sun are on opposite
sides of the Earth.
b
vi. Quadrature – When the elongation is near 90.
c. Copy the diagram to the right and draw a planet in
a
each of the following configurations; opposition,
inferior conjunction, superior conjunction and
e

quadrature.
c
a. Opposition
b. Quadrature

c. Inferior Conjunction
e
b
d. Superior Conjunction
d
e
e. Maximum Elongatin
d
3. Open the Early Modeling (Ptolemy’s Model Simulation [swf]) module and read it. There are no
questions to answer.
4. Open the Heliocentrism module and read it. There are no questions to answer.
5. Open the Elongations and Configurations module
a. Read the module.
b. Answer the following questions
i. How are inferior planets different from superior planets?
Inferior planets appear to cycle the zodiac in one year on average, have a maximum
elongation and go retrograde at inferior conjunction. While superior planets take longer
than 1 year to cycle the zodiac, can be seen at opposition and go retrograde and brighten
at opposition.
ii. List the planetary configurations that an inferior planet goes through.
Inferior conjunction to maximum elongation to superior conjunction to max elongation
to inferior conjunction.
iii. List the planetary configurations that a superior planet goes through.
Superior conjunction to quadrature to opposition to quadrature to superior conjunction.
iv. Why are inferior planets never seen at opposition?
Inferior planets are never seen at opposition because their orbits are within, or smaller
than the Earth’s orbit around the Sun. To be seen at opposition a planet must be situated
outside the orbit of the Earth. Inferior planets are never outside the Earth’s orbit.
v. Why would a superior planet appear brightest, as seen from the Earth, when it is in
opposition?
Planets “shine” by reflected light from the Sun. The closer a planet is to Earth the
brighter that reflected light could appear. When a superior planet is at opposition the
distance between the planet and the Earth is at a minimum. Thus the superior planet
appears brighter at opposition because it is closer to the Earth.
6. Open the Planetary Configurations Simulator [swf] module
a. Check the boxes for the following in the simulator
i. Label Orbits
ii. Show Elongation Angle
iii. Pause for 5 seconds
iv. Radius of Observer’s planet’s orbit: Select Earth
v. Radius of Target planet’s orbit: Select Mercury
6
vi. Start Animation
vii. Answer the following Question: In what configuration does Mercury appear to go
retrograde (Watch the Zodiac Strip)? Inferior conjunction
b. Set Radius of Target planet’s orbit: Select Mars
i. Answer the following Question: In what configuration does Mars appear to go retrograde
(Watch the Zodiac Strip)? Opposition
c. Answer this question: What appears to be the rule for when inferior planets appear to go
retrograde and when superior planets appear to go retrograde?
Inferior planets go retrograde at inferior conjunction and superior planets go retrograde at opposition.
7