Capella: Reloj en El Cielo

Distancia Lunar la Luna & Capella

El 23 de julio no pude dormir, algo me dijo que me levantara. Salí al balcón, el cielo estaba despejado y todas las luces de los apartamentos cercanos estaban apagadas.

La luna no estaba del todo llena, pero era absolutamente hermosa a unos 128 grados. Entonces, de repente, lo vi solo. Al principio pensé que era un planeta, pero al revisar la tabla de estrellas era Capella.

Pude medir la distancia angular entre Capella y la extremidad cercana de la Luna:

Distancia lunar observada = 75deg 8min

Corrección para SD e IE:

Distancia Lunar_app = 75deg 8min + 15min + 2min = 75deg 25min

Yo también medi la altitud de la Luna y la Capella antes y después de la distancia lunar. Luego interpolé por el tiempo LD.

Ha_moon = 31deg 11.3min

Ho_moon = 31deg 56.4min

Ref = 1.5min, PA = 46.6min

Ha_capella = 19deg 7.5min

Ho_capella = 19deg 4.8min

Ref = 2.7min

Usando la Fórmula Dunthorne, yo inserte el Ha, Ho para la Luna y la Capella y obtuve la Distancia Lunar Geocéntrica en el tiempo de medición.

LD_geo = 75.25597deg

Asume que el tiempo está en algún lugar entre 0700GMT y 0800GMT. Yo calculé el Lunar Distance_geo como la gran distancia del círculo entre MoonGP y CapellaGP en estos dos momentos.

LD_geo@0700hrs = 75.357039deg

LD_geo@0800hrs = 74.90875deg

LD_geo@07xyhrs = 75.25597deg

Usando interpolación lineal el tiempo es:

[(0.101069/.448289)*60min]+07:00:00 = 07:13:31.6sec

El tiempo de medición real fue:


Time Error = 6.6seconds



AIS Automatic Identification System for Ships is a traffic system that uses VHF transponders on vessels to periodically send out location information. It was developed by Swedish inventor Hakan Lans and is similar in concept to the ADS-B transponder system used on aircraft for position reporting.

AIS uses two VHF marine channels 87B (161.975 MHz) and 88B (162.025 MHz). Transmission is by 9.6Kbps GMFSK modulation using HDLC packet protocol. VHF channel access is by SOTDMA Self Organized Time Division Multiplexing. AIS uses navigational information from external on board GPS, Inertial Navigation and Ship Control systems. AIS has several different classes of equipment such as Class A, Class B, Base Station and Aids to Navigation. Depending on the Class, different types of information are transmitted when the ship is in port, or underway.


AIS can be decoded using very simple equipment. An RTL-SDR receiver as described in an earlier post can be used together with a simple vertical whip antenna installed outdoors with line of sight to the shipping of interest. Packet decoding can be done by programs like Multipsk, a popular amateur radio program developed by Patrick Lindecker F6CTE.

RTL-SDR Receiver
Multipsk AIS Decoder F6CTE
AIS MMSI 316030796
Marine VHF AIS Antenna


#1 – “Automatic Identification System”, Wikipedia

#2 – “All About AIS”, Created by IMO/IEC Experts

#3 – “RTL-SDR Receiver”, NooElec-NESDR

#4 – “MULTIPSK” Digital Mode Decoder by Patrick Lindecker F6CTE

Lunar Distance As Seen In Toronto

Lunar Distance Moon – Jupiter July 15th_2019_02:07:00GMT

Sunday July 14th was an excellent evening to measure a Lunar. The sky was perfectly clear and the Moon and Jupiter were clearly visible from my apartment balcony. This is generally not the case as there has been so much local construction in recent years.

The distance measured from the Moon_NearLimb to the centre of Jupiter = 16deg 1min

Sextant Index Error = 2min off

MoonHP = 55.7min

Calculation of Moon Semi Diameter at Earth’s Surface

Moon Semi Diameter + Augmentation = 15.3min

Lunar Distance_apparent = 16deg 1min + 2min (IE) + 15.3min (SDs) = 16deg 18.3min

MoonGP: GHA = 52deg 40.7min DEC = 21deg 57.6minS

JupiterGP: GHA = 69deg 55.4min DEC = 22deg 10.5minS

Calculation of Geo Centric Lunar Distance

Geo Centric Lunar Distance = 15deg 58.5min

Moon – Toronto/Hc/Az

Hc_moon = 19deg 54 min (Seen in Toronto)

