This paper is submitted by Fernando Martín Asín and Rosa Chueca Castedo, faculty members of the College of Technical Topographical Engineering of the Polytechnic University of Madrid
It highlights the main differences observed on the two hemispheres. We will point out the differences observed as regards to seasons (see details in the Annex), constellations, the moon, planets, comets, and other starts of our sky.

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First, let’s remember the geographic coordinates of both Universities:

MADRID: Longitude = 0 h 14 m 45 s (W to Greenwich) - Latitude = +40º 24’

ROSARIO: Longitude = 3 h 53 m (W to Greenwich) - Latitude = -34º 36’

          As regards to latitudes, please notice that both cities, though having opposite signs, share almost a symmetrical position as to Equator.

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          Probably, the most significant difference between hemispheres lays on seasons since they are exactly reversed. When we are in summer in our country, you are in winter in Argentina. When we are in spring, you are in autumn. Many times people take advantage of this fact and just in a few hours by plane, they are able to leave the hot summer of their place for the cold winter of the other hemisphere or the opposite. Enclosed in the Annex, please find how to calculate season’s duration. In fact, if our winter is the shortest season in the year; your winter, on the other hemisphere, will be the longest season.

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          Let us continue with our satellite, the moon. Whenever we explain its movements, we focus on the special language we use in our hemisphere, e.g. “the moon lies”. We use this expression because when the moon shows us a “D” shape (in Spanish, initial letter of the word “decrease”), in fact, it is a waxing moon. On the contrary, when we see a “C” shape (in Spanish initial letter of “crescent”), it is a waning moon. In Argentina, the situation is exactly the opposite, then we say that the moon does not lie in the southern hemisphere.

          The moon is the satellite of the Earth. It has been said that “it is man’s faithful mate” and the poet’s inspiration source. There is so much to say about our beloved moon!

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          Another interesting topic is the observation of planets. We are here giving only a few details about them because the only difference found is that they are always observed—as with the moon— very near to the Ecliptic. We know that ecliptic latitudes of planets are always small, except with Mercury, first planet in our solar system and even more so in the case of Pluto, the last one. These planets together with the stars orbit the sky with different slants from the horizontal depending on the hemisphere on which we are standing as observers.

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          And now let’s search for comets and asteroids. Certainly, it is their slant which determine whether it results easier to observe them from Argentina or from Spain. We took advantage of this topic in our classes and we usually tell our students that we, Spanish observers, find it rather difficult to spot comets since some hours before we see a part of the sky, many other countries, e.g. Japan, have already seen and searched it. The reason is the position of that country in the terrestrial sphere; in other words, the geographic longitude the inhabitants enjoy.

          Likewise, we could also say that we observe a part of the sky four hours before Argentine people do. Therefore, since the sky moves counter clockwise, it is always easier to spot comets in Spain rather than in Argentina. We would like to develop this topic and we will do it when our paper is accepted. Another point to take into account is the comet’s particular position on the sky which would favour a better view from negative latitude.

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          To finish our presentation, we will speak about constellations. About how it is that some which are hard to spot on the northern hemisphere due to their stars slants, are so spectacularly seen on the other hemisphere. Short time ago, a working mate commented us about how marvellous it was for her to spot Scorpious constellation while travelling along a latitude quite near to Rosario. She was amazed when she spotted it in its full grandeur, especially because it is so difficult to see it from our country.

          Now let’s move to the Southern Cross. Some time ago, I told my mates about my experience with this constellation when I spotted it while on a trip to Brazil. I commented on the difficulties I had to detect it and how great I felt when I managed to see it.

          It is also interesting to remark the great feelings of surprise one experiences when the nearest to the sun star—Centaurus or Rigil Kent—is spotted from the southern hemisphere. This star is 4,3 light years and takes position 4 as regards to brightness.

          Then, we are going to speak about a number of constellations that we can appreciate on this hemisphere and that are forbidden on our latitudes. We thank the opportunity to speak to the population of this marvellous country of Argentina. We would like to comment about constellations which, for us, are circumpolar and difficult to see from there. For example, Ursa Major, Ursa Minor, Cassiopeia, Draco (Dragon) and many others.

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          Another exciting topic is to observe the differences on the sky during day movement by passing from a positive latitude site to a negative one. I have always been curious at observing how stars orbit without going past the zenith when we are observers on northern latitudes. Instead, stars crossing the sky approach the North Pole, i.e. they cross the “first vertical”, but to the north.

          We are not seeking a full understanding on the part of the reader, we are only trying to get some awareness about how different it may be to be an observer on one place or another.

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          We are also making commentaries on some expressions taken from Argentine books:

          For example, when these books giving a definition of the Vernal Point, they speak about the “Autumnal Equinox” and our books speak about “Spring Equinox”.
          It sounds rather odd to our ears when you speak about your summer hours running from September 1st to March 1st.
          We also read that you observe the stars Alpha Crux and Beta Crux at maximal digressing position to determine the meridian.

