Lunar Distance – DST to EST – Telecommunications, Navigation & Electronics

Introduction

Fig.1 Joshua Slocum “Sailing Alone Around the Word” (Ref.1)

Saturday November 5th was an ideal evening to measure a Lunar from my balcony. It was unseasonably warm at 20degC and I had just removed all the gear, as my balcony is going to be rebuilt for the third time in five years, so I might as well enjoy the last few jack hammer free evenings (Ref.2). The sky was perfectly clear and the Moon and Jupiter were clearly visible. Also the time was going to switch back from DST to EST later that evening, so celebrating Joshua Slocum’s navigation using Lunars and an old tin clock seemed appropriate (remember all it takes is one big solar X flare… and get out your slide rule/sextant!).

Lunars Procedure

Figure 2 is a resume of the Lunars procedure. The concept of Lunars is to get an accurate time when your watch is not calibrated. Joshua Slocum used an old tin clock. You need to have the Moon and a Celestial Body visible. You measure the altitude of the Moon & CB before and after you measure the Lunar Distance, recording all the times. Then you interpolate to find the altitudes at the time of the LD measurement. Once you have the altitudes Hs, you adjust for Refraction, Parallax and Semi Diameter. This gives the Ha or apparent altitudes for the Moon & CB. Then with the Ha values and Apparent Lunar Distance you can solve for the Geocentric Lunar Distance. Tables list the Geocentric Lunar Distance vs. Time, so you can then determine the correct time.

Stark Tables allow you to do this with pen/paper only (Ref.3). In this post since I don’t have a water horizon from my balcony, I will calculate Hc for the Moon/Jupiter since I know the time and my location and will generate Ha as would be done in a real situation (I have an artificial horizon but it is not accurate with my sextant).

Measurements

Fig.3 Stellarium View Looking East at 19:29 DST from QTH

Fig.4 NavAlgos Stars & Planets 19:29 DST from QTH (Ref.4)

Fig.5 Moon Semi Diameter as seen from Earth Surface = 15.76min

Time DST/UTC	Observed Lunar Distance	Apparent Lunar Distance
19:10/23:10	14deg 11.5min	14deg 27.3min
19:21:30/23:21:30	14deg 19min	14deg 34.8min
19:29:30/23:29:30	14deg 26min	14deg 41.8min
Index Error=0deg Temp=20degC Moon SDs=15.76min Lat=43deg 42.588’N Long=79deg 24.078’W	App. Lunar Dist = Obs. Lunar Dist + SDs

Fig.6 Lunar Distance Measurements

Figure 3 shows the Stellarium view from my location looking East, clearly showing the Moon & Jupiter. Figure 4 shows the Navigational Algorithms view (Ref.4). Figure 5 shows a calculation of the Moon semi diameter as seen on the Earth’s surface. This value is added to the measurements to give the Apparent Lunar Distance. Figure 6 is a table of measurements taken. I used one horizon shade as the moon was very bright. I tilted the sextant at an angle parallel to a line joining Jupiter to the Moon centre and brought Jupiter down to the point it just rested on the right limb of the moon. I used the last reading for calculations.

Sight Reduction

Fig.7 Observer Horizon and Apparent Lunar Distance

Fig.8 GHA & DEC Moon & Jupiter Nautical Almanac & NavAlgos

Fig.9 Spherical Triangle North Pole – QTH – MoonGP Hc=26.440148d Az=113.2971d

Fig.10 Spherical Triangle North Pole – QTH – JupiterGP Hc=31.19356d Az=128.7405d

Fig.11 Moon & Jupiter Refraction Rm=1.9min Rj=1.6m

Fig.13 Lunar Distance Apparent Moon – Jupiter =14.679171deg

Fig.14 Geocentric Lunar Distance Moon – Jupiter = 14.329335deg

Moon
Hc (Fig.9)	26deg 26.4min
Refraction (Fig.11)	1.9min
PA (Fig.12)	51.4min
Ha = Hc + R – PA	25deg 36.9min
Jupiter
Hc (Fig.10)	31deg 11.6min
Refraction (Fig.11)	1.6min
Ha = Hc + R	31deg 13.2min
Apparent Lunar Distance Calculated (Fig.13)	14deg 40.8min
Apparent Lunar Distance Measured (Fig.5)	14deg 41.8min
Error	1.0min
Geocentric Lunar Distance Calculated (Fig.14)	14deg 19.8min

Fig.15 Sight Reduction

Figure 7 shows a spherical diagram based on the Observer Horizon and Zenith showing where the Moon & Celestial Body actually are (Ho/Hc) and where they appear to an observer Ha. As mentioned before, I will use Hc to derive Ha, since I don’t have a water horizon. Figures 8 – 10 are used to solve for Hc_moon/Az_moon & Hc_jupiter & Az_jupiter. Figures 11 & 12 are used to solve for Ha_moon & Ha_jupiter. Figures 13 & 14 then solve for the Geocentric and Apparent Lunar Distances. The solutions of these triangles give the Apparent/Geometric Lunar Distances.

The value of the Geocentric Lunar Distance can be compared against a table of values to determine the time. So for instance we can use NavAlgos to derive a table. Figure 16 shows bracketing values at 23:00 & 00:00hrs.

Fig.16 GeoLD for 23:00 & 23:29:30 & 00:00

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References

#1. – “Sailing Alone Around the World”, Captain Joshua Slocum’
Dover, New York, 1956 0-486-20326-3

#2. – “Lunar Distance as Seen in Toronto”,
https://jeremyclark.ca/wp/nav/lunar-distance-as-seen-in-toronto/

#3. – “Stark Tables for Clearing Lunar Distance”
https://www.amazon.ca/dp/091402521X/

#4. – “Navigational Algorithms”, Andres Ruiz Gonzalez,
https://sites.google.com/site/navigationalalgorithms/

#5. – “Celestial Navigation Basics & Equipment”
https://www.clarktelecommunications.com/celnav.htm

Introduction

Lunars Procedure

Measurements

Sight Reduction

References

By Jeremy Clark