Az_moon = 153deg 40.2min

Jupiter – Toronto/Hc/Az

Hc_jupiter = 23deg 32.6min (Seen in Toronto)

Az_jupiter = 170deg 25.5min

Ha_moon = Hc_moon + R – PA

Ha_moon = 19deg 54min + 2.7min – 52.6min = 19deg 4.1min

Ha_jupiter = Hc_jupiter + R = 23deg 32.6min + 2.2min = 23deg 34.8min

Lunar Distance_apparent

Lunar Distance_apparent_calculated = 16deg 14min

Lunar Distance_apparent_measured = 16deg 18.3min

Error = 4.3min

Intercept en la Playa del Condado Puerto Rico

Miré hacia el Caribe desde la playa del Condado, imaginé que Ponce de León estaba parado en el mismo lugar, midiendo el ángulo del sol con su astrolabio.

Ponce de León conocía su posición exacta porque le preguntó al Taíno Cacique Agueybaná dónde se encontraban exactamente en la galaxia. Así pudo calcular su intercepción.

Tomé una medida y los parámetros fueron:

El Tiempo = 16 de marzo de 2019 11:53:15GMT

Hs = 18grd 10.5′ ( Miem. Inf.)

Alt de Ojo = 2m

Error de Sextante = +4′

Ha = Hs +/-EdeS – Incl = 18grd 10.5′ + 4′ – 2.5′ = 18grd 12′

Ho = Ha – R + SD = 18grd 12′ – 2.9′ + 16.1′ = 18grd 25.2′

Intercept = Ho – Hc = 18grd 25.2′ – 18grd 23.4′ = 1.8′ = 1.8Nm

El Almanaque Náutico Sábado 16 de Marzo de 2019.

Playa del Condado de Tierra Google
Triángulo Náutico

Castillo San Felipe del Morro

Castillo San Felipe del Morro

Recientemente visité el Castillo San Felipe en San Juan Puerto Rico. Nunca he visto una fortificación tan enorme e impenetrable como esta. Me imaginé que era un soldado español en el siglo XVI y que el pirata Drake apareció alrededor de la Punta Escabron. Tomé el rumbo de la brújula y disparé el cañón, ajustándome al rango.

San Juan
San Felipe – Punta Escabron
Brújula Global

Golden Globe Race 2018 – 50 Year Anniversary


The Golden Globe Race 2018 commemorates the original Sunday Times Golden Globe 1968, a non-stop, single handed round the world yacht race.  It was won by Sir Robin Knox-Johnston in Suhaili. Nine contestants entered and only Knox-Johnston finished. Bernard Moitessier decided not to finish but go around the world for a second time! (Ref.1). Several fascinating movies were made about this race, one of them being “Deep Water” (Ref.2). This year’s Golden Globe celebrates the technology current around 1968. Contestants have to follow strict guidelines on boat design < 1988 and ensure all devices and instruments are of the 1968 period (Ref.3). Eighteen skippers started the race at Les Sables-d’Olonne in France on July 1st, and now eight remain, presently rounding New Zealand.

Celestial Navigation for Position Determination

In 1968 GPS was still on the drawing board. Electronic navigation systems were expensive and complicated. They consisted of using RDF radio direction finding or hyperbolic coastal navigation systems such as Decca and Loran. For most sailors, the sextant was an indispensable tool. According to Sir Robin Knox-Johnston’s book “A World of My Own” (Ref. 6) on November 18th: “At midday I set sail again to clear Solander Island, as we had drifted slowly down onto it during the morning”. Let’s work out the basics of what a meridian passage sextant sighting would have looked like for Sir Robin on this date. Figure 1 shows the location of Solander Island on the southern tip of New Zealand as seen from Google Earth.

Figure 1 Google Earth View of Solander Island on Southern Tip New Zealand

Reading off Google Earth or an appropriate chart, we determine the coordinates of the southern tip of Solander Island:

Latitude = 46deg 35′ South

Longitude = 166deg 54′ East

We can use modern software to regenerate the Nautical Almanac page for November 18th_1968 (Ref.4) which is shown in Figure 2. We can double check these values with the Nautical Almanac for The Year 1968 (Ref.5) which is available on line. Let’s figure out the sextant angle Hs measured for a meridian passage on this date and for this location. Knowing that the sun travels 15 degrees every hour, we can determine the time difference between Solander Island and Greenwich = 11hrs 7.6minutes [[166+(54/60)]/15 = 11.126667].