          In short, we are so enthusiastic about observing the sky that we are always encouraging others to join us. Argentina has a privileged position regarding sky observation—as compared to Spain—since Argentineans are able to watch constellations that are rather difficult to see from our country.

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          Let’s profit from this opportunity and talk a little about the 89 constellations the sky superbly displays in front of our eyes. These constellations help us to understand our own position and to locate planets. We know that these planets—according to the time of the year we are observing them— are constantly changing their position against the background of the stars.

          In Spain, in summer—winter, in your country—if we raise our eyes to the sky, we can easily detect the “Summer Triangle” on our zenith. Even in autumn, we are able to marvel at this triangle. It is built up by three stars: Vega, Deneb and Altair from the constellations of the Lyre, the Swan and the Eagle respectively. In my opinion, this triangle invites us to search for the most beautiful double star in the sky: Albireo.

          In the gravity centre of the Summer Triangle, we find the beta star of the Swan. Let me tell you an anecdote I really enjoy narrating. At my college time, I had the honour of having a great professor who loved music. He frequently spoke about Mussorgsky plays.

          Once, our professor told us the story of a play composed by this musician. In this story, the most terrible storm struck and frightened the population of a little village in the Alps. At dawn, when the storm was over, the peaceful landscape emerged with Mussorgsky descriptive music and a moment later, a bell from a tiny church rang far in the distance and a flute of a shepherd sounded in the mountain.
And our professor used to say that “only for the sound of that bell and the tunes of that flute life was worth living!”

          I would like to paraphrase his expression and speak about Albireo from the Swan. The sole pleasure of splitting that start makes life worth living!. I have witnessed such feeling in those who spot this double star for the first time. It is a wonderful experience.

          With the help of an ordinary telescope, we can split that star and the weak spot of light of 3,1 magnitude breaks in two within the range of the instrument. I invite my readers to try this experience.

          Two stars build up Albireo. They are located 500 light years away, 34” distant one from the other, their magnitudes are 3,1 and 5,4.

          I often add that on splitting Albireo, we can appreciate two dewdrops, one tinted in red and the other in blue—one a ruby, the other a turquoise.

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          The Milky Way run through Cygnus constellation. It is rather easy to picture the swan formed by the stars of the constellation.

          Another important detail is the star M 27 from Messier Catalogue. It is also known as Dumb-Bell, the name given to the brightest and largest nebula on the sky. It was spotted by Carlos Messier in 1764.

          We turn our eyes to the north and we find Ursa Major, Ursa Minor with the north star Polaris, Draco and Andromeda with the surprising M 31, and finally Corona Borealis and so many others that we are not mentioning here.

          Another detail. In the old times, the collection of stars received the name of “asterism”. >From the very beginning, they have been compared to animals, divinities, heroes and ordinary objects. In the old times, the Greeks named many of the constellations with this kind of words.

          Ptolemy (100-178 B.C.)recorded 48 constellations in his Almagest. In the following centuries, J.Bayer (1572-1625) and others identified 12 constellations on the northern hemisphere and around 50 on the southern one. Astronomers identified some others and today we have 89 constellations.

          To the north of the Zodiac, there are:

Andromeda, Aquila (Eagle), Bootes (Herdsman), Camelopardalis (Giraffe), Canis Minor (Little Dog), Cassiopeia (Queen Cassiopeia), Cepheus (King Cepheus ), Coma Berenices (Berenice´s Hair), Corona Borealis (Northern Crown), Cygnus (Swan), Delphinus (Dophin), Draco (Dragon), Equuleus (Colt), Hercules, Lacerta (Lizard), Lynix (Lynx), Lyra (Lyre), Pegasus (Pegasus), Perseus (Perseus), Sagitta (Arrow), Triangulum (Triangle), Ursa Major (Great Bear), Ursa Minor (Little Bear), Vulpecula (Little Fox)

          Then, the 13 well know from the Zodiac. We are going to speak about them later.

