Books about physics, astrophysics and astronomy regarded as important classics

This post is mostly inspired (with some additions and modifications) from and answer I wrote at .

I will try to give a list of famous , influential books or classic books having a significant historical importance in the fields of physics , astrophysics and astronomy . It’s a somewhat extensive list but it’s not exhaustive.

Starting with Antiquity :

Then advancing to more recent times:

Al Sufi stars

Copernicus book

Below is a page from the Astronomia Nova (in 1609) showing the three models of planetary motion known in the seventeenth century (free image from Wikipedia) :

Astronomia Nova

Newton's Principia


Carnot reflexions

  • Recherches sur la théorie des quanta (Researches on the quantum theory) , and The Current Interpretation of Wave Mechanics: A Critical Study , by Louis de Broglie .
  • Collected papers , The interpretation of Quantum Mechanics , and Statistical Thermodynamics , by Erwin Schrödinger .
  • The Physical Principles of the Quantum Theory , by Werner Heisenberg .
  • Books and papers by Paul Dirac , such as The Principles of Quantum Mechanics and Lectures on Quantum Field Theory .
  • Space, Time and Gravitation: An Outline of the General Relativity TheoryThe Internal Constitution of Stars , and The Nature of the Physical World , by Arthur Eddington .
  • Problems of Cosmology and Stellar Dynamics , An Introduction to the Kinetic Theory of Gases , and  The Growth of Physical Science , by James Hopwood Jeans .
  • The Theory of Sound , by John William Strutt, 3rd Baron Rayleigh .
  • Problems of Atomic Dynamics , Atomic Physics , Principles of Optics , Experiment and Theory in Physics , and A General Kinetic Theory of Liquids , by Max Born .
  • Books and papers by David Bohm , such as Quantum Theory , Causality and Chance in Modern Physics , The Undivided Universe.

Some more recent well known , insightful and/or widely used books would include :

  • The Large Scale Structure of Space-Time , by Stephen Hawking and George F. R. Ellis .
  • Speakable and Unspeakable in Quantum Mechanics , by John Stewart Bell .
  • Classical-Mechanics , by Herbert Goldstein .
  • Classical Electrodynamics , by J.D. Jackson .
  • Galactic Dynamics , by Binney and Tremaine .
  • The Quantum Theory of Motion: an account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics , by Peter Holland .
  • Photons and Atoms: Introduction to Quantum Electrodynamics , by Claude Cohen-Tannoudji , Gilbert Grynberg and Jacques Dupont-Roc .
  • Introduction to Elementary Particles , by D.J. Griffiths .
  • Condensed Matter Field Theory , by Alexander Altland .
  • The Standard Model and Beyond , by Paul Langacker .
  • The Road to Reality , by Roger Penrose .
  • Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law , by Peter Woit .
  • The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next , by Lee smolin .
  • Farewell to Reality: How Modern Physics Has Betrayed the Search for Scientific Truth , by Jim Baggott .

Additional relevant links :……

Astronomy in the medieval Islamic world

Indian astronomy

Chinese astronomy


Regarding gravitational waves

Gravitational waves have become a popular topic recently , and this post presents material I have written for an answer at (with a few modifications).

Gravitational waves are changes in curvature similar to ripples in space-time . They are an indirect result of the special theory theory of relativity , and were explicitly proposed by Einstein in 1916 in the framework of his theory of general relativity . He showed that the acceleration of mass generates gravitational fields which are time-dependent and are capable of transporting energy (as gravitational radiation ) from their source at the speed of light .
Gravitational waves are quadrupolar in nature , whereas electromagnetic waves are dipolar . Oscillating multipole moments of the mass distribution of a system produce gravitational radiation .
Many attempts have been made to detect gravitational waves , but no direct evidence of their existence has been observed until their recent detection in February 2016 .

