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2. The Lunar Cycle STARS Teacher Workshop

3. Sunshine State Standards Earth and Space Standard SC.E.1.2.2 knows that the combination of the Earth’s movement and the moon’s own orbit around the Earth results in the appearance of cyclical phases of the moon.

4. The Moon The is Moon 3.7 times smaller than the Earth and has a diameter of 2476 km Orbits the Earth in a counterclockwise direction. The moon rises in east and sets in the west. The moon is in the sky for roughly 12 hours each night

5. Phases of the Moon Roughly every 29 days we see a complete cycle of the Moon phases. (Synodic Month) Phases are caused by the relative position of the Moon with respect to the Earth and the Sun (more) There are 8 phases of the Moon: New moon, waxing crescent, first quarter, waxing gibbous, full, waning gibbous, third quarter, waning crescent Waxing phase appears to be lit on the right side. Waning appears to be lit on the left side.

6. Phases of the Moon

8. Phases of Moon Activity Materials: White Styrofoam balls, or something similar, at least 2” diameter, for each student. Blank overhead transparencies and overhead markers – one for each group of four or five students. Ask students, “If you were the Earth and the ball was the Moon, show me the motion of the Moon.” Tell students that they should hold the ball slightly above their heads as they move it around. Darken the room as much as possible. Turn on a single bright light. (An overhead projector works well if set in a corner facing out into the classroom, but warn students to look away as you first turn it on.) Tell students that the light is the Sun, they are the Earth and the ball is the Moon. Standing in place, they should move the Moon around checking the shadows that form on it, trying to spot the different lunar phases. They should try to figure out the positions of the three objects for the different lunar phases.

9. Phases of Moon Activity If you are the earth. The baseball is the Moon and the Sun is the Sun What side of the baseball (Moon) is dark and what side is light? What phase of the moon does it represent? The new moon We see the dark side of the moon

10. Phases of Moon Activity If you are the earth. The baseball is the Moon and the Sun is the Sun What side of the baseball (Moon) is dark and what side is light? What phase of the moon does it represent? The new moon We see the dark side of the moon

11. Phases of Moon Activity If you are the earth. The baseball is the Moon and the Sun is the Sun. What side of the baseball (Moon) is dark and what side is light? What phase of the moon does it represent? The full moon The side of the moon we see is lighted

12. Phases of Moon Activity If you are the earth. The baseball is the Moon and the Sun is the Sun. What side of the baseball (Moon) is dark and what side is light? What phase of the moon does it represent? The full moon The side of the moon we see is lighted

13. The Point of Reference What is a point of reference? Definition of reference: A standard for measuring or judging eg. A point of reference. Definition of reference frame: A set of coordinate axes in terms of which position or movement may be specified or with reference to which physical laws may be mathematically stated. Also called reference frame. Take for example the sound of a car passing by. We’ll use a person standing on the sidewalk as the car passes as one point of refernence and the person driving the car as another point of reference. What does the person in the car hear? What does the person standing on the sidewalk as the car passes by hear? A different sound is heard based on the reference point.

14. The Month Thirty days has September, April, June and November all the rest have thirty one... What defines a month? A unit of time corresponding approximately to one cycle of the moon's phases, or about 30 days or 4 weeks. (Abbr. mo.) One of the 12 divisions of a year as determined by a calendar, especially the Gregorian calendar. Also called calendar month. A period extending from a date in one calendar month to the corresponding date in the following month. Sidereal Month, Anomalistic Month, Synodic Month, etc. Lets see how the point of reference affects how the month is determined.

15. Sidereal Month The sidereal month is defined as the time it takes for the Moon to return to the same position relative to the stars; it is equal to 27.3 days. The sidereal month represents the time it takes for the Moon to complete its orbit around the Earth In the picture on the right the length of the sidereal month is shown as the time for the Moon to go from a full moon to a gibbous moon. What is the point of reference?

