The binoculars or binoculars –

We would be surprised at the amount of objects that can be seen with binoculars. We have at our disposal star clusters, some nebulae, the Andromeda galaxy and the entire Milky Way full of stars to explore.

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If we want to observe the sky more closely, binoculars offer us that possibility. They are cheaper and easier to use than telescopes.

We recommend not to acquire a telescope as the first piece of equipment of the amateur astronomy. It is true that telescopes offer large increases, but precisely because of this, it is more difficult to find the celestial object that we are looking for. With binoculars it is much easier to locate, thanks to its small increases, the celestial objects. To this we must add that they show the images to the right. That is why we must spend time exploring the sky with binoculars and thus acquire a better preparation to find objects later with a telescope.

We would be surprised at the amount of objects that can be seen with binoculars. If we look for a dark place, we have at our disposal star clusters, some nebulae, the Andromeda galaxy and the entire Milky Way full of stars to explore.

We can also observe Jupiter and its satellites, as well as the craters of the Moon. Comets tend to look better with binoculars, like sun and moon eclipses, and planetary conjunctions.

Con prismáticos podemos ver la bella Galaxia de Andrómeda, también llamada M31.


Magnification of binoculars

There are binoculars of many types and magnifications. In the shop it is convenient that we check the smoothness of the mechanism, the clarity of vision at the edges of the field and how they adapt to our hands and eyes.

The most frequent models in astronomy are the 7 X 50. The first number represents the increases. In this case, it would be 7 increases. There are models that offer up to 16 or 20 magnifications, but such power has its drawbacks: by reducing the field of vision, it is more difficult to locate objects, and the vibration of the hands makes the images appear blurry.

The second number tells us about the opening of the front lenses, in millimeters. In the previous example, 7 X 50, would be 50 millimeters. There are smaller models, 35 or 42 mm. of aperture, but 50mm binoculars or binoculars offer brighter images. This is very important when it comes to finding weak objects in the sky. In stores we can find binoculars with a larger opening, with 60 or 80 mm lenses, but they are very heavy and difficult to hold.

The best choice consists of binoculars of 7 X 50 or 10 X 50. In both cases, they offer a good balance between increases, lightness of the image and lightness. We must avoid fixed-focus binoculars and those with zoom, because they offer insufficient quality images when we want to observe specific objects such as stars.

Los trípodes son imprescindibles para prismáticos de 11 X 70 en adelante.

Large binoculars, of 11 X 70, 20 X 80, 25 X 100, etc., are not a good choice for beginners due to their high cost, since they cost the same as a small telescope, and also because of the difficulty of its management In addition, we must add the purchase of a tripod, indispensable element for binoculars so heavy. Although the fact is that large binoculars offer really spectacular panoramas of the sky and serious observers should consider them as a possibility.

It is very important to consider the ocular relief, which means the distance between the eyes and the eyepieces to see the specific field. If the observer wears glasses to see from a distance, it may be more comfortable to have them on during observation with binoculars. In this case, we must choose binoculars with 18 or 20 mm of ocular relief, at least, and finished in retractable rubber flaps. These models leave a lot of space between the eyepiece and the eye so that we can see the entire field even with the glasses on, and the eye is at the right distance. If glasses are not worn, we extend the rubber flaps so that the eyes are at the correct distance.

The binoculars of 7 increases offer, the majority, a field of 7 degrees, enough to see the box of the Big Dipper. Models of 10 or more magnifications have smaller fields of vision, for example, 5 degrees, still suitable to provide spectacular images of the sky.

There are binoculars that bring marked in the box the field that they cover in degrees, although sometimes they do not give it in degrees, but in meters covered to 1000 m of distance. In this case, the field spanning 1000 m should be divided by 17.5 to obtain the field in degrees.


Some binoculars with wide field eyepieces provide larger fields than normal, can reach up to 7 or 10 degrees for models of 10 magnifications. The bad thing is that in this case, the quality of the image sometimes suffers, and the binoculars show distorted stars at the edges of the field. They also tend to have a rather reduced eye relief. If we look for binoculars that have a comfortable eye relief, wide field and quality images, the price of these is higher.

Types of prisms

We can choose between two types of prisms for binoculars. The Amici prisms make the binoculars H-shaped with straight sides. Porro prisms give binoculars a zigzag or N-shaped profile. Porro prisms are preferable for astronomy. If we buy an economic model with Amici prisms we can get annoying sparkles in the form of points in the bright stars. The ideal ones are binoculars with Porro prisms made of BAK4 glass, which offer better illuminated fields than those produced with the cheaper BK7.


We must also take into account the type of surface treatments applied to the lenses, as well as the number of lenses treated. Treated lenses improve light transmission and contrast. Economical binoculars offer single-layer treatments on the most important optical surfaces, while those with better quality have multi-layer treatments on all optical surfaces. We can see this by looking into the binoculars through the front lenses. If we appreciate internal reflections of white color, it means that this model has lenses with minimal treatment. Some binoculars that have totally treated optics will have few reflections, weak and of green, blue or purple tones.

The more stable the binoculars are held, the better images they will offer. We can appreciate weaker stars and finer details. To make sure, the easiest way is to sit in an armchair and rest your elbows on the arms of the seat with binoculars in your hands. Or better yet, attach the binoculars to a photographic tripod that is solid.

A good tripod offers firmness, but it makes the observation of the highest areas of the sky more difficult. For binoculars of 11 X 70 or more, a tripod is essential, although they can also be used for small models, since we will have better images.


The celestial coordinates –

To define locations in the sky, we use declination and right ascension.

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To define locations, on Earth we use longitude and latitude. Likewise, we divide the continents into countries. In astronomy we do something similar and also divides the sky into regions, as if they were countries: they are the constellations.

Imagine that, as the ancients thought, the sky was a sphere with all astronomical objects attached to it. If we cross the Earth with a stick or shaft that enters through the north pole of the planet and leaves the south pole, and we extend it on both sides in space, this axis will touch the sky in two points: they are the north and south celestial poles . It is as if the celestial sphere revolved around these two poles, although we already know that it is the Earth that moves.

If we stretch the line of the Earth’s equator and stick it to the celestial sphere, we can trace over it the celestial equator. This line will cut the sky in half in the northern and southern hemispheres, just as the equator divides the Earth into two hemispheres.

Now we will draw on the celestial sphere concentric lines parallel to the equator, centered at the poles. These celestial parallels, such as the latitudinal latitude lines, measure at what distance from the equator, either to the north or to the south, there is a point in the sky. A star that is in the celestial equator has 0º of declination. If that star were in the celestial north pole, its declination would be + 90º, and if it were halfway between the equator and the north pole, it would have + 45º.

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Each degree of decline has 60 arc minutes (‘) and every minute of arc, it contains 60 arc seconds (“).

Now let’s draw lines in a north-south direction, from the north pole to the south. These are the so-called straight ascension lines, and they measure the position of the celestial objects towards the east or the oste. The celestial equivalent of the Greenwich meridian, with 0º length, is the so-called vernal point: the point of the celestial equator where the Sun meets every year at the time of the spring equinox.