The Einstein field equations describe the interactions between space-time curvature and mass , as Maxwell’s equations describe and specify the relationship between electric charge and electromagnetic fields .
The field equations have a solution represented by a weak oscillating perturbation to the curvature of space-time , and this solution is a gravitational wave .
These waves can be regarded as an oscillating perturbation to a flat Minkowski space-time metric , or also as a tidal force oscillating between free test masses , or as a strain oscillating in space-time .
More explicitly , one can show that a wave equation represents the solutions in free space for the metric perturbations of a nearly flat space-time , with waves propagating at the speed of light ( this is a weak gravitational field approximation) .
One can take a coordinate system where the metric has components :
g_ {\mu\nu} = \eta_ {\mu\nu} + h_ {\mu\nu}
\eta_ {\mu\nu}  is the Minkowski metric in special relativity , and
h mu nu

After some calculations the  solution to Einstein’s equations in free space can be written as :

wave eq


hbar mu nu

So the metric perturbations propagate in free space as waves at the speed of light .
A primary example of a source of gravitational waves is a pair of neutron stars , or two black holes , or one of each type of these astrophysical objects .
Observing supernova explosions or the orbital motion of binary pulsars may possibly give and indirect proof of the existence of gravitational waves .
The image below represents gravitational waves generated by two neutron stars orbiting each other (image source : File:Wavy.gif ) :
wavy anim


Ways of detecting gravitational waves include resonant mass detectors , free mass detectors , detectors in space , cosmic background measurements , and monitoring pulsar signals .
External disturbances and the effects of thermal noise in the detecting system should be avoided , the possible interaction between detectors and gravitational waves being very weak .
In 1974 Russell Hulse and Joseph Taylor discovered and observed the orbital period of a binary pulsar . They confirmed that the orbit was accelerating at the rate predicted by the emission of gravitational waves according to the theory of general relativity .
The LIGO (Laser Interferometer Gravitational-Wave Observatory) detectors
are used to attempt to observe directly cosmic gravitational waves . They can detect extremely small strains (of the order of  one part in 10²¹ ).
In the quantum theory of gravity , a quantum field whose excitations are gravitons represents the gravitational field .
Gravitons may be regarded as the normal modes of oscillation of a (gravitational) gauge field , produced by a mass current of accelerating masses .
Some (online) links and resources :
Gravitational wave
McGraw-Hill Encyclopedia of Science and Technology , 10th Edition .

To make this answer complete  , it should be noted that the expression gravity waves is also used to refer to waves studied in oceanography , meteorology and fluid dynamics .
Used in this sense , a gravity wave is a liquid surface layer wave controlled by gravity and not by surface tension .
The surface tension of water becomes unimportant at wavelengths greater than a few centimeters . On the ocean surface or interfaces , all significant waves are gravity waves .
In meteorology , gravity waves are transverse atmospheric waves where the restoring force is caused by the effect of gravity on density and pressure fluctuations .
See for example the Wikipedia article Gravity wave .
The expressions gravity waves and gravitational waves are sometimes used interchangeably for both meanings (i.e. for waves related to general relativity and waves related to fluid dynamics) , so this might cause some confusion.

As an update to the information above , something new took place in the history of the detection of gravitational waves on 11 February 2016 .
For the first time, scientists have observed ripples in the fabric of spacetime called gravitational waves, arriving at Earth from a cataclysmic event in the distant universe. This confirms a major prediction of Albert Einstein’s 1915 general theory of relativity and opens an unprecedented new window to the cosmos.[…]
The gravitational waves were detected on Sept. 14, 2015 at 5:51 a.m. EDT (09:51 UTC) by both of the twin Laser Interferometer Gravitational-wave Observatory (LIGO) detectors, located in Livingston, Louisiana, and Hanford, Washington.[…]
Based on the observed signals, LIGO scientists estimate that the black holes for this event were about 29 and 36 times the mass of the sun, and the event took place 1.3 billion years ago. About three times the mass of the sun was converted into gravitational waves in a fraction of a second—with a peak power output about 50 times that of the whole visible universe. […]
The discovery was made possible by the enhanced capabilities of Advanced LIGO, a major upgrade that increases the sensitivity of the instruments compared to the first generation LIGO detectors, enabling a large increase in the volume of the universe probed—and the discovery of gravitational waves during its first observation run.
As and additional note , it is generally preferable to have other precise experiments confirming the detection and presence of gravitational waves.

Question: what is the square root of 36 ? – Part Two

I will continue with answers and results equal to the square root of 36 ( originally answered at ). This time the results are mostly related to physics.