          And to the south of the Zodiac:

Antlia (Air Pump), Apus (Bird of Paradise), Ara (Altar), Auriga (Charioteer), Caelum (Chisel), Canes Venatici (Hunting Dogs), Canis Major (Larger Dog), Carina (Keel), Centaurus (Centaur), Cetus (Whale), Chamaeleon (Cameleon), Circinus (Compasses), Columba (Dove), Corona Australis (Southern Crown), Corvus (Crow), Crater (Cup), Crux (Southern Crux), Dorado (Goldfish), Eridanus (River), Fornax (Furnace), Grus (Crane, Bird), Horologium (Clock), Hydra (Female Water Snake), Hydrus (Male Water Snake), Indus (Indian), Leo Minor (Smaller Lion), Lepus (Hare), Lupus (Wolf), Mensa, (Table Mountain), Microscopium (Microscope), Monoceros (Unicorn), Musca, (Fly), Norma (Square), Octans (Octant), Orion (Hunter), Pavo (Peacock), Phoenix (Phoenix), Pictor (Painter’s easel), Pisces (Fishes), Pisces Austrinus (Southern Fish), Puppis (Stern), Pyxis (Compass), Reticulum (Reticle), Sculptor (Sculptor´s Workshop), Scutum (Shield), Serpens Caputi (Serpent´s Head), Serpens Cauda (Serpent´s Tail), Sextans (Sextant), Telescopium (Telescope), Triangulum Australe (Southern Triangle), Tucana (Toucan), Vela (Sails), Volans (Flying Fish).

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          This presentation will be incomplete unless we include some words about the Zodiac, the area where the sun moves in its apparent movement around the Earth in a year.

          I am making reference to those 12 constellations we learnt in our childhood. In fact, they are 13 with Ophiuchus between Scorpious and Sagittarius.

          Every Zodiac constellation has changed its position with the passing of time. This is due to the phenomenon called “Precession of the equinoxes” or “Retrogradation of Aries point” discovered by Hipparch, in the II century B.C.

          Every constellation gradually changed its position as compared to the original ones dated from 2000 years ago—when the correspondence with the 12 months of the year was established.

          Probably, those who have read some of my books (Professor Martin Asin speaking), particular “Atlas of the Sky” or a more recent one named “Constellations of the Sky”, may recall my advise as regards to cartographic representations; for the sky a stereographical projection, for areas near to the poles a polar design and for wedge-like divisions of the celestial sphere a meridian scheme.

          Although we have cited the 88 constellations present in the sky, I always sustain that they are 89 since Serpens, in my opinion, should be counted as two.

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          Finally, I would like to remind everybody, especially those who follow horoscope advices, that we all have our Zodiac sign changed. Horoscopes from magazines and newspapers does not resemble in the least the rigorous position of the Sun as it enters and leaves each constellation.

          Actually, the first of the 13 signs must be Pisces and not Aries. Currently, when the Sun is on the Vernal Equinox, the constellation over which it is projected is Pisces, although 2000 years ago it was Aries. Besides, to make matters worse, there is Ophiuchus—the thirteenth sign—located between Scorpious and Sagittarius.

ANNEX

HOW TO CALCULATE SEASON'S DURATION

          We feel it useful to make the calculus in reference to the year 2000. We know that season’s duration is gradually changing and will continue so until the year 6500 in which two seasons will coincide:

          Spring = Summer and Winter = Autumn

          Nowadays, seasons are organised according to their length—being the shortest the first and so on:

          Winter – Autumn – Spring - Summer

          This order corresponds to an observer on the northern hemisphere. For observers on the southern hemisphere, the order is reversed:

          Summer – Spring – Autumn - Winter

          Let’s calculate the four season’s length taking into account the “Ecliptic Longitude of Perigee”. This datum changes every year and this year 2000 is 282º 56‘ 18”. I invite our readers to revise some Astronomy concepts which will be useful to follow our explanations.

          First, let us remember that in Astronomy, apart from the True Sun—the only one that exists and gives light— we speak about two other Suns: the Fictitious and the Mean one. The Fictitious is an ideal Sun moving along the Ecliptic at a steady speed and it coincides with the True one at Perigee and Apogee points. The Mean Sun is another ideal Sun moving along the Equator at a steady speed and it coincides with the Fictitious one at Aries and Libra points.

          We relate the three Suns using the Equation of Time. We define this equation as the difference in right ascension between the True and the Mean Sun.

          We use this Mean Sun to measure time in our ordinary life. We relate mean, civil, official and legal hours to the period of time called mean day and we get the hour of our watches. The mean day is defined as the period of time the Mean Sun takes to pass twice through the meridian of a place. Then, dividing that value by 24 hours we get the mean hour, and dividing the latter by 60, the mean minute and likewise the mean second.

          When we study the “Equation of Time”, we said that it is the resultant of the two functions named “Equation of the Centre” and “Reduction to the Equator” (Readers may study these concepts in the Astronomy book written by one of the speakers of this presentation) The “Equation of the Centre” is fundamental to understand how to calculate season’s duration.

          We are going to use some diagrams with the three Suns we have already defined. You can clearly appreciate what Function Q (“Equation of the Centre”) represents on this diagram—the difference in the ecliptic longitude of the True Sun and the Fictitious one.

          We remind that the True Sun moves at variable speed throughout a year. It is so because it obeys Kepler´s Laws, especially the 2nd, which relates the areas swept by the Earth-Sun Vector. The Fictitious Sun, instead, moves at steady speed along the same plane of the Ecliptic.

