NAME: _____________________________________________ PHYS 1404 – Determining the Distance to the Moon using Small Angle Formula PURPOSE: To utilize your understanding of the Small Angle Formula to...

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NAME: _____________________________________________ PHYS 1404 – Determining the Distance to the Moon using Small Angle Formula PURPOSE: To utilize your understanding of the Small Angle Formula to calculate the distance to the Moon using simultaneous observations of the Moon’s location from two places on Earth. DESCRIPTION: Figure 1 has the Moon and several stars near the edge of the Moon located as seen from Dallas, TX on March 23, 2018 at 9:08:31 pm CDT). Figure 2 has the Moon and several stars near the edge of the Moon located as seen from Waco,TX on the EXACT SAME time and date. (Radio communication and careful timing can be used to accomplish this.) In both figures the center of the Moon’s disk has been identified with a crosshair. The locations in Dallas and Waco where the photographs are simulated are exactly 147.19 km apart. In this lab we will measure the angular separation of the Moon relative to the background stars from two locations and then use the Small Angle Formula to determine the distance between the Earth and the Moon on this date. We will also explore the use of scaling techniques to determine the input data with which to determine the parallax angle for the Moon. INSTRUCTIONS: 1) Using a ruler, measure the distance in mm between the two objects labeled HIP26677 and TYC1306-1360-1 and record this value here: _______________mm 2) The measured angluar separation of these two objects is 15.4 arcminutes. Divide this number by your measurement in Step 1 to obtain the scale factor for this figure. This factor is used through the rest of the lab to convert mm into arcminutes. Record your answer here: Arcminutes per mm 3) Measure the distance from the center of the Moon to TYC1306-1360-1 in mm and record this value here: ___________mm. 4) Use the scale factor obtained in Step 2 to determine the angular separation between the center of the Moon and TYC1306-1360-1 by multiplying their separation in mm by the scale factor and record that value here: ____________ arcminutes (Dallas Location) 5) Repeat Steps 3 and 4 to obtain the separation between the Moon and TYC1306-1360-1 from the Waco,TX location and record that value here: ___________ arcminutes (Waco location) 6) The DIFFERENCE between the separation for the Moon and TYC1306-1360-1 at the two locations is the parallax angle for the Moon against the background stars. Record that value here: Moon’s Parallax Angle (α) = _______________ arcminutes 7) CONVERT the Moon’s Parallax Angle into arcseconds. Record that value here: Moon’s Parallax Angle (α) = _______________ arcseconds 8) Use the Small Angle Formula below to determine the distance (d) to the Moon. For this type of calculation, D is distance between Waco and Dallas. Remember in this formula the parallax angle MUST be in arcseconds!! 9) Show your work below: 10) Record your distance to the Moon here. ________________ km Note: The distance from the Earth to the Moon between:Perigee = 363,396 km and Apogee = 405,504 km. Figure 1: The Moon as seen from Dallas, TX (Lat.: 32.7825°, Lon.: -96.8207) on March 23, 2018 at 9:08:31 pm CDT Figure 2: The Moon as seen from Waco, TX (Lat.: 31.489°, Lon.: -97.0926) on March 23, 2018 at 9:08:31 pm CDT 265 , 206 d D a = = d SKY FAMILIARIZATION WITH THE SC001 STAR CHART PHYS 1404 - LAB 04 – THE ORBIT OF THE MOON NAME ______________________________ DATE _______________________ During this lab, you are going to plot the orbit of the moon on a star chart as it moved from August 1, 2004 to August 30, 2004. The coordinates for the moon for each day are located in the table on the back of this page. Using the coordinates, place a dot on the chart to mark the moon’s position on that day. Be sure to number each moon position. Connect each dot as you go so that you will be able to see the Moon's orbital path across the chart. 1. Is the Moon’s orbit in the same plane as the Earth’s orbit? (Hint - Does it follow the ecliptic exactly) ________________________________________________________________ 2. If not, by how much is the Moon’s orbit inclined to the Earth’s orbit? (Hint - Measure the number of degrees declination between the ecliptic and moon path at the widest gap) _________________________________________________________________ 3. On each of the following days, in what constellation was the moon roughly located? Day 1 ______________________________________________________ Day 9 ______________________________________________________ Day 13 ______________________________________________________ Day 18 ______________________________________________________ Day 24 ______________________________________________________ Day 28 ______________________________________________________ 4. How many minutes of right ascension does the Moon cover on average each day in its orbit around the Earth? ​​​​​​​​​​​​​​​​​​​​​​________________________________________________________________ 5. Determine the Moon's approximate sidereal period from the data provided. (Hint – How many days did it take for the moon to get back to roughly the same place in the sky?) _________________________________________________________________ DON’T FORGET TO TURN IN YOUR STAR CHART WITH MOON ORBIT PLOT! Questions = 10 points, Chart = 10 points DAYRIGHT ASCENSIONDECLINATION 10 hours 34.5 minutes0 degrees 58 minutes 21 hours 22.4 minutes7 degrees 10.3 minutes 32 hours 10 minutes12 degrees 53 minutes 42 hours 58 minutes17 degrees 53 minutes 53 hours 48 minutes22 degrees 0 minutes 64 hours 40 minutes25 degrees 4 minutes 75 hours 32.5 minutes26 degrees 57 minutes 86 hours 26 minutes27 degrees 34 minutes 97 hours 20 minutes26 degrees 52 minutes 108 hours 16 minutes24 degrees 52 minutes 119 hours 7 minutes21 degrees 38 minutes 129 hours 59 minutes17 degrees 13 minutes 1310 hours 50 minutes11 degrees 51 minutes 1411 hours 37 minutes6 degrees 4 minutes 1512 hours 28 minutes0 degrees 41 minutes 1613 hours 16 minutes - 6 degrees 4 minutes 1714 hours 21 minutes- 15 degrees 28 minutes 1815 hours 15 minutes- 20 degrees 45 minutes 1916 hours 13.5 minutes- 24 degrees 58 minutes 2017 hours 16 minutes-27 degrees 46 minutes 2118 hours 20 minutes- 28 degrees 49 minutes 2219 hours 25 minutes-27 degrees 58 minutes 2320 hours 28 minutes-25 degrees 20 minutes 2421 hours 28 minutes-21 degrees 10 minutes 2522 hours 23 minutes-15 degrees 52 minutes 2623 hours 15 minutes- 9 degrees 51 minutes 270 hours 4 minutes- 3 degrees 30 minutes 280 hours 52 minutes2 degrees 51 minutes 291 hours 39 minutes8 degrees 53 minutes 302 hours 29 minutes14 degrees 40 minutes