The sky is divided into 24 hours (h) of right ascension, and each of them has 60 minutes (m). Therefore, the vernal point has 0 hours of right ascension (?).

To identify any place on Earth we can give its position in longitude and latitude. But it is easier to imagine where it is if we place it in a specific country. The same happens in heaven. It is convenient to learn to locate some of the most important constellations to be able to orient yourself in the night sky. Thus, the stars will stop appearing as points and begin to be known figures.

Ptolemy , Greek astronomer, listed a total of 48 constellations of vague borders. Currently, we divide the sky into 88 constellations with clear boundaries, as was officially agreed in 1930.

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Some constellations are very old, such as Leo and Taurus (Taurus), which were already known by the Sumerians. Orion, the hunter, has been known for thousands of years. The Chaldeans of Mesopotamia called it Tammuz, the Syrians called it Al Jabbar, the Giant. For the ancient Egyptians he represented Sahu, the soul of Osiris. It was the Greeks who gave it its current name in honor of a mythical giant and so-called great hunter.

Other constellations are from the seventeenth and eighteenth centuries. Some were introduced to map the Southern Celestial Hemisphere, which was unknown in Europe before the conquest of America and the era of explorers that began in the sixteenth century. The Southern Cross (Crux), for example, was defined as a constellation for the first time by Andrea Corsali, who sailed to the tropics in 1515 with a Portuguese expedition.

Thus, the constellations are only some figures that we trace in the sky for convenience, linking one star with another as if it were a drawing. Normally, the stars of a constellation are not related to each other in space. For example, Betelgueuse, the star of Orion’s left shoulder, is 427 light years from Earth, while Bellátrix, the right shoulder, is 243 light years away. The stars of the Orion belt are at distances between 800 and 900 light years.

If we could travel to another part of the galaxy and contemplate the stars of Orion, we would not see the same as from Earth. The aliens from other planets will see very different figures, although their constellations include many of the stars we see from here.


What to see in September? –

Objects visible in the sky in September

This is a list of some of the brightest and most interesting celestial objects that can be seen in the September night sky.

The objects are grouped in three blocks. Those that can be easily seen with the naked eye , without binoculars or telescopes, which can be easily seen with binoculars and those that can be seen require a telescope .

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Meaning of the abbreviations in the Type column

Gal Galaxy
Its T Star
Double Double Star
Var Variable Star
Neb Nebula
ND Diffuse Nebula
NP Planetary Nebula
DO NOT Dark Nebula
AC Open Cluster
CG Globular Cluster


  • Naked eye
  • With binoculars
  • With telescopes

Objects visible to the naked eye in the southern hemisphere in September.

Altair Aql Its T The brightest star of the Eagle. Its name means “eagle in flight”. Dist 16.7 to
to Centauri Cen Double The bright star closest to the Sun at 4.4 at the telescope appears as a bright double star. Period of 80 years.
ß Centauri Cen Its T Together with Alpha Centauri forms the so-called “Pointer of the Cross”. Dist 525 al
Coalsack Cru Neb The dark nebula visible to the naked eye most famous. It requires dark skies. Its name means “Sack of coal”. Dist 600 al
Deneb Cyg Its T The brightest star in the Swan. Bluish supergiant of about 20-25 solar masses and a radius between 200 and 300 solar radios. He has a short life left and will become a supernova within a few million years. One of the greatest known supergiants. Dist 1,400 to
Achernar Eri / td> Its T The brightest star of Eridanus, The River. Its name in Arabic means “the end of the river”. Dist 140 al
to Herculis Her Var Semi-regular variable. Its magnitude varies between 3.1 and 3.9 in 90 days. He has a companion of mag 5,4.
Vega Lyr Its T The 5th brightest star in the sky. A blue-white star. Dist 25 al
Fomalhaut PsA Its T The brightest star of Pisces Austrinus. Its name in Arabic means “the mouth of the fish”. Dist 25 al
Antares Sco Its T Supergiant red star. Its name means “rival of Mars”. Dist 135.9 al
Spica Vir Its T Its name in Latin means “ear of wheat” and it is found in the left hand of Virgo. Dist 250 al

Objects easy to see with binoculars in the southern hemisphere in September.

NGC 6397 Ara CG It is believed to be the closest globular. Dist 7000 al
M2 Here CG One of the most compact and rich accumulations known. It contains about 150,000 stars.
? Centauri Cen CG The largest and brightest globular cluster in the sky. It contains several million stars. Dist 18000 to the estimated Age 12 billion years.
NGC 4755 Cru AC The Jeweler Outstanding cluster of stars. A lot of contrast of colors, with a central red supergiant surrounded by blue stars. Dist 7600 to
? Cygni Cyg Its T Pulsating variable star of long period. Magnitude that oscillates between +3,62 and +15,00 in 407 days, the greater change of luminosity known in a star. Distance 300 to
LMC Dor Gal Large Cloud of Magellan. A galaxy neighboring the Milky Way, the third closest. Dist 180000 al
M13 Her CG The best globular cluster in the northern hemisphere. Discovered by Halley in 1714. Dist 23000 al
R Hydrae Hya Var It is a bright red giant variable of long period. Its mag varies between +3.5 and +10.9 during 389 days.
R Lyrae Lyr Its T Variable star that goes from mag 5 to 3.88 in 46 days. It is a red giant in the last stages of its life.
e Lyrae Lyr Double Famous double double. The binoculars show a double star. More increases reveal that each is double as well. It is located at 180
M10 Oph CG At 3 degrees from the weakest M12. Both can be glimpsed with binoculars. Dist 14000 al
? Pavonis Pav Var Typical Cepheid variable. Its mag varies between 3.9 and 4.8 in 9.088 days.
NGC 6752 Pav CG One of the best and most beautiful globular in the sky. Dist 14000 al
M15 Peg CG One of the densest clusters of the Milky Way. The only known globular containing a planetary nebula. Mag 14. Distance 33.600 to
M8 Sgr ND Lagoon Nebula Bright nebula crossed by a dark black line. Dist 5200 to the Discovered in 1747 by Guillaume Le Gentil .
M22 Sgr CG A spectacular globular cluster. It has found 32 variable stars and a planetary nebula. Dist 10000 al
M25 Sgr AC Brilliant cluster located about 6 degrees N of the teapot. Dist 1900 al
M4 Sco CG A globular closed. It can just be visible without optical help. Dist 7000 to Perhaps the globular cluster closest to the Solar System. It was the first in which individual stars were resolved.
M6 Sco AC Butterfly Cluster. More than 30 stars with binoculars of 7 increases. Dist 1960 al
M7 Sco AC Superb open cluster, also called Ptolemy’s Cluster. Visible to the naked eye Age 260 million years. Dist 780 al
NGC 253 Scu Gal Call the Galaxy the silver coin. We see it almost singing. It is a barred spiral discovered by Caroline Herschel in 1783. Dist 12.9 million
M5 Be CG Beautiful globular cluster. The telescope will reveal point stars. Dist 25000 al
NGC 6025 TrA AC Small open cluster in the Milky Way. Dist 2700 al
47 Tucanae Tuc CG Spectacular object, the second brightest cluster. A telescope will reveal stars. Near the edge of the Small Magellanic Cloud. Dist 20000 al
SMC Tuc Gal Small Cloud of Magellan Neighbor of the Milky Way. It requires dark skies. Dist 210000 al
Cr 399 Vul AC Broschi or Hanger Cluster. It is not really a cluster. Composed of about 40 stars. Ideal for binoculars. Dist 218 to 1140 al

Objects easy to see with telescopes in the southern hemisphere in September.

