Astronomy Assignment #10: The Apparent Motion of the Moon and Planets

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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).

  1. 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.

  1. 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.

  1. 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 halfof 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.

  1. 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 re-aligned with the Sun. For those of you that like the numbers it goes like this.

  1. The Earth moves around the Sun in its orbit.
  2. So after one lunar sidereal period of 27.3 days, the Moon is misaligned from the Sun by 26.9.
  3. Thus the Moon must revolve around the Earth an additional .
  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. 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.

  1. What are the real angular separations for New and Gibbous phase?

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.

  1. 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.

  1. 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.

  1. 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..

  1. 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).

  1. 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 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.

  1. 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 planetsgenerally 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.

  1. 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.

  1. 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.

  1. 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 phase when it was on the other side of the Sun from the Earth close to superior conjunction. See the figure.

  1. 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 ( and perform the following tasks:

  1. Open the Basic Observations module
  2. Read the module.
  3. Answer the following questions
  4. List the three pieces of evidence that the Ancient Greek Astronomers/Philosophers used to assert that the Earth was a sphere.
  5. The lower part of a ship disappears below the horizon first.
  6. 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.
  7. The shadows of the earth on the moon during a lunar eclipse are consistent with the earth being a sphere.
  8. What is retrograde motion?
  9. 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.
  10. What does the Greek word “planet” translate into English as?
  11. The Greek word for planet is ἀστὴρ πλανήτης (astēr planētēs), meaning "wandering star". (from wikipediea)
  12. Open the Elongation module
  13. Read the module.
  14. Define the following planetary configuration terms
  15. Elongation– the Sun-Earth-Planet angle, always less than 180
  16. 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.
  17. 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.
  18. 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.
  19. Opposition– When the elongation is near 180 and the planet and Sun are on opposite sides of the Earth.
  20. Quadrature– When the elongation is near 90.
  21. Copy the diagram to the right and draw a planet in each of the following configurations; opposition, inferior conjunction, superior conjunction and quadrature.
  1. Opposition
  2. Quadrature
  3. Inferior Conjunction
  4. Superior Conjunction
  5. Maximum Elongatin
  1. Open the Early Modeling (Ptolemy’s Model Simulation [swf]) module and read it. There are no questions to answer.
  2. Open the Heliocentrism moduleand read it. There are no questions to answer.
  3. Open the Elongations and Configurations module
  4. Read the module.
  5. Answer the following questions
  6. 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.

  1. List the planetary configurations that an inferior planet goes through.

Inferior conjunction to maximum elongation to superior conjunction to max elongation to inferior conjunction.

  1. List the planetary configurations that a superior planet goes through.

Superior conjunction to quadrature to opposition to quadrature to superior conjunction.

  1. 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.

  1. 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.

  1. Open the Planetary Configurations Simulator [swf] module
  2. Check the boxes for the following in the simulator
  3. Label Orbits
  4. Show Elongation Angle
  5. Pause for 5 seconds
  6. Radius of Observer’s planet’s orbit: Select Earth
  7. Radius of Target planet’s orbit: Select Mercury
  8. Start Animation
  9. Answer the following Question: In what configuration does Mercury appear to go retrograde (Watch the Zodiac Strip)?Inferior conjunction
  10. Set Radius of Target planet’s orbit: Select Mars
  11. Answer the following Question: In what configuration does Mars appear to go retrograde (Watch the Zodiac Strip)?Opposition
  12. 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.

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