Figure 2 Regenerated Nautical Almanac Nov 18th_1968

From Figure 2 we can determine the GMT when the Sun GHA is directly on Suhaili’s meridian of 166deg 54’East or GHA = 360deg – 166deg 54′ = 193deg 6′. At 0hrs GMT the GHA is approx 184deg and at 0100hrs GMT the GHA is approximately 199deg. Interpolation for 193deg 6′ gives GMT = 0hrs 37minutes 33secs [[(9+23/60)/(14+59.8/60)]*60]. The Sun DEC at this time is 19deg 12′ S.

Figure 3 Oblique Spherical Triangle

Now we are in a position to calculate the sextant angle. Figure 3 shows the oblique spherical triangle formed by the position of the observer on Suhaili, the Sun GP and the North Pole at meridian passage. The Zenith Distance Zd = 90deg – Ho. The Zenith Distance is also equal to the arc distance between the Sun GP and the observer latitude since they are directly on the meridian.

Zd = 46deg 35′ – 19deg 12′ = 27deg 23′.

Ho = 90deg – 27deg 23′ = 62deg 37′.

Let’s assume Sir Robin took lower limb sightings, his height of eye above the water was 3m and his Plath sextant had no errors. We can convert our calculated Ho–>Ha–>Hs with the following equations:

Ho = Ha – R + PA +/- SD

Ha = Hs +/- Index Error – Dip

R = Refraction = 0.0167/tan(Ha+7.32/(Ha+4.32)) deg at 10degC/1010mb = 0.5′

Dip = 1.76xsqrt(Heye_m) = 1.76xsqrt(3) = 3′

SD = 16.2′ from Nautical Almanac page Nov 18th_1968

Ha = Ho + 0.5′ – 16.2′ = 62deg 37′ + 0.5′ – 16.2′ = 62deg 21.3′

Hs = Ha + Dip = 62deg 21.3′ + 3′ = 62deg 24.3′


#1 – “Sunday Times Golden Globe Race”

#2 – “Deep Water”

#3 – “GGR Golden Globe Race 1968 Website”

#4 – “The PyAlmanac”, Python Script to Write Nautical Almanac Using PyEphem, Python2.7, TeXLaTeX

#5 – “The Nautical Almanac for The Year 1968”, US Naval Observatory & UK HMSO, Google Digitized Books, University of California Library;view=1up;seq=1

#6 – “A World of My Own: The first ever non-stop solo round the world voyage”, Robin Knox-Johnston, ISBN: 978-0713668995

Maiden – Whitbread Round The World Race 1989

Just saw Alex Holmes’ s documentary “Maiden” at the Toronto International Film Festival. It’s about Tracy Edwards all female crew that sailed around the world in the Whtibread 1989 race. It follows Tracy’s early life and the various steps leading up to the race. An incredible study of courage, persistence and bravery in the face of incredible opposition, problems and of course mother nature. Any one interested in sailing or adventure this is for you.  A testament to the optimism of youth.

Norfolk to Lord Howe Islands Great Circle Distance

On March 31st 1931, Sir Francis Chichester left the Northern Tip of New Zealand on an East to West flight across the Tasman sea. He stopped to refuel at Norfolk Island and Lord Howe Island. Let’s determine the great circle distance and bearings that his Gypsy Moth float plane Madam Elijah ZK-AKK had to fly between these two points using the Spherical Haversine law.


The great circle distance using the Spherical Haversine law is:


GCD = 895.3Km (483.4Nmiles), Bearing of Lord Howe Island = 249.9deg. This agrees with the Google Earth plot.

Intercept at Trillium Park Lat = 43.6296degN Long = 79.4095degW


“I must go down to the seas again, to the lonely sea and the sky, And all I ask is a tall ship and a star to steer her by;” from Sea Fever by John Masefield

Currently I am calibrating my 3 sextants from several known locations in Toronto. One requires a water horizon and the other 2 have bubble horizons. Trillium Park is gorgeous, it’s like looking out over the Pacific ocean! I am also reading Ian Strathcarron’s biography of Sir Francis Chichester “Never Fear”. I love Chichester’s cure for mental & physical scurvy: Scotch Whiskey + Lemon!!