NGC 7009 Aqr NP Saturn Nebula It requires an 8-inch telescope to see the resemblance to the planet Saturn and its rings, seen in profile.
NGC 7293 Aqr NP Call Nebula of the Helix. Estimated age 10,600 years. Distance 680 to
NGC 5128 Cen Gal Crossed by a dark strip. Strong radio source. Dist 11 mill al
Albireo Cyg Double Beautiful double star. Contrast of colors orange and blue greenish. Sep 34.4 “.
? Delphini Of the Double They appear yellow and white. Mags 4.3 and 5.2. Dist 100 to The double Struve 2725 in the same field.
M83 Hya Gal Classic spiral seen from the front in a beautiful field of stars. Discovered in 1752 by Lacaille.
5822 Lup AC Large and attractive cluster. Dist 1800 to The open cluster NGC 5823 to the south.
ß Lyrae Lyr Double Binary eclipsing. Its magnitude varies between 3.3 and 4.3 in 12,940 days. The weakest blue star in mag 7.2.
M57 Lyr NP Ring Nebula. Magnificent object. Smoke ring shape. Dist 4100 to
M20 Sgr ND Trifid Nebula A telescope shows 3 lines of dust sectioning the nebula. Dist 5200 al
M17 Sgr ND Omega nebula It contains the cluster NGC 6618. Dist 4900 al
6124 Sco AC It contains 5 bright stars squeezed near the center. Chain of 7 stars. Dist 1600 al
M11 Sct AC Wild Duck Cluster. It looks like a globular with binoculars. Shape of V. Dist 5600 to
M16 Be ND Nebula of the Eagle. It requires large aperture telescopes. Dist 8150 al
M27 Vul NP Dumbbell nebula. Large, shaped like two lobes. The most spectacular planetary. Dist 975 al

Keep in mind that all objects, except the stars, appear more impressive when viewed through large binoculars or a telescope .

Tips for observing the night sky

When observing the night sky , and in particular the objects of deep sky, such as star clusters, nebulae and galaxies, it is always better to do it from a dark place. Avoid direct light from street lighting or other sources. If possible, it should be observed from a dark place away from the light pollution that surrounds most large cities today. You can see more stars when your eyes have adapted to the darkness, usually around ten to twenty minutes after being exposed to light.

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If you need to use a flashlight to see a map of the sky, you should cover the bulb with red cellophane. We can also buy flashlights with red light that can be easily found in stores.

Finally, even though the Moon is one of the most impressive objects to see through a telescope, its light is so bright that it illuminates the sky and makes many of the weak objects more difficult to see. Therefore, it is convenient to observe the night sky on moonless nights, preferably in the New Moon or in the Lower Quarter.


Ephemerides November 2018 –

The most outstanding astronomical events for the month of November 2018 in the northern and southern hemispheres

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The sky of the month of November 2018 in the northern hemisphere


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Map of the northern hemisphere sky, seen from Madrid on November 15, 2018 at 12:00 a.m.

  • 2. Moon near Regulus (morning sky) at 6 o’clock TU.
  • 6. Moon very close to Spica (morning sky) at 3 o’clock TU.
  • 6. Moon near Venus (at 17º of the Sun, morning sky) at 9 o’clock TU. Mag. -4.3.
  • 6. Mercury at its highest east elongation (at 23º of the Sun, evening sky) at 3:00 pm TU. Mag. -0.2.
  • 7. New Moon at 4:02 PM. Beginning of the lunation 1186.
  • 9. Mercury at 1.8º of Antares (at 23º of the Sun, evening sky) at 12 o’clock TU. Mags. -0.1 and 1.0. Moon and Jupiter close.
  • 11. Moon near Saturn (evening sky) at 4:00 PM. Mag. 0.6.
  • 14. Moon in apogee (farthest from Earth) at 16h UT (distance 404.339 km, angular size 29.6 ‘).
  • 14. Venus at 1.3º east of Spica (at 28º of the Sun, morning sky) at 20h TU. Mags. -4.5 and 1.0.
  • 15. Crescent Moon at 14:53 TU.
  • 16. Moon near Mars (evening sky) at 5 o’clock TU. Mag. -0.3.
  • 17. Leonid meteor shower peak at 10pm TU. It arises from the remains expelled by Comet Tempel-Tuttle. It produces very fast (71 km / sec). 10 to 15 meteors per hour are expected under dark skies.
  • 23. Moon near the Pleiades (midnight sky) at 5 o’clock TU.
  • 23. Full Moon at 5:40 TU.
  • 23. Moon near Aldebaran (midnight sky) at 9pm TU.
  • 26. Jupiter in conjunction with the Sun at 7 o’clock TU. Go to the morning sky (not visible).
  • 26. Moon in perigee (closest to Earth) at 12:07 TU (366,620 km, angular size 32.6 ‘).
  • 26. Moon near Castor (morning sky) at 18h TU.
  • 26. Moon near Pollux (morning sky) at 23 o’clock TU.
  • 27. Mercury in inferior conjunction with the Sun at 9 o’clock TU. Mercury passes into the morning sky. Not visible.
  • 27. Moon near the Manger Cluster M44 (morning sky) at 10pm TU.
  • 29. Moon near Regulus (morning sky) at 11 o’clock TU.
  • 30. Moon in Waning Quarter at 00:20 TU.
  • 30. Venus at its maximum brightness at 2h TU. Mag. -4.7.

All hours in Universal Time (TU).

Good heavens! See you next month!

The sky of the month of November 2018 in the southern hemisphere

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Download a large image to print it.
Map of the southern hemisphere sky, seen from Buenos Aires on November 15, 2018 at 12:00 a.m.