With physics one has to take into account the units and the corresponding dimensions of the equations and of the constants.

6 and the square root of 36 are dimentionless numbers , so the result must be dimentionless .
If the result is a simple fraction with numerator and denominator , then the units usually cancel out.
In other cases when one deals with logarithms one should multiply with the inverse dimensions to get a dimentionless result.
In one or two results where I didn’t look for the inverse units  I multiplied the equation with a quantity I called (U) ,  which represents the inverse of the units by which one should multiply the result to get a dimentionless number.

Here are the results :

square root of 36 physics


One possible way to explain what I have done here is the following:
If some people , living on an isolated fictitious island or on an another hypothetical planet , attached a great importance to and had a fixation on  the square root of 36 (or the number 6) for one reason or another , and got accustomed to the use of 6 as a fundamental constant ,  unit or number , then they would have likely  tried to construct a system of measurement  based on the number 6 , and  to express physics and math formulas ,equations , constants and rules in relation to 6.

After all , 6 or \sqrt{36} is equal to :

  • The floor of  2 \pi :
    2 \pi \approx 6.2831853071795864769 ;6=\lfloor 2 \pi \rfloor
  • \frac{1}{60} of the circumference of a circle in degrees.
  • It is also  one tenth of 60 seconds which make up a minute , one tenth of 60 minutes which make up an hour , one fourth of 24 hours which equal a day on Earth , one half of  12 months which make up a year , etc.
  • A peculiar ‘hexacentric’ system , so to speak.

Or this can be seen as a (creative) exploration of or exercise in advanced math and physics in order to express many equations , formulas and constants in relation to the number 6 (or \sqrt{36} ) .
Or whatever.

Apologies to Isaac Newton , Leonhard Euler , Bernhard Riemann , Einstein , Stokes , Coulomb , Avogadro , Lagrange , and others (wherever they may be) , for playing around with their equations , formulas , constants , and/or functions.

And one more addiction to this answer :

Does the future of humanity depend on answering what is the square root of  36 , or not?
Have philosophers from Antiquity to the present overlooked this fundamental question , which goes beyond the Kantian categories of space and time set out in his Critique of Pure Reason , and beyond Nietzsche’s Beyond Good and Evil , ushering the transmutation of all values and a defining moment for a new era  in the history of Humankind?
It’s just a square root , for common sense’s sake (or is it?).

Anyway , enough philosophizing.

Here are ( 3=\frac{\sqrt{36}}{2} ) more answers to \sqrt{36} , this time with images :

\sqrt{36}  is equal to :

The number subjected to a geometric rotation in the following image (done with Mathematica and some Photoshop) :

number 6 rotated

The number expressing the power and the coefficients in the equation of the curve in the polar plot below :

number 6 polar plot

The number expressing the degree of the root  and the power of the variables in the 3D plot below :

sinc number 6

The rotated number  and the polar plotted curve in the first two images  above seem to exhibit symmetry.
Symmetry is an very important property in science , math , physics , equations , nature , and wherever it is found.

Online sources and reference works related to what I have written in this answer can be found in my pages about Science books problem solvers and philosophy books in this site/blog.

Some other online sources:

Calendars ,days of the week , and dates

There are different calendar systems that are still used or were used in the past . Examples include the Julian calendar , the Gregorian calendar , the Hebrew calendar , the Islamic and the Iranian calendars , the French Republican calendar , etc. Most calendars use astronomical events and cycles as their basis: the day is based on the rotation of planet Earth on its axis , the month is based on the Moon revolving around the Earth , and the year is based on the period of revolution of the Earth around the Sun.The influence of the gravitational force from other planets may cause the length of a particular year to vary by several minutes. The Gregorian calendar was introduced in 1582 .Dates before October 1582 are usually given in the Julian calendar .

