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 XXXXXXXXXXkm 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 TYC XXXXXXXXXXand 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 TYC XXXXXXXXXXin 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 TYC XXXXXXXXXXby 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 TYC XXXXXXXXXXfrom the Waco,TX location and record that value here:
___________ arcminutes (Waco location)
6) The DIFFERENCE between the separation for the Moon and TYC XXXXXXXXXXat 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.: XXXXXXXXXX°, Lon.: XXXXXXXXXXon March 23, 2018 at 9:08:31 pm CDT
Figure 2: The Moon as seen from Waco, TX (Lat.: 31.489°, Lon.: XXXXXXXXXXon March 23, 2018 at 9:08:31 pm CDT
265
,
206
d
D
a
=
=
d
SKY FAMILIARIZATION WITH THE SC001 STAR CHART
PHYS XXXXXXXXXXLAB 04 – THE ORBIT OF THE MOON
NAME
______________________________
DATE _______________________
During this lab, you are going to plot the o
it 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 o
ital path across the chart.
1. Is the Moon’s o
it in the same plane as the Earth’s o
it?
(Hint - Does it follow the ecliptic exactly)
________________________________________________________________
2. If not, by how much is the Moon’s o
it inclined to the Earth’s o
it?
(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 o
it 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