  • 2. Moon near Regulus (morning sky) at 6 o’clock TU.
  • 6. Moon very close to Spica (morning sky) at 3 o’clock TU.
  • 6. Moon near Venus (at 17º of the Sun, morning sky) at 9 o’clock TU. Mag. -4.3.
  • 6. Mercury at its highest east elongation (at 23º of the Sun, evening sky) at 3:00 pm TU. Mag. -0.2.
  • 7. New Moon at 4:02 PM. Beginning of the lunation 1186.
  • 9. Mercury at 1.8º of Antares (at 23º of the Sun, evening sky) at 12 o’clock TU. Mags. -0.1 and 1.0. Moon and Jupiter close.
  • 11. Moon near Saturn (evening sky) at 4:00 PM. Mag. 0.6.
  • 14. Moon in apogee (farthest from Earth) at 16h UT (distance 404.339 km, angular size 29.6 ‘).
  • 14. Venus at 1.3º east of Spica (at 28º of the Sun, morning sky) at 20h TU. Mags. -4.5 and 1.0.
  • 15. Crescent Moon at 14:53 TU.
  • 16. Moon near Mars (evening sky) at 5 o’clock TU. Mag. -0.3.
  • 17. Leonid meteor shower peak at 10pm TU. It arises from the remains expelled by Comet Tempel-Tuttle. It produces very fast (71 km / sec). 10 to 15 meteors per hour are expected under dark skies.
  • 23. Moon near the Pleiades (midnight sky) at 5 o’clock TU.
  • 23. Full Moon at 5:40 TU.
  • 23. Moon near Aldebaran (midnight sky) at 9pm TU.
  • 26. Jupiter in conjunction with the Sun at 7 o’clock TU. Go to the morning sky (not visible).
  • 26. Moon in perigee (closest to Earth) at 12:07 TU (366,620 km, angular size 32.6 ‘).
  • 26. Moon near Castor (morning sky) at 18h TU.
  • 26. Moon near Pollux (morning sky) at 23 o’clock TU.
  • 27. Mercury in inferior conjunction with the Sun at 9 o’clock TU. Mercury passes into the morning sky. Not visible.
  • 27. Moon near the Manger Cluster M44 (morning sky) at 10pm TU.
  • 29. Moon near Regulus (morning sky) at 11 o’clock TU.
  • 30. Moon in Waning Quarter at 00:20 TU.
  • 30. Venus at its maximum brightness at 2h TU. Mag. -4.7.

All hours in Universal Time (TU).

Good heavens! See you next month!

Universal Time : Tue, Dec 25 2018 14:18:08 (Real time)


Women astronomers –

The great unknown of astronomy


We could not think of modern astronomy without the enormous work of all those women who, with their effort, dedication and love of science, have left us their legacy. All those women who, from different countries of the world, have contributed to the progress of astronomy, most of them forgotten by history. The presence of women in astronomy is 4000 years old.

The high priestess En’Heduana created the first known calendars. He lived in Babylon 2300 years ago. C.

Aglaonike (2nd century BC) lived in ancient Greece and predicted eclipses.

In Alexandria, Hypatia (4th century), was a great philosopher, mathematician and astronomer. Some attribute the invention of the astrolabe, three treatises on geometry and algebra, letters from heaven and a planisphere. She died with her throat cut.

It is unknown if there were female astronomers during middle age. Only one Spanish Muslim is known, from the time of the Caliphate of Córdoba, called Fátima de Madrid . His father was an astronomer too and she helped him. He wrote many works of astronomy, called Corrections of Fatima. A work of his, called Treaty of the astrolabe, is preserved in the Library of the Monastery of El Escorial.

In the 16th century Sofia Brahe helped her brother Tycho Brahe to calculate eclipses.

During the seventeenth and eighteenth centuries astronomy was considered an artisanal activity. During those centuries, 14% of German women were engaged in astronomy.

The astronomer Maria Cunitz (1604 – 1664), was called the “Palas de Silesia” (Pallas was the god of wisdom). He wrote “Urania Propitia”, which were like the “Rudolphine Tables” but new and simplified, more precise and simple to use, and also divulged Kepler’s Laws. It became well known throughout Europe.

Maria Eimmart lived at the same time as Galileo. She was the daughter of an astronomer and made 250 drawings of the moon, with which a precise map of the moon could be made.

Maria Wilckelmann Kirch (Germany, 1670 – 1720) was an advanced woman for her time. He published works on conjunctions and discovered a comet in 1708, but it was attributed to her husband. The Berlin Academy awarded her a gold medal, although it did not help her after her husband died, to find a job. She requested to take the position of her husband, but was not accepted as a woman.

Caroline Herschel (Germany, 1750 – 1848), sister of the famous astronomer William Herschel who helped. He discovered 17 nebulae and eight comets. In 1787 he was recognized as an astronomer in his own right and was granted an annual salary of 50 pounds. After the death of his brother he returned to his hometown and wrote a Catalog of 2500 nebulas. The Royal Society awarded him a gold medal.

Mary Sommerville (England, 1782 – 1872). She had to marry her cousin, much older than her, to fulfill her dream of entering the intellectual environments of the time. He published several books, the last at 89 years.

The professionalization of astronomy in Europe in the nineteenth century led to the disappearance of women in science. On the other hand, the opposite happened in the United States.

Maria or Mariel Mitchell (1818 – 1889), daughter of an astronomer. He discovered a comet that bears his name, for which he was awarded a medal, he studied sunspots, asteroids and the movements of the planets.

Professor Pickering, of the University of Harvard, hired a group of 21 women, known as the Harem of Pickering to perform tedious works of classification and cataloging of the stellar spectra up to magnitude 9. Among them, the following four stood out.

Williaminna Fleming (1857 – 1911) was the first woman to be hired at Harvard. He discovered white dwarfs, 10 novae, 52 nebulae and hundreds of variable stars.

Annie Jump Cannon (1863 – 1941) created the system of spectral classification of stars.

Antonia Maury (1866 – 1952) invented a classification system with subscripts for the different luminosities of each stellar type.

Henrietta Leavitt (1868 – 1921) discovered the period-luminosity relationship for Cepheid stars and 1,777 variable stars.

At the Paris Observatory, the Sky Charter was projected, mapping all the stars up to magnitude 11. Twenty-one observatories participated from all over the world. They hired many women because they were cheaper and more efficient, but their jobs were anonymous.

In Spain, the Navy Observatory of San Fernando (Cádiz) hired “four lady plate measurers” and invested 30 years of their life to develop this work.

Charlotte Moore Sitterly (1898 – 1990), American astronomer, published books on the solar spectrum.

Cecilia Payne-Gaposchkin (1900 – 1980) was the first woman to make observations at the Monte Palomar Observatory because of her extraordinary reputation but only for a few hours and as a courtesy of the director.

Peggy Whitson

Margaret Burbidge (1919-) had to use her husband’s name to develop most of her work prior to 1967.

Vera Rubin (1928 -) was the first woman to legally use the Monte Palomar telescope in 1964.

Margaret Geller (1947 -) has been awarded an honorary doctorate in Spain for her studies on the distribution of galaxies in the universe.

Jocelyn Bell (1943 -) had to overcome the tremendous injustice of not considering her for the Nobel Prize in Physics for the discovery of pulsars. The prize was awarded to his thesis director.

“This is a battle that young women will have to fight. Thirty years ago we thought that the battle would end soon, but equality is as elusive as dark matter. ” (Vera Rubin)


Earrestenes of Cyrene –

He was born in Cyrene, the present city of Shahhat in Libya in the year 276 a. C.

He studied in Alexandria and Athens. He was a disciple of Ariston of Chios, Lisanias of Cyrene and Callimachus. He was also a great friend of Archimedes.