Here is a list of leap years in the Gregorian calendar from 2016 to 2416 (done with the help of Mathematica) :

2016 , 2020 , 2024 , 2028 , 2032 , 2036 , 2040 , 2044 , 2048 , 2052 , 2056 , 2060 , 2064 , 2068 , 2072 , 2076 , 2080 , 2084 , 2088 , 2092 , 2096 , 2104 , 2108 , 2112 , 2116 , 2120 , 2124 , 2128 , 2132 , 2136 , 2140 , 2144 , 2148 , 2152 , 2156 , 2160 , 2164 , 2168 , 2172 , 2176 , 2180 , 2184 , 2188 , 2192 , 2196 , 2204 , 2208 , 2212 , 2216 , 2220 , 2224 , 2228 , 2232 , 2236 , 2240 , 2244 , 2248 , 2252 , 2256 , 2260 , 2264 , 2268 , 2272 , 2276 , 2280 , 2284 , 2288 , 2292 , 2296 , 2304 , 2308 , 2312 , 2316 , 2320 , 2324 , 2328 , 2332 , 2336 , 2340 , 2344 , 2348 , 2352 , 2356 , 2360 , 2364 , 2368 , 2372 , 2376 , 2380 , 2384 , 2388 , 2392 , 2396 , 2400 , 2404 , 2408 , 2412 , 2416 .

In the Gregorian calendar , most years that are multiples of 4 are leap years . The years 2100, 2200, 2300 are not leap years .

Below is a list of the days of the week each one corresponding to the first day of the year (Gregorian calendar) from the year  2016 to 2036 :

  • 1/1/2016 : Friday.
  • 1/1/2017 : Sunday.
  • 1/1/2018 :Monday.
  • 1/1/2019: Tuesday.
  • 1/1/2020: Wednesday.
  • 1/1/2021: Friday.
  • 1/1/2022: Saturday.
  • 1/1/2023: Sunday.
  • 1/1/2024: Monday.
  • 1/1/2025: Wednesday.
  • 1/1/2026: Thursday.
  • 1/1/2027: Friday.
  • 1/1/2028: Saturday.
  • 1/1/2029: Monday.
  • 1/1/2030: Tuesday.
  • 1/1/2031: Wednesday.
  • 1/1/2032: Thursday.
  • 1/1/2033: Saturday.
  • 1/1/2034: Sunday.
  • 1/1/2035: Monday.
  • 1/1/2036: Tuesday.

Next I give the day of the week corresponding to the 4th of July from the year 2015 to 2020:

  • 2015: 4th of July is a Saturday.
  • 2016: 4th of July is a Monday.
  • 2017: Tuesday.
  • 2018: Wednesday.
  • 2019: Thursday.
  • 2020: Saturday.

The day of the week corresponding to the 14th of July (Bastille day in France) from the year 2015 to 2020:

  • 2015: 14th of July is a Tuesday.
  • 2016: Thursday.
  • 2017: Friday.
  • 2018: Saturday.
  • 2019: Sunday.
  • 2020: Tuesday.

Easter Sunday date (Western churches and Greek Orthodox churches) for 4 years:

  • 27 March 2016 (Western), 1 May 2016 (Greek Orthodox).
  • 16 April 2017 , same date for Greek Orthodox churches.
  • 1 April 2018 , 8 April 2018.
  • 21 April 2019 , 28 April 2019.

Here are days of the week corresponding to some important historical dates and people (after 1582 the dates are in the Gregorian calendar) :

  • The most accepted date for the Death of Genghis Khan  ( Julian calendar) is 18 August 1227 , which was a Wednesday.The date in the Gregorian calendar would be  Wednesday 25 August 1227.
  • Columbus reached America : Friday 10 October 1492 (Julian calendar). The date in the Gregorian calendar would be Friday 21 October 1492.
  • First publication of Philosophiæ Naturalis Principia Mathematica by Isaac Newton: Saturday 5 July 1687 ( Gregorian).
  • Date of birth of Carl Friedrich Gauss : Wednesday 30 April 1777.
  • Date of death of Carl Friedrich Gauss: Friday 23 February 1855.
  • Death of Napoleon Bonaparte : Saturday 5 May 1821.
  • Date of birth of Jules Verne : Friday 8 February 1828.
  • Date of birth of Pierre Simon Laplace : Wednesday 23 April 1749.
  • Death of Pierre Simon Laplace : Thursday 5 April 1827.

Another day of the week and date: Sunday , 31 July 2072 (this date is somewhat important for me).

