Lesson 1: Phases of the Moon

Transcription

1 Lesson 1: Phases of the Moon The moon takes 29.5 days to revolve around the earth. During this time, the moon you see in the sky appears to change shape. These apparent changes, which are called phases, occur because the moon changes position relative to the Earth and sun. The relative positions of the moon, Earth, and sun determine how much of the moon is illuminated by sunlight. To watch a simplified animated summary of the phases of the moon:

2 Moonrise from Earth: Let s first define what we mean by rising and setting. You must first consider the section of the sky where the visible part of the sky meets the surface of the earth the horizon. When a celestial object is above the horizon, we can see it in the sky. When the object is below the horizon, the surface of the earth prevents us from seeing it. The earth s rotation causes the sky to appear to move. As it moves, it carries the celestial object with it. When an object crosses the horizon and is visible, we call that rising. When the object passes below the horizon, we consider that setting. The time depends on the phase of the moon. It rises about 30 to 70 minutes later each day than the previous day. REMEMBER: The sun only illuminates the side of the sun that is facing the SUN. LINK:

3 Calculation of Elongation Elongation is an astronomical term that refers to the angle between the Sun and a planet, as viewed from Earth. We can find the approximate rising and setting times for the sun and moon by assuming that both move along the celestrial equator at constant rates, with the sun completing a complete trip in one year and the moon in one month. For this simple discussion of elongation, let us assume the following: 1. The sun rises at 6h and sets at 18h every day of the year at all latitudes. 2. The rising and setting times of the moon are 12 hours apart. 3. The rising and setting times of the moon depend only on its elongation or phase. When the moon s phaase is first quarter, the elongation is 90 o. If we draw lines from the sun and the moon to our eyes, the angle would be 90 o. In the last quarter, the elongation is 270 o. To find the times of moonrise and moonset, we must change the elongation from angular measure into time measure. The celestial sphere turns once every 24 hours. During this time, a point of the sky has traveled through the angle of 360 o, or one complete circle. Thus the angle of 360 o is equal to 24 hours. For example, the angle 90 o is one quarter of a complete circle. (360 o / 4 = 90 o ). One quarter of 24 hours is 6 hours. The angle 90 o expressed in time units is 6h. Therefore, when the elongation is 90 o (phase = first quarter), the moon lags 6h behind the sun, in rising, setting, and crossing the meridian or any other point or line of reference. Similarly, when the elongation is 270 o (phase = last quarter), the sun lags behind the moon by 6h. For a general rule, convert the elongation from degrees to hours by dividing the angle in degrees by 15. angle in hours = angle in degrees / 15 Add the result of time to sunset or sunrise to find the time of moonset or moonrise. Moonset (rise) = sunset (rise) + elongation in hours If the time of moonset or moonrise is greater than or equal to 24h, subtract 24. For example if we calculate the moonrise to be 26h. Since a day has only 24h, we know the calculation has carried us 2h into the next day. We subtract 24h and we have the correct time. Recall that the sun rises at 6h and sets at 18h.

4 EXAMPLES: 1. An angle of 60 o. What is the measure in hours? a. 60 o / 15 = 4h 2. An angle measures 345 o. What is the measure in hours? a. 345 o / 15 = 23h 3. An angle measures 150 o. What is the measure in hours? a. 150 o / 15 = 10h Now let us work with the elongation measure in hours to determine moonrise and moonset. 1. The elongation of the moon is 13h. When does it rise? i. 6h + 13h = 19h b. When does the moon set? i. Moonrise + 12h = Moonset ii. 19h + 12h =31h (Since the hour is greater than 24, subtract) iii. 31h 24h = 7h 2. The elongation of the moon is 20h. When does it rise? i. 6h + 20h = 26 h (Since the hour is greater than 24, subtract) ii. 26h 24h = 2h b. When does the moon set? i. Moonrise + 12h = Moonset ii. 2h + 12h =14h 3. The elongation of the moon is 17h. When does it rise? i. 6h + 17h = 23h b. When does the moon set? i. Moonrise + 12h = Moonset ii. 23h + 12h =35h (Since the hour is greater than 24, subtract) iii. 35h 24h = 11h. Now let s try a more difficult but more practical problem. Lets choose the phase of the moon and find the times of moonrise and moonset. Since the elongation angles for each phase are across a range, choose a value within that range to do the conversions. 1. The phase of the moon is full. a. The angle of elongation is 180. Therefore to find hours: b. 180 o / 15 = 12h 2. When does it rise? b. 6h + 12h = 18h 3. When does it set? a. Moonrise + 12h = Moonset b. 18h + 12h =30h (Since the hour is greater than 24, subtract) c. 30h 24h = 6h

5 1. The phase of the moon is waning crescent. a. The angle of elongation is >270 o and <360 o. Therefore to find hours: b. I choose 300 o, a number within the range d. 300 o / 15 = 20h 2. When does it rise? b. 6h + 20h = 26h (Since the hour is greater than 24, subtract) c. 26h 24h = 2h 3. When does it set? a. Moonrise + 12h = Moonset b. 2h + 12h =14h Last one: The phase of the moon is full. 1. The angle of elongation is 0 o. Therefore to find hours: a. 0 o / 15 = 0h 2. When does it rise? b. 6h + 0h = 6h 4. When does it set? a. Moonrise + 12h = Moonset b. 6h + 12h =18h Finally let us find the phase of the moon given the time of moonrise or moonset. 1. The moon rises at 23h. What is its phase? a. 23h x 15 = 255 o. 255 o is in the range of >180 o and <270 o b. So Waning Gibbous 2. The moon sets at 2h. What is its phase? a. Moonset = Moonrise + 12h b. 2h = Moonrise + 12 c. Moonrise = 14 d. Moonrise = Sunrise + Elongation e. 14 h = 6 h + Elongation f. Elongation = 8 h g. 8h x 15 = 120 o. 120 o is in the range of >90 o and < 180 o h. So Waxing Gibbous

6 Summary of Phase, Elongation, Moonrise and Moonset Phase Elongation Hr Moonrise Moonset New 0 o Waxing Crescent 15 o o o o o First Quarter 90 o Waxing Gibbous 105 o o o o o Full Moon 180 o Waning Gibbous 195 o o o o o Last Quarter 270 o Waning Crescent 285 o o o o o New 360 o

7 We have learned a method, which allows us to predict approximately when the moon will rise and set, given that we know its phase. The basic assumption in this method is that the moon and sun move along the celestial equator at constant rates, the moon completing one circuit in one month, the sun in one year. Now let us allow the moon and the sun to move along the ecliptic at constant rates. Now the times of moonrise, moonset, sunrise, and sunset vary with the season and the location (latitude). Now we shall let the moon move along its actual orbit, which is inclined to the ecliptic at an angle of 5 o, while the sun moves along the ecliptic. We shall introduce the eccentricities of the orbits of the earth and the moon, for the earth s orbit around the sun and for the moon s orbit around the earth.