It had the nickname of Beta (as the second Greek letter) and also that of Pentatlos, the athlete who is able to be part of several specialties but maybe because of that he is not capable of being excellent in any of them, he always remains second, nickname very hard for a philosopher whose bases have served for later scientific findings.

From 236 a. C. and until the end of his life he worked in the Library of Alexandria. According to Suidas, Eratosthenes lost his sight and left himself to die of hunger when he was eighty years old, although according to Luciano he arrived at eighty-two.

Esfera armilar

It is attributed the invention of the armillary sphere that was still used in the seventeenth century. Probably he will use this instrument for his astronomical observations, but it is only known that thanks to this sphere he determined the obliquity of the ecliptic. He calculated that the interval between the tropics was 11/83 of the Earth’s circumference, so the result was 23º 51 ’19 “, a figure that Claudio Ptolemy later adopted. According to some, Eratosthenes actually obtained a figure of 24º, and it was Ptolemy who tuned up to 23º 51’19 “.

Observing the eclipses, he calculated that the distance to the Sun was 804,000,000 stadiums. If the stadium measured 185 meters, this gave 148,752,000 kilometers, a figure very close to the astronomical unit. He also calculated that the distance to the Moon was 780,000 stadiums, although in reality it is almost three times greater. He also calculated that the diameter of the Sun was 27 times greater than that of the Earth, although in reality it is 109 times larger.

He is credited with the work Katasterismoi, which includes the nomenclature of 44 constellations and 675 stars.

He studied the prime numbers. The “sieve of Eratosthenes” is still used, although modified.

To calculate the size of the Earth he invented a trigonometric method and the notions of latitude and longitude, although it seems that they had already been used previously.

Eratosthenes had read in a papyrus of the Library of Alexandria where he worked, that on June 21, summer solstice, when at noon, the sun is closer to the zenith than any other day of the year, this star passed exactly through the zenith on Syene, in Egypt (the current Aswan). This was easily demonstrable simply by sticking a vertical stick on the ground and observing that it did not cast any shadow. It was also demonstrated by the fact that the sunlight reached the bottom of the wells. If the same was done in Alexandria, 800 kilometers north of Syene, the stick cast a short shadow, which meant that in that city the midday sun was a little over 7 degrees south of the zenith.

The distance between the two cities could be taken from the caravans that traded between these cities, or perhaps obtained the data of one of the hundreds of thousands of papyri that existed in the Library of Alexandria. Some people say that perhaps he used a regiment of soldiers to count the steps between the two cities. Thus, he calculated that the distance was 5,000 stadiums, from which he could deduce that the circumference of the earth was 252,000 stadiums. If Eratosthenes used the Egyptian stadium, which is 52.4 cm, it gives a total of 39,614.4 kilometers, that is, an error of less than 1%.

Posidonius, 150 years later, returned to these calculations and obtained a slightly lower figure, amount that would adopt Ptolemy and on which Christopher Columbus based to demonstrate the viability of his trip to the West Indies. With the measures of Eratosthenes that trip might never have been made.

He also calculated the distance of the Earth to the Sun in 804 million stadiums, which gives a figure of 139,996,500 kilometers and the distance from the Earth to the Moon in 708,000 stadiums, 123,280.5 kilometers. These calculations were made using data obtained during lunar eclipses.

Ptolemy tells that Eratosthenes measured the inclination of the Earth’s axis with great accuracy, since it obtained a value of 11/83 of 180º, that is, 23º51’15 “.

The result of these works of geodesy left them in his book “On the measurements of the Earth”, lost at present, although other authors, like Cleomedes, Teón de Izmir and Strabón reflected in their works details of these calculations.

Mapa de Eratóstenes de Cirene

Eratosthenes contributed to the progress of science with many other works. He devised a calendar with leap years. He created a star catalog that contained 675 stars. He drew the route from the Nile to Khartoum with great precision, including the two Ethiopian tributaries of the Nile, suggesting that the lakes were the source of the river. Many other scholars previous to Eratosthenes had studied the Nile, in their eagerness to explain the behavior of the river, but even Thales was mistaken in his theory. It was Eratosthenes who first came up with the correct answer by deducting that it sometimes rained very hard in the river source regions and this could be the explanation for the flooding of the river later on.

De Eratosthenes is also one of the most beautiful maps of the ancient world, the first with a network of meridians and parallels.


Multiple soles –

The universe is a huge set of suns, and ours is just one more.

Image result for multiple soles astronomy

But there is one more question: if the Earth moves and the stars are placed at arbitrary distances, why do the most distant ones not show a parallax with respect to the closest ones?

An obvious explanation was given to this question, which was immediately admitted: because the nearest stars were so far away that their parallaxes were too small to be detected with the instruments of 1800. Even Copernicus gave this same answer when they criticized the absence of parallax in against his heliocentric theory.

If the stars moved at the speed of the planets it would be possible to estimate the distance at which the stars move.

The fastest self-movement is Barnard’s Star, which was discovered by the American astronomer Edward Emerson Barnard in 1916. Its movement is 10.3 seconds of arc per year, insignificant, since the circumference is divided into 360 degrees , each degree in 60 minutes and each minute in 60 seconds. A second of arc is 1 / 1,296,000 of the sky. The Moon has a diameter of 31 arc minutes, so a second would also be 1/1860 of the diameter of the Moon. Jupiter is a simple point of light in the sky, but its diameter, at first glance, is 30-50 seconds of arc, depending on how far it is from Earth.

Comparación de tamaños

Therefore, if we say that the Barnard star moves 10.3 seconds of arc a year, it is like saying that in a year it travels more or less 1/180 of the diameter of the Moon or ¼ of the diameter of Jupiter. In spite of everything, this own movement is so fast if we compare it with the others, that this star is sometimes called “Barnard’s fugitive star”. The normal thing is that the own movements are of 1 second of arc per year, and sometimes less.

Comparación de tamaños

Assuming that Barnard’s star moved perpendicular to our line of sight with the same velocity as the Earth around the sun, that is, at 28.8 kilometers per second, in a year he would have traveled 940,000,000 kilometers. For this distance to correspond to 10.3 seconds of arc, the star would have to be sixteen billion kilometers from Earth. Then, it would show a parallax of only 1 second of arc. Assuming that it moved at a speed greater than that of the Earth, as it actually happens, we could say that its distance is still greater and its parallax, therefore, still smaller.

To observe in the sky the smallest ellipse, of 1 second of arc or less, of a star was very difficult for the astronomers. It is that if we saw a coin of 20 cents of euro to six kilometers of distance. An own movement of 1 second of arc a year is not difficult to observe, but it is that they accumulate from year to year. After a century, a star that moves 1 second of arc per year will have moved almost 2 minutes of arc in the sky, and this is perfectly visible with a telescope. On the other hand, parallactic movements go from one side to the other without accumulating with the passage of time.

The stars are tens of billions of kilometers from us and, still, we see them. At that distance, an object with a brightness as huge as the Sun would appear as a small dot of light.

And, on the contrary, any star that is the same distance as the Sun, would have a much greater brightness.

In other words, the Sun is a star that only differs from the others in that we see it from a distance of millions of kilometers instead of billions of kilometers, as it happens with other stars.