The Islamic calendar is a lunar calendar ( based on the motion and phases of the Moon) of 12 months  with alternating months of 29 and 30 days , and  a year made of 354 days , which is about 11 days shorter than the length of the year in the Gregorian calendar. In the table below I give the day of the week corresponding to the first day of the year (Islamic calendar) and the corresponding Gregorian date for a number of consecutive years:

Year(Islamic calendar) First day of the year Gregorian date
1/1/1437  Thursday  15 October 2015
1/1/1438  Monday  3 October 2016
 1439  Friday  22 September 2017
 1440  Wednesday  12 September 2018
 1441  Sunday  1 September 2019
 1442  Thursday  20 August 2020
 1443  Tuesday  10 August 2021
 1444  Saturday  30 July 2022
 1445  Wednesday  19 July 2023
 1446  Monday  8 July 2024
 1447  Friday  27 June 2025
 1448  Wednesday  17 June 2026
 1449  Sunday  6 June 2027
 1450  Thursday  25 May 2028
 1451  Tuesday  15 May 2029
 1452  Saturday  4 May 2030
 1453  Wednesday  23 April 2031
 1454  Monday  12 April 2032
 1455  Friday  1 April 2033
 1456  Tuesday  21 March 2034
1457 Sunday 11 March 2035
1458 Thursday 28 February 2036
1459 Tuesday 17 February 2037
1460 Saturday 6 February 2038
1461 Wednesday 26 January 2039
1462 Monday 16 January 2040
1463 Friday 4 January 2041
1464 Tuesday 24 December 2041
1465 Sunday 14 December 2042
1466 Thursday 3 December 2043
1467 Tuesday 22 November 2044

A good online calendar converter can be found in here.

A number of scholars , thinkers and scientists in the past  have written books and studies about calendars , the chronology of world history and historical events (such as Isaac Newton’s The Chronology of Ancient Kingdoms and al Biruni‘s The Chronology of Ancient Nations , also known as The Remaining Signs of Past Centuries).

Newton Chronology of ancient kingdoms

However , historical chronology and dates before the beginning of the Christian Era are mostly approximate , uncertain or imprecise. Therefore I think a better and more accurate chronology of ancient History (and of World History in general) ought to be constructed , using rigorous historiographical and historical methods , and unbiased scientific reasoning , analysis , and methods.

Images of Jupiter and Saturn and some related info

After a close look  at planet  Mars in a previous post , here are images and info related to Jupiter and Saturn.

Jupiter is the biggest planet in the solar system , fifth from the Sun between Mars and Saturn.It
was named after the Roman king of the gods.

This first image of Jupiter shows the planet with the (multicolored) ring system surrounding it.The Grest Red Spot is also visible (image made with Universe Sandbox).

Jupiter rings and Great Red Spot

The faint diffuse ring system  of Jupiter was  identified by the Voyager 1 spacecraft in 1979.The
ring system consists mostly of dust particles , and comprises three main parts: the halo closest to
Jupiter, the main ring ,and the gossamer ring outside the main ring.

The Great Red Spot (GRS) of Jupiter is a huge high pressure anti-cyclonic storm , similar to a big
hurricane.Three planets each having the same size of the Earth could comfortably fit in it.
The image below gives a detailed view of the GRS and its surroundings (made with Starry Night).

Great Red Spot

Next is a picture of Saturn with its ( multicolored ) system of rings .Planet Earth is shown to the right of Saturn. Image made with Universe Sandbox.

Saturn rings and Earth

Saturn is the second largest planet in the solar system after Jupiter.
Saturn has bright rings made of lots of small particles having sizes from a centimeter to a few
meters to more than a kilometer.The particles of the rings are composed mainly of aggregated
water ice pieces and some rocks.The rings extend away from Saturn and have a very large
diameter ,but they are very thin and have a thickness of less than one kilometer.Galileo first
observed the rings in 1610 ,but he thought they were large moons on both sides of planet Saturn.
A few decades later in 1655 Christian Huygens explained that Saturn was in fact surrounded by
rings.These rings were divided into many sections by astronomers and scientists.The D ring is
closest to Saturn ,the F, G ,E rings and the Phoebe ring are the outermost rings .

The final image below is of Saturn and its rings in March 2015 (made with Starry Night and a touch of Photoshop;the lighting is an added effect).