          This Fictitious Sun will describe 360º angle in a Tropical Year of 365.2422 mean days In fact, to be more accurate, this Fictitious Sun describes a bit smaller angle because the Aries Point retrogrades 50.2” every year. This phenomenon is called “Precession of the Equinoxes” or “Retrogradation of Aries Point”.

          Now, we are going to calculate spring duration with the help of these concepts and the other three season’s can be estimated likewise.

          In the diagram, we can see both the Ecliptic and the Equator planes, and the Perigee Point of the Earth Orbit located between the “Tropic of Capricorn” or “Winter Solstice” and Aries Point. In other words, around January 2nd or 3rd , the Sun is on the furthest end of the apsis line—the point where the Sun is nearer to the Earth speaking about the apparent movement of the Sun around the Earth, instead of the real movement of the Earth around the Sun. All these concepts are the same considering one or other movement.

          The Sun at crossing the Perigee Point on January 3rd, poses us a paradox because it makes us think that when the Sun is nearer to the Earth, we are in winter in our hemisphere. We clearly realise that this paradox does not apply to Argentina. When the Sun is nearer to the Earth, you are in summer.

          Now then, following this reasoning, we are representing the True and Fictitious Sun with the letters T and F and it becomes clear that the difference from the Perigee Point to both Suns is Q (“Equation of the Centre”). In the Astronomy book mentioned before, it is:

          Q = v – nt = 2.e.sin nt + 5/4 e2.sin 2.nt

where v and nt are true and mean anomalies respectively. The value of nt represents the daily mean movement of the Sun, i.e. the angular speed of the Fictitious Sun. The value of e in the formula represents the eccentricity of the Earth orbit. e = 0.0168.

          For our calculus, we are going to use the expression that relates true and mean anomalies. We move nt, and we have

          nt = v – 2.e.sin nt - 5/4 e2.sin 2.nt

          We calculate the value of nt with this expression and successive reiterations. Then, we will have the point when the True Sun is in Aries and the same when it is in the Tropic of Cancer. These are the points where spring begins and ends. Our calculus starts by assuming that nt = v. The value of v is

          360º - 282º 56´18” = 77º 03´42”

Please remember that 282º 5618” is Perigee longitude.

          In this way, we obtain a first value for nt. Then we substitute it in the previous equation and we calculate again nt. And we continue like that until we get a value which is not very different from the previous one. This value corresponds to the position of the Fictitious Sun when the Spring begins. It tells us the nt value at the beginning of the season.

          With the help of a calculator, we solve the problem and we get successively the following angles for the value of x in the diagram:

                          77º 03’ 42”
                          75º 11’ 29.81”
                          75º 12’ 19.47”
                          75º 12’ 19.08”
                                   75º 12’ 19.09”

          When the True Sun has advanced other 90º, the spring will finish. Following the same method as before, we get the following successive values for y :

                          167º 03’ 42”
                          166º 38’ 33.82”
                          166º 37’ 45.80”
                          166º 37’ 44.28”
                                  166º 37’ 44.23”

Then, spring will last: y – x = 91º 25’ 25.14"

This value is equivalent to 92 days, 18 hours 12 minutes and 16 seconds.

We consider the year is 365.2422 days long, the time the Fictitious Sun describes 360º, and we take this reference value to convert degrees into hours and the like.

          Following analogue reasoning, we could get m and n values which give us the Fictitious Sun positions at the beginning of autumn and winter.

                          m = 258º 55’ 42.53”
                          n = 347º 29’ 02.31”

          Taking the diagram as a guide, it is easy to see the length of the four seasons:

  Spring:
  y – x = 91º 25’ 25.14” = 92 days 18 hours 07 minutes and 06 seconds

  Summer: m – y = 92º 17’ 58.30” = 93 days 15 hours 26 minutes and 44 seconds

  Autumn: n – m = 88º 33’ 19,78” = 89 days 20 hours 16 minutes and 49 seconds

  Winter: p + x = 87º 43’ 16.78” = 88 days 23 hours 58 minutes and 07 seconds

          We could check these times using the data of a yearbook that contains the dates the seasons begin. We would be able to see that they coincidence with the ones we have calculated.

          Adding up the four results corresponding to season's duration, we get 365 days 4 hours 48 minutes and 46 seconds: This value equals the 365.2422 days that represent the Tropical Year length. It is rather curious to see that the difference between winter and summer is almost four days.

          Evidently, it is not necessary to insist that seasons are reversed in the southern hemisphere. However, please remember that when we speak about spring it corresponds to autumn in the southern hemisphere. Likewise, when we refer to summer, autumn and winter on our hemisphere, it corresponds to winter, spring and summer respectively on the other hemisphere.

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