The universe is a huge set of suns, and ours is just one more.

If the Sirius star were as bright as the Sun and if the light that reaches us is smaller, it is only due to the enormous distance that separates us from it. Sirius has a magnitude of -1.6 and the Sun of -26.9, this means that the Sun is 25.3 times brighter than Sirius. Each magnitude represents an increase in brightness of 2,512, so the brightness of the Sun is 13,200,000,000 times that of Sirius.

The brightness of a luminous object varies in inverse proportion to the square of the distance, which means that if we move the object away from the previous one, the brightness will decrease by ¼; if we move it away five times the previous one, its brightness will be reduced by 1/25.

If Sirius shines 1 / 13,200,000,000 times less than the Sun, it is because it is 115,000 times farther away, since 115,000 X 115,000 equals 13,200,000,000. If the Sun is 150,000,000 kilometers away from us, Sirius must be about 16 billion kilometers away.

This billions of kilometers does not tell us anything. Let’s use other units . Recall that one light-hour is 1,080,000,000 kilometers. At 300,000 kilometers per second, the light travels in a year 9.440.000.000.000 of kilometers, but we can round in ten trillions of kilometers.

So, Sirius is 16 billion kilometers or two light-years from Earth. And since Sirius is one of the closest stars, we will have to measure all stellar distances in light years. A ray of light takes to get from the Sun to Earth eight minutes, and between the Sun and Pluto, five and a half hours.


The celestial vault –

If the Universe only consisted of the solar system,
the problem of its size would have been solved in 1700.

But the solar system is not the universe, we lack the stars.

In 1700 it was still possible to believe that a vault limited the universe and that the stars were fixed as little lights, and also that this vault was far beyond the end of the solar system. That’s what Kepler thought.

The measures of parallaxes that had been used to calculate the scale of the solar system in the seventeenth century were not good for the stars. The separation between two nearby stars hardly varied at all, however widely separated were the terrestrial observatories from which they were measured. Even placing the two observatories at opposite ends of the Earth, no change in the position of the stars was noticed. This should not surprise us, because although the stars were a little beyond Saturn, this distance is too large for the parallax could be measured with the means available in 1700.

Image result for celestial vault

But the surface of the Earth was not the astronomer’s only resource for solving this problem. Although the diameter of the Earth does not measure more than about 12,000 kilometers, in its movement around the Sun the entire planet moves through space and between the two extremes of the average orbit a distance of 299,000,000 kilometers. So if the position of the stars was recorded one night and it was recorded again another night, but half a year later, the astronomer would have made two observations from two positions separated by a distance equivalent to 23,600 times the diameter of the Earth. The angular distance between the edge and the center of the ellipse would be the stellar parallax .

This method can not be applied to planets because they describe such a complicated trajectory in space that any displacement caused by the movement of the Earth is masked. Trying to separate the own movement of the planet from the other one that it has by virtue of the movement of the Earth would be a very complicated work, and it would give inaccurate results that those that can be obtained by the parallax method. As the stars remain practically fixed throughout the year, with them you can use that method.

During the ten years that elapsed between 1800 and 1809, astronomers could not detect the parallax of any star. The reasons for this were very varied.

It could happen that Copernicus and Kepler were wrong and that the Earth did not revolve around the Sun, but that it was the immobile center of the Universe. If it had been like that, it would have been impossible to observe any parallax. When Copernicus first exposed the heliocentric theory , one of the strongest arguments against him was that no parallax could be performed. But there were too many reasons in favor of the heliocentric theory , so, although no stellar parallax had been observed, that theory ended up steadily in astronomical thought. The Earth does move, so the absence of parallaxes had to be explained by other causes.

Although the Earth moves, no parallax could be observed if all the stars were at the same distance, because the parallax can only be measured when observing the position that a nearby object occupies with respect to another one farther away. If the celestial vault were rigid, all the stars would have an identical displacement even if the observer’s position changed and no parallax could be observed.

There were several arguments that led to think that the distances between the Earth and the stars could be variable. It could happen that the stars were distributed in a very wide space, and the Universe did not have a rigid border.

The brightness of the stars changes, made evident to anyone who has looked at the night sky. Hipparchus was the one who tried for the first time to systematize these differences in brightness, for which he divided the stars into six classes or magnitudes. The brightest ones classified them in the first magnitude, those that shone a little less in the second magnitude, and thus until arriving at the sixth, within which the weakest stars were included that could be observed with the naked eye.

Image result for celestial vault

At present, astronomers measure the brightness of stars with instruments that, of course, did not exist in antiquity, and specify the different magnitudes with great mathematical precision. A difference of 5 magnitudes translates into a quotient of 100 measured in brightness, which means that a star of magnitude 1 is 100 times brighter than another of magnitude 6. So a difference of a single magnitude represents, in brightness, a quotient of 2,512, since 2,512 X 2,512 X 2,512 X 2,512 X 2,512 is equal to 100.

There are currently very precise measurement methods that allow you to define the magnitude of a star up to tenths of a magnitude. The star Aldebaran, for example, has a magnitude of 1.1, while Regulus is of magnitude 1.3, which is somewhat dimmer. The magnitude of the Polar Star is 2.1.

There are many brighter stars than Aldebaran, of magnitude greater than 1.0. Procyon has magnitude of 0.5, and Vega, still brighter, of 0.1. The stars that shine the most are assigned negative magnitudes. Sirius has a magnitude of -1.4.

Besides the stars, the planets, the Moon and the Sun are also included. Venus, Mars and Jupiter, sometimes have a higher brightness than the brightest stars: Jupiter can reach a magnitude of – 2.5, Mars of -2.8 and Venus of -4.3. The full Moon has a magnitude of -12.6 and the Sun of -26.9.

At the opposite extreme, there are stars with magnitude less than the sixth and are invisible to the naked eye. When Galileo focused his telescope for the first time towards the sky, in the year 1609, he saw hundreds of stars impossible to detect until then. Today you can see stars of magnitude 7, 8, 9 and much more up and down the scale of brightness. The most powerful telescopes that exist today can distinguish thousands of stars of magnitudes greater than 23.

If all stars had the same brightness, we might think that the difference in apparent brightness was due only to distance. The closest stars appear brighter than the farther ones, just as the nearby streetlamps seem to shine more brightly than the more distant ones.

In 1700 there was nothing to suggest that all stars had an identical brightness. If all the stars were at the same distance from the Earth, it could be because there was a real difference in the brightness and not an apparent difference, that is, there were simply brighter and dimmer stars, just as some light bulbs give more light than others

The Greeks had recorded the relative positions of the stars. The first to do so were Aristilos and Timocares de Alejandría, in the 3rd century BC. C. Hipparchus worked in a more systematic way, and in the year 134 a. C. had registered the position of more than 800 stars. He also made the first star map, which was enriched by Ptolemy with some two hundred more stars.