Saturn and rings

The rings of Saturn lie within the Roche limit.Inside this borderline distance (approximately 2.44
Saturn radii ) a celestial body or moon disintegrates due to the stronger tidal forces of Saturn and
rings are formed  , while outside it a body or disk of orbiting material is expected to accrete and

A general formula for calculating the Roche limit is:

The Roche limit

The Roche limit varies for rigid bodies and for fluid satellites.

Additional reference work related to this post and the Roche limit :
Planets, Stars and Stellar Systems , Volume 3:Solar and Stellar Planetary Systems ( edited by Terry D. Oswalt ,
Linda M. French and Paul Kalas).

Images of planet Mars and related input

It was by studying the orbit of planet Mars and the obesrvational data collected by Tycho Brahe that
Johannes Kepler was able to formulate his laws of planetary motion in the early 1600s ,
concluding that the orbits of the planets are ellipses, with the Sun at one focus of the ellipse.
The Martian atmosphere is very thin , composed mainly of carbon dioxide (between 95% and
96%) ,and  contains nitrogen , oxygen ,argon and traces of water vapor.
Mars appears to have a red or red-orange color.Its surface , rocks and soil contain dust composed
mainly of iron which reacted with oxygen , giving iron oxide or rust.This red colored dust has been
carried by storms into the atmosphere and has covered most of the Martian surface and  landscape.

The following images of Mars were made with Redshift and Starry Night.

We begin with an image of Mars from a position behind the moon Deimos.The date for the image is February 2015.

Deimos Mars and Phobos

Phobos and Deimos were discovered in 1877 by Asaph Hall.Both have irregular shapes.Phobos (with a diameter of 22.2 km across or 13.8 miles) is larger than Deimos (with a diameter of 12.6 km or 7.8 miles) and is closest to Mars.

Next is an image of Mars showing also Phobos , Deimos and some planets of the solar system.

Mars Phobos Deimoes and planets

The third image features Phobos and Mars with Planum Boreum , the North polar cap of Mars , consisting mostly of water ice.

Mars and PlanumBoreum

Below is a detailed image of Planum Boreum and its surroundings , including Vastitas Borealis , the largest lowland region of Mars.

 details of Planum Boreum

Click here to view an enlarged and more detailed image of Planum Boreum.

Here is a simple way to find the surface gravity g for Mars.The same equation used to determine
the value of g on Earth’s surface can also be used to determine the acceleration of gravity or
surface gravity on the surface of other planets.
We equate the force of gravity at the surface of a planet,or the force on an object in a gravitational
field F=mg (also called weight) with the force of gravity between objects in space given by the
Universal Law of gravitation F =\frac {G M m} {r^2} .

The value of g obtained here may be very slightly different from values cited in textbooks because
we used specific  and more detailed or accurate values of the constants.
The ratio of the surface gravity of Mars compared to Earth is 3.72761/9.80665 or 0.38011,which
means the surface gravity of Mars is about 38% that of Earth.

Mars is close to Earth and the fourth planet from the Sun , and it has become famous in the past
decades or years  because people and humans have been planning and wanting to go and set foot on the
red planet , some people intending to go there in an unprepared  and unrealistic way.
I think it must be taken into account that a manned mission to Mars and the first mission/trip ( or even trips) to
Mars should be undertaken as part of an international enterprise with international cooperation and an international crew , consisting of people very well prepared ,well trained ,well versed in science ,engineering , technology , astronautics and aviation (preferably having pilot skills) , and having planned everything to the tiniest detail in order
for the crew to go land on Mars , stay there for a short determined period of time , conduct
experiments , establish a base for future trips , and come back to Earth safely.
Not to offend anyone ,but this is not a game or a one-way voyage with uncertain or harmful results and consequences.This will be a very important event in the history of humankind , and not everyone is ready,
prepared or able to make the journey to Mars .

Some joyful astro images with comet Lovejoy

I couldn’t help making a pun with the word Lovejoy (nice name by the way , could have added that Lovejoy has lovely colors too)… Anyway , this is another astronomy related event happening in 2015 : comet Lovejoy , officially named C/2014 Q2 (other Lovejoy comets were discovered earlier) , makes its nearest approach to planet Earth in January 2015 and is visible crossing the night sky.