16. Anomalistic Month Very similar to the sidereal month in that it involves the time it takes for the Moon to return to the same position on its orbit... The moons orbit around the earth is actually elliptical. Its more like an oval than a circle. There are two points in the moons orbit that are of interest. The Apogee and Perigee. The Apogee is the point in the Moon’s orbit that is farthest from the Earth. The Perigee is the point in the orbit of the Moon that is closest to the Earth. The Anomalistic Month is the time is take for the Moon to orbit form Apogee to Perigee and Back to Apogee. How is this different from the sidereal month The Apogee and Perigee are not fixed points. They circle around. The Anomalistic Month is approximately 27.55 days. Longer than the sidereal month. What is the point of reference?

17. Synodic Month The synodic month is defined as the time it takes for the Moon to return to the same position relative to the Sun, e.g. from full moon to full moon. The synodic month is equal to 29.5 days. The sidereal month is shorter than the synodic month because of the revolution of the Earth around the Sun, as can be seen at the right. The Moon doesn't have to travel as far around its orbit to line up with the same distant star. What is the point of reference? Helpful Applet at http://www.sumanasinc.com/ webcontent/anisamples/astron omy/sidereal.html http://www.sumanasinc.com/ webcontent/anisamples/astron omy/sidereal.html

18. The Calendar Date A Gregorian date is a date in the Gregorian Calendar, a Julian date is a date in the Julian Calendar In astronomical formulas that contain the date it is not convenient to write it in the form month/day/year. Day, Month, Year of Gregorian Calendar can be converted to the Julian Day Number (JD). The Julian Day Number is a real number that can be used within a formula. The Julian Day number system was invented by the astronomer John W. F. Herschel The Julian day number system is a system of numbering days on the Julian Calendar.

19. Gregorian to Julian Day We’re used to seeing the date in it Gregorian Form e.g. 1/10/2005 To find the Julian Day Number for 1/10/2005 we use the formula: Now let’s calculate the value of JD In the equation j = the year, m = the month, and d = the day

20. Calculate Moon on 1/10/2005 First Calculate Rule: If m is less than 2 then m = m +12 and j = j-1 Second Calculate

21. Calculating New and Full Moon where JD is for the Julian Day Number And the value of k will tell us the phase on the moon Next we use this formulas to solve for the phase of the moon

22. Calculate Moon on 1/10/2005 Plug in the JD and solve for k.

23. The Moon when k = 61.98326 The value of k gives the phase of the moon whole number for k yields a date for a New Moon a whole number + 1/4 a First Quarter + 1/2 a Full Moon, + 3/4 a Last Quarter

24. Let’s Check The Calculation The Phases of the Moon Applets http://imagiware.com/astro/moon.cgi http://www.qsl.net/g3yrc/Moon.htm

25. References The Phases of the Moon Applet http://imagiware.com/astro/moon.cgi Causes of the phases of the moon http://64.233.187.104/search?q=cache:E_2MAtg9eGEJ:pumas.jpl.nasa.gov/PDF_Examples/03_10_04_2.pdf+cause+of+phases+ of+the+moon&hl=en Julian Day Numbers http://www.hermetic.ch/cal_stud/jdn.htm Phases of the Moon Lesson http://www.ioncmaste.ca/homepage/resources/web_resources/CSA_Astro9/files/html/module3/lessons/lesson4/phasesMoon.html The Sidereal and Synodic Months http://www.sumanasinc.com/webcontent/anisamples/astronomy/sidereal.html What is the Orbital Period of the Moon? http://starchild.gsfc.nasa.gov/docs/StarChild/questions/question32.html Webster’s Online Dictionary http://www.websters-online-dictionary.org/definition/english/mo/month.html Moon’s Life Cycle http://home.hiwaay.net/~krcool/Astro/moon/moonlif.htm Astronomy Answers: Julian Day Numbers http://www.astro.uu.nl/~strous/AA/en//reken/juliaansedag.html Astronomy Answers:AstronomyAnswersBook: The Moon http://www.astro.uu.nl/~strous/AA/en/antwoorden/maan.html Science NetLinks: Lunar Cycle http://www.sciencenetlinks.com/lessons.cfm?DocID=426 Calculate the Moon Phases Applet http://www.qsl.net/g3yrc/Moon.htm