Halley studied the position of the stars, and in 1718 he realized that there were at least three stars, Sirius, Procyon and Arthur, who were not in the place the Greeks said. There was a difference so great that the possibility that he or the Greeks had made a mistake was very remote. Halley found that Arthur had moved a degree with respect to the position assigned to him by the Greeks, so he thought that those stars had moved. This meant that those stars were not totally fixed, but had a much slower own motion compared to that of the planets, so it was impossible to detect it in a day or even a year.

The existence of stars with own movement supposed a tremendous blow against the hypothesis of a fixed celestial vault. It seemed that some stars were not subject to the vault, and began to think that perhaps none of them was, is more, perhaps there was no vault .

Although the stars were not fixed to the celestial vault, it did not mean that they were all located at the same distance. You could think that, without being fixed to anything, they were distributed along a strip of space.

This was very unlikely since only a small part of the stars showed visible movement of their own. Of course, a star could move without that movement being visible, even with the passage of many years, since its trajectory could be parallel to the line of sight.

Image result for celestial vault

But if the stars moved in random directions, the number of those that moved more or less at right angles to the line of sight should at least be the same as those moving in a direction parallel to it. And if the stars had their own movement, at least half of them should be able to be seen. However, after thorough investigations it was shown that visible own movements were the exception.

But if not all stars are at the same distance, but are at very variable distances, and if all move at the same speed more or less, and do so in random directions, you can reach some conclusions.

No star that moves in a direction parallel to the line of sight will have a visible movement of its own, either distant or close. Of those that move in a direction perpendicular to the line of sight, those closest to Earth will have their own movement greater than that of the farthest ones. This is so because it is precisely the bright stars that most frequently have a more similar self-movement. The three stars in which a movement of their own was detected for the first time, Sirius, Procyon and Arthur, are among the eight brightest stars in the sky. Obviously, a nearby star will present an intense brightness and its own movement will be measurable. According to this, it is logical that the number of stars with measurable own movement is very small, since only the closest ones are sufficiently close so that a proper movement is visible, however small it may be. There are millions of stars that are too far away to show visible movement, even if centuries pass.

In the middle of the 18th century, it was already assumed that there was no rigid celestial vault, nor a strip through which the stars moved. On the contrary, the stars were distributed throughout a huge and indefinite space. In fact, it was the German philosopher Nicolás de Cusa who first suggested this idea, but at that time it was a mere speculation, and now it is a result obtained from meticulous observations.


The size of the solar system –

A few years ago, a more perfect method than parallax was discovered to measure the distances of celestial bodies.

Image result for size of solar system

It consists of emitting microwaves to space. Microwaves are very short radio waves, like those used in radar. When the waves reach a celestial body, they bounce off it and are picked up and detected on Earth again. The speed at which the microwaves move is known; The time between the emission and reception can also be measured with great precision. Therefore, this technique allows to know, with greater precision than the parallax method, the round trip distance traveled by the microwaves and, therefore, the distance of a celestial body.

There are four ways to express distances, all of them very interesting to know.

They can be expressed in millions of miles. This unit is very common in Great Britain and the United States to measure great distances.

They can also be expressed in millions of kilometers. The kilometer is the unit that is normally used in civilized countries, except for the Anglo-Saxons, to measure great distances. It is also used by scientists from all over the world, including the United States and Great Britain. One kilometer is 1093.6 yards or 0.62137 miles. We can also say that a kilometer is 5/8 of a mile.

If we want to avoid millions of miles or kilometers, we can establish that the average distance from Earth to the Sun is worth an “astronomical unit”, which is abbreviated UA Thus, we can express the distances in UA, where 1 AU is worth 92,950,000 of miles or 149.588.000 of kilometers. Normally, it is said that 1 AU equals 150,000,000 kilometers.

And finally, distance can also be expressed in terms of the time it takes for light to travel. In a vacuum, the light moves at a speed of 299,792.5 kilometers per second, although this value can be rounded up to 300,000 kilometers per second without making an excessive error. It also equals 186,282 miles per second.

Thus, we can define a distance of 300,000 kilometers as “a second-light”, that is, the distance traveled by light in a second. Sixty times that amount, that is, 18,000,000 kilometers is “one minute-light”, and sixty times this, 1,080,000,000 kilometers, is “one light-hour”.

Average distance from the Sun

Planet Millions of miles Millions of Km Astronomical units Light hours
Mercury 35.9 57.9 0.387 0,0535
Venus 67.2 108.2 0.723 0.102
land 92.9 149.5 1,000 0,137
Mars 141.5 227.9 1,524 0.211
Jupiter 483.3 778.3 5,203 0,722
Saturn 886.1 1428.0 9,539 1,321

Therefore, from the time of Cassini it was already known that the diameter of the solar system, from one end of Saturn’s orbit, to the other, measured almost three billion kilometers.

This figure was also overcome with the passage of time. In 1781, this diameter increased twice as much, when William Herschel , the German-English astronomer, discovered Uranus. This diameter was doubled again twice, in 1846, when the French astronomer Urbain Jean Joseph Leverrier discovered Neptune, and in 1930, when the American astronomer Clyde William Tombaugh discovered Pluto.

Average distance from the Sun

Planet Millions of miles Millions of Km Astronomical units Light hours
Uranus 1782 2872 19,182 2.66
Neptune 2792 4498 30,058 4.26
Pluto 3671 5910 39,518 5.47

As the outermost orbit is that of Pluto, and not that of Saturn, we see that the diameter of the solar system is not three billion kilometers, but twelve billion. A beam of light would take almost half a day to traverse the solar system.

The English scientist Isaac Newton formulated the law of universal gravitation in 1684. This law explains in a direct mathematical way, the existence of the Keplerian model of the solar system and allows to calculate the orbit of a celestial body around the Sun even if it is only visible during part of said orbit.

This also made possible the study of comets. Formerly, and also in medieval times, astronomers believed that comets arose at irregular intervals and that they followed trajectories not subject to any natural law. People thought that comets predicted some kind of disaster.

The English astronomer Edmund Halley , friend of Newton , applied the gravitational calculations to the comets, and observed that some appeared in the sky every seventy-five or seventy-six years. In 1704, Halley formulated the hypothesis that all comets were really a single body that moved around the Sun in a regular ellipse, but so elongated, that most of the orbit was very far from the Earth. In that case, it was not visible, but every 75 or 76 years it passed closer to the Sun and the Earth and then it could be seen.

Cometa Halley

Halley calculated the comet’s orbit and predicted that it would be visible again in 1758. Sixteen years after Halley’s death, the comet reappeared, and since then the comet is called “Halley’s Comet.” The first appearance of this comet dates from the year 240 a. C.

At the time of its closest approach to the Sun, the Halley comet is only ninety million kilometers away from it, reaching across the orbit of Venus, although at the moment of its maximum distance from the Sun, the Halley is about three times and average Saturn’s orbit, about 5300 million kilometers. This means that in the year 1760, astronomers had already realized that the solar system was much greater than the Greeks had imagined.

Comet Halley is one of the closest to the Sun. There are others whose orbits around the Sun are so elongated that they are only visible every many centuries and even millennia. They move away from the sun, not billions of kilometers, but hundreds of billions. In 1950, Jan Hendrik Oort, Dutch astronomer, formulated a theory according to which it is possible that a great cloud of comets exists with orbits very distant from the Sun and therefore never visible.