First , here are four images of the orbit diagram of the comet in the solar system. The images are taken from the JPL Small-Body Database Browser. It is the same image zoomed in four times.

.lovejoy comet zoomed in


Second , we have the path of comet Lovejoy and its position in relation to the constellations , viewed from three cities. Two cities are located in the Northern Hemisphere (Paris and Alexandria) , and one city in the Southern Hemisphere (Rio de Janeiro).The dates ( all in January 2015) and the info related to the views are given at the bottom of each image.Images were made with RedShift and some Photoshop.

Lovejoy comet viewed from 3 cities

And the third set of three images gives the orbit and position of the comet in the solar system during three different dates (July 2014 , January 2015 and February 2016).

comet Lovejoy 3 dates

Lovejoy C/2014 Q2 has a solid icy nucleus with a width of 2 or 3 miles.The coma or cloud surrounding the frozen solid nucleus at the head of the comet is made of gas and dust . Comets have two tails , a dust tail and an ion or plasma tail , always pointing away from the Sun.The tail reaches its greatest extent at about the closest approach to the Sun . The design and the physics of the plasma tail are related to the interaction between the cometary plasma and the solar wind. The Lovejoy comet is not making too much dust and has a more developed ion gas tail.The blue color of the ion tail is explained by the presence of Carbon monoxide ions. Diatomic Carbon molecules fluorescing by solar ultraviolet radiation and the chemical compound cyanogen are mainly responsible  for the observed or apparent green color of the comet.
Comet Lovejoy has a highly elliptical orbit like all comets ; it has a  long orbital period (comets with long periods come from the Oort cloud) and has passed through the solar system about  11500 years ago. The comet’s orbit is a little changed due to gravitational perturbations by the planets , and it will not return into the solar system for about 8000 years.

2015 the year , the number , and some of their characteristics

The year 2015 has begun (wish it will be a happy year for everybody) and here are some properties of the corresponding number (worked out with the help of Mathematica).

First , a list of the representations of 2015  in various number base notations:

2015 base notation

2015 in roman numerals: MMXV;

2015 can be represented as:


2015=\frac {92^4 - 1} {35553}

2015-relation-1 2015-relation-2

Here is a big one (obtained with Mathematica by solving x^3 + x^2 + x = 2015 ):


2015=5 x 13 x 31


The last relation above can be  derived from the trigonometric equation:


I have mentioned these types of trigonometric relations in a previous post.

The number of prime numbers up to 2015 is 305 , the last  prime number before 2015 is 2011 ,  and the prime number which comes after 2015 is 2017.

The last Mersenne prime number before 2015 is:

The Mersenne prime number which comes after 2015 is:

The last Sophie Germain prime (n is a Sophie Germain prime if 2n + 1 is also prime) before 2015 is 2003 , and the Sophie Germain prime which comes after 2015 is 2039.

The Riemann prime counting function is given by:

Riemann prime counting function

where li(x) is the logarithmic integral and  μ(n) is the Möbius function.

And below is a graph showing the natural distribution and the number  of prime numbers π(n) less than or equal to n (blue colored curve , here n=2015) along with the distribution of primes given by the Riemann counting function (orange colored curve) up to 2015 :



Moving to other fields of science , I will mention briefly a few events taking place in the year 2015:

In the field of space exploration , the New Horizons spacecraft will get closest to the dwarf planet Pluto in July 2015.

In the following image (made with the help of Starry Night and Photoshop) the longer red arrow near the name of a planet indicates the direction towards the place where the planet is located on its orbit.

Pluto and New Horizons

The Dawn spacecraft will arrive at the dwarf planet Ceres between Mars and Jupiter in March 2015.

Concerning astronomy and sky events , there will be a solar eclipse in March 20 , a lunar eclipse in April 4 , a partial solar eclipse in September 13 , and a lunar eclipse in September 28.

And that is it for now.

Rosetta’s path and the encounter with comet 67P/Churyumov–Gerasimenko

Here is a video animation I have  made of the Rosetta spacecraft on it way to  comet 67P/Churyumov–Gerasimenko . It shows the path of Rosetta (in yellow) since its launch in 2004 until it approaches and meets the comet (orbit in blue). The animation was made using the Starry Night astronomy program.

The same  video with shorter length , less effects and a slightly better resolution can be viewed at this link.

The coordinates of comet 67P  were not prebuilt in my version of Starry Night , so I had to program the orbital elements of Churyumov–Gerasimenko myself. After researching I used the following  elements :

Eccentricity (e): 0.640980 ;  pericenter or perihelion distance (q): 1.243230 AU ;

Node : 50.1423 °  ;  argument of pericenter ( w ) : 12.7854°  ;

Inclination (i): 7.0402°  ; pericenter time (Tp) : 2457247.5683  ;

Epoch : 2456967.5  ;  Magnitude : 11 ;

 North pole right ascension: 69.00°  ;  North pole declination: 64° ;

Rotation rate : 2 rotations/day  .

Here is also a slideshow of the position and orbit of Rosetta at different dates . In the last three images the position of the Dawn spacecraft is shown as well. Dawn entered the orbit of the Vesta asteroid (or protoplanet)  in July 20 , 2011 , and completed  its fourteen month survey mission of Vesta in late 2012. Dawn is getting nearer to the dwarf planet (or large asteroid) Ceres and will arrive there in early 2015. The images were created and prepared with the Redshift astronomy software.

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Last but not least , here is a an image I’ve prepared ( with Starry Night and Photoshop ) showing the path and orbit of the Rosetta spacecraft from its launch in 2004 to the end of 2014 , including the orbit of comet 67P/Churyumov–Gerasimenko ,  with annotations recounting briefly the important steps of the Rosetta mission.

 Rosetta path and mission.

About languages I know and languages I’m getting to know

I have a problem. Could be a problem , or not.The thing is , I read a lot , and in more than one language.

At present I know three languages very well , and I’ve read literary books and various kinds of books in these languages.But I have also other books and coursebooks for learning other languages , some are in print form and others are ebooks along with online learning material I’ve downloaded . Audio files are generally  helpful while learning a new language.The three languages I know best are English , French and Arabic . I’ve studied and learned other  languages intermittently , depending on the circumstances or on how much free time I had.

For example , a few years ago I met a Russian girl and I had a relationship with her , and that gave me the incentive to learn Russian.Then I met a German girl , and that encouraged me to start learning German using a coursebook I had bought two years earlier.I have a Spanish language coursebook as well , so I’ve studied recently the first few chapters of this book.Of course the Spanish language is interesting and useful since it is spoken not only in Spain but in most of Central and South America and in many countries around the globe.



I have additionally a Portuguese language coursebook waiting to be read ,  and a Chinese language textbook for beginners and a Chinese language learning software I haven’t used yet . Now  the Portuguese and Spanish languages are more or less related to each other , but learning Chinese could be more difficult as it is a non-alphabetic language and uses characters such as logograms , pictograms and ideograms . I’ll have to see if or when I will have enough time to start learning these languages.

Moving to another group or type of languages , I’ve been using and working with the Mathematica software and the (Wolfram) Mathematica programming language for more than fifteen years , and I have occasionally used in the past programming languages such as QBasic and the BASIC-like language of the TI-92 Plus calculator. I have also studied web programming for a certain period of time  , and I got to know well a number of programming (and scripting ) languages. These include HTML , PHP (and the MySQL database management system which uses the SQL query language) and JavaScript.

However , I have to say that among the languages I know the most important one is a language called Mathematics.This is the essential and fundamental language of the exact sciences , and according to good old Galileo , the mathematical language is the one in which the great book of Nature and the Universe is written.

And if you are of the opinion that Mathematics is not as important as other languages for communicating and connecting people , think again.
From Astronomy and Astronautics to Physics and Chemistry to electronic devices and components (which use disciplines such as solid-state physics , circuit and signal analysis , differential and difference equations , Fourier analysis , etc) , to computers (which use fields such as Boolean algebra , binary logic ,  and combinatorics)  , to Biology , Psychology , Economics and business studies , Mathematics and applied math are indispensable to any  study or research in science and engineering . Programming languages are more or less related to applied , discrete and computational math and to mathematical logic. Even the social and human sciences use math and statistics to  get a reputation for exactness , precision and scientificity .