Therefore the solar system could have a diameter of one billion kilometers or more. A beam of light would need forty days to cover this distance, so the diameter of the solar system could be estimated at more than 1 light-month.

On the other hand, the insignificance of the Earth is not only a question of distances. Through a telescope, the four outer planets, Jupiter, Saturn, Uranus and Neptune, become fully measurable spheres. But any of them is a giant compared to the Earth, although they are dwarves if we compare them with the Sun.


This is the ‘PaleBlueDot’ photograph of Earth taken by Voyager 1 on July 6, 1990. Earth is the relatively bright particle inside the blue circle.

Each of these giant planets has a satellite system, and next to them the Earth is insignificant. Of the outer satellites, the first to be discovered were the four largest of Jupiter, observed by Galileo through his first telescope in 1610. Of the great satellites, Triton, the satellite of Neptune, was discovered last. It was detected in 1846 by the English astronomer William Lassell. Later smaller satellites were discovered.

Equatorial diameter

Body Miles Km Earth diameter = 1
land 7929 12753 1,000
Neptune 27700 44600 3.50
Uranus 29200 47000 3.68
Saturn 75100 121000 9.5
Jupiter 88700 143000 11.2
Sun 864000 1392000 109.0


The parallax –

To calculate the distance of a planet, parallax can be used.

Image result for parallax

Parallax consists of putting a finger before the eyes. The background should not be uniform. Without moving the head or finger and looking first with one eye and then with another, you can see that the position of the finger in relation to the background changes. If we bring the finger closer to the eyes and look again first with one eye and then with the other, the two positions of the finger against the background will cover a larger part.

This is because between the two eyes there is a separation of several centimeters, so the imaginary line that joins the finger with one of the eyes forms an angle with the imaginary line that joins the finger with the other eye. If we extend these two imaginary lines to the bottom, we will have two points that correspond to the two apparent positions of the finger.

The closer to the eyes we put the finger, the greater the angle and the greater also the apparent displacement.

If the eyes were more separated, the angle formed by the two lines would increase more, and thus the apparent displacement of the finger against the background would be greater.

El paralaje

This can also apply to a planet. It is true that the Moon is so far away that we can not see any difference when we look with both eyes. But if we look at the Moon against the starry background of the sky, from two observatories some hundreds of kilometers away, we will notice something. From the first observatory we will see that one of the edges of the Moon is at a certain distance from a specific star, while in the second observatory the distance between the same edge and the same star will be different.

Knowing the apparent displacement of the Moon against the starry background and the distance between both observatories, the distance aided by trigonometry can be calculated.

This experiment could be done perfectly, because the apparent displacement of the Moon with respect to the starry background when changing the position of the observer is very large. Astronomers have normalized this displacement for the case that one of the observers is seeing the Moon on the horizon and the other just above his head. The base of the triangle will then be equal to the radius of the Earth and the angle with vertex on the Moon is the “equatorial horizontal parallax”. Its value is 57.04 minutes of arc, or 0.95 degrees of arc. A really appreciable displacement, because it is equivalent to twice the apparent diameter of the full Moon. It is a magnitude that can be measured with enough precision, and allows to get a good value for the distance of the Moon. This distance, calculated with the help of parallax, matches very well with the figure obtained by that old method based on the shadow projected by the Earth during a lunar eclipse.

Unfortunately, the conditions in the year 1600 did not allow to place the observatories at a sufficient distance, which, together with the enormous distance to which the planets are located, made the apparent displacement against the starry background too small to be measured. accurately.

Later, the telescope arrived, invented or reinvented by the Italian scientist Galileo Galilei . The telescope allowed an angular distance not detectable to the naked eye to be easily measured.

The planets with major parallaxes are the closest, that is, Mars and Venus. Venus, in its closest approach to the Sun passes so close to him that it is impossible to observe it, except in the transits, where it can be seen against the bottom of the solar disk. So, the only case to measure parallax was the planet Mars.

The first telescopic measurement of a planetary parallax was made in 1671. The two observers were Jean Richer, French astronomer, leading a scientific expedition to Cayenne, in French Guiana and the Italian-French astronomer Giovanni Cassini, who stayed in Paris. They observed Mars with the maximum possible simultaneity and took note of their position with respect to the closest stars. Calculated the difference of positions observed and known the distance from Cayenne to Paris, the distance of Mars was calculated at the time of measurement.

Once this was done, we already had the scale of the Kepler model, which would allow us to calculate all the other distances of the solar system. Cassini estimated that the distance between the Sun and the Earth was 140,000,000 kilometers, nine million kilometers below the actual figure, but an excellent result for the first attempt.

Later, more accurate measurements of planetary parallaxes were made. Some on Venus, on the occasions that pass right between the Earth and the Sun, and that can be seen as a small dark circle crossing the Sun’s disk. These transits took place in 1761 and 1769. If the transit is observed from two different observatories , it can be verified that the moment in which Venus comes into contact with the solar disk and also the moment in which it separates from it, which is the duration of the transit, varies from one observatory to another. Known these variations and the distances between the two observatories, you can calculate the parallax of Venus. Having this data, one can calculate the distance to Venus, and then the distance to the Sun.

The German astronomer Johann Franz Encke , in 1835, used the existing data of the transits of Venus to calculate the distance from the Sun, and the figure was 153,450,000 kilometers. It exceeded a bit of the actual figure, but only about 3,000,000 kilometers.

In order to obtain more exact values, the main difficulty was that Venus and Mars were seen by the telescope as tiny spheres, which prevented to fix accurately the position of the planet. Especially disappointing was Venus, because the thick atmospheric layer that it had produced optical effects that prevented seeing during the transit the exact moment of contact with the solar disk.

Suddenly an unexpected event happened. The Italian astronomer Giuseppe Piazzi, in 1801, discovered a small celestial body whose orbit was between Mars and Jupiter, and called it Ceres. It had a diameter of less than 800 kilometers. As the century progressed, hundreds of even smaller planets were discovered, all between the orbits of Mars and Jupiter. They were the asteroids. Sometime later, in 1898, Karl Gustav Witt, a German astronomer, discovered Eros, an asteroid far from the asteroid zone. A part of its orbit passed through that of Mars, and very close to Earth as well.

It was estimated that in 1931 Eros would approach Earth. It was a good opportunity to calculate the parallax. Since Eros is very small, it is estimated that its maximum diameter is 24 kilometers, and it has no atmosphere that could blur its contour, it would be observed as a bright spot and its position could be well calculated.

A large project was organized on an international scale. Thousands of photographs were taken and studied, and it was concluded, from the parallax and the position of Eros, that the Sun is a little less than 150,000,000 kilometers from Earth. This is an average, because the Earth describes an ellipse around the Sun, not a circumference. The perihelion, or minimum distance between the Earth and the Sun, is 147,000,000 kilometers and the aphelion, maximum distance of 152,200,000 kilometers.