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1. Motion of the Earth, Celestial Sphere

These are a few things we learn from primary school times.  Our Earth revolves around the Sun in one year. At the same time, it also rotates around its own axis in 24 hours. But are we revolving or rotating in Clockwise or Counter Clockwise direction?  The answer to that depends only upon where we look from.!! If you look from the North Pole of the Sun or the Earth, both our daily and years rotations are in Counter Clockwise direction.  But, if you go to the South Pole then both would be in Clockwise direction.

When we look at the sky throughout the year, we could feel that the sky is a sphere covering our Earth. If we extend our Equator to the sky, that plane is called the “Celestial Equator”. Similarly, if we draw a line through our Axis, that would pass through both N/S Poles and extend to the sky. Those two points are called the “Celestial Poles”. All the Northern stars appear to revolve around the Celestial North Pole and all the Southern stars appear to revolve around the Celestial South Pole. The stars on or near the Celestial Poles appear to remain constant. For example, Polaris/North Pole star does not look like moving at all.

2. Motion of the Sun, the Ecliptic

Now, coming to the motion of the Sun. As our Earth is revolving, we get a feeling that the Sun’s position is changing and it is moving through the sky.  It is apparently moving through the Celestial Sphere and completes one full circle in one year. That means the Sun moves “through” the stars every day. That motion is just nearly 1 degree (360/365.25 exactly) per day. On the contrary, the position of the stars changes everyday night. Assuming that we look at one particular star at 9PM one day. The same star would have moved around 1 degree to the West at 9PM on the next day. So, after one month, the same star would appear 30 degrees to the West at the same time.  In another word, the star would star rising early.

Because of the Earth’s axial tilt of 23.5 degrees, the Sun appears to go North and South during the course of one year and because of that, we have seasons. The Sun crosses the Celestial Equator on two days, March 21 and September 22. These two days are called Vernal (Spring) Equinox and Autumnal Equinox. On both of these days, there would be 12-hour equal day and night. The Sun reaches a maximum of 23.5 degrees North on June 22 and 23.5 degrees South on December 22 and these two days are called Summer Solstice and Winter Solstice respectively. Of course all from Northern hemisphere, in Southern hemisphere, it would be the opposite. So, if we draw the Sun’s motion throughout the Celestial Sphere, it follows a Sinusoidal motion, crossing the Equator on both Equinoxes and peaking on Solstices. The apparent path followed by the Sun is called the Ecliptic.

3. Nakshatras and Rashis

There are 12 Rashis and they are named Mesha (Aries) to Meena (Pisces). There are 27 Nakshatras with names, Ashwini to Revati.   Both Rashis and Nakshatra are used to divide the Ecliptic, that means the apparent path of the Sun in a year. Each Rashi corresponds to 30 degrees of arc (360/12) and each Nakshatra corresponds to 13 degrees 20 minutes (360/27) of arc. That way, each Rashi has 2.25 (30/12) Nakshatra. That is how you get Ashwani, Bharani and Kruttika first Quarter to be in Mesha Rashi and so on.

Moon takes 27.3 days to revolve around the Earth, so typically the Moon passes through each Nakshatra in a day and it takes 2.25 days to pass through each Rashi. Whereas, the Sun takes a year to go through the Ecliptic. That means, the Sun stays in each Rashi for around 1 month and it stays in one Nakshatra for around 13.5 days. So, when we say current Nakshatra and Rashi, it means that the moon is near to that particular Nakshatra and the Sun is in that particular Rashi and typically that is 1 day and 1 month respectively.

4. Sidereal Year, Tropical Year and the Precession of the Equinox

What is the meaning of a Year? We say that it is time for the Earth to complete one revolution around the Sun. It also means that the time taken to complete one full year cycle of the seasons. Now consider that our Earth’s axis is fixed with an axial tilt of 23.5 degrees and it is pointing at the North Pole star named the Polaris, all the time throughout the year, millennia after millennia. That is not entirely correct. Now, imagine a spinning top, what children used to play. The top spins very fast, but the axis also rotates very slowly. Many times, the axis rotates in the opposite direction of the motion.  Exactly the same is happening to our Earth also.

The axis of the Earth is rotating in the opposite direction of the motion at an extremely slow rate. One full rotation takes around 25920 years to complete. Now, let us start counting from an Equinox with exact day-night match, say March 21. One sidereal year is the time taken for our Earth to complete one full cycle, that is 360 degrees, that means the Sun seen at one particular star to the Sun seen at the same star after a year. Since the axis is rotating in the opposite direction, the next Equinox comes slightly before the Earth completes a 360-degree cycle. That means the seasons complete one full cycle, just slightly before the Earth completes one full circle of revolution around the Sun. One full cycle of the seasons is called the Tropical year.  The Tropical year takes 359 degrees 59 minutes and 10 seconds of Arc around the Sun and the difference is 50 Arcseconds.

That is the difference between the Sidereal and the Tropical year. One denotes the cycle of the motion around the Sun and the other denotes the cycle of the seasons.
Sidereal Year = 365 days 6 hours 9 minutes
Tropical Year = 365 days 5 hours 48 minutes.
Difference = 20 minutes 24 seconds in one year, or 50 Arc-Second of circle per year.

This seems to be small, but over a period of time, it could add up a lot. It could be

1 Day in every 71 years
1 Degree in every 72 years
1 Month in every 2160 years
1 extra Year in 25772 years (between 25700 to 26000 years)
Considering Rashi and Nakshatra, it could be
1 Rashi in 2160 Years (25920/12)
1 Nakshatra in 960 Years (25920/27)

In the Indian system, Ayanamsa is the Sanskrit term used to denote the Precession of the Equinox.

5. Solar and Lunar Calendar

We definitely would have heard about the Solar and the Lunar Calendars. Lunar calendars start either on a Full Moon or a New Moon day. Since 12 Lunar months fall short of the Solar year by around 12 days, all these calendars use some kind of Intercalcation or leap months in every 2 or 3 years. So, in fact, all Lunar Calendars followed in India are LuniSolar, means they get synchronized to the Solar Calendar.

Within the Solar Calendar system, there are also two subtypes – using either the Sidereal or the Tropical year. Most of the Indian systems, both the Solar and the Lunar (or Lunisolar) calendars finally get synchronized to the Sidereal year. Whereas the “Indian National Calendar” or the Shalivahana Shaka Calendar standardised by the Government of India uses the Tropical year starting on the Vernal Equinox, that is on March 21.

Normally Vikram Samvat calendar is used in North and West India, where the Lunar month starts on a Full Moon day. In Karnataka, Andhra, Maharashtra, and Bengal, the Lunar month stats on a New Moon day. Calendars used in Tamil Nadu and Kerala are pure Solar Calendar, where the month starts on a Sankranti day.

In India, we use 27 Nakshatras and 12 Rashis (Zodiac Signs). The 27 Nakshatras are from Ashwini to Revati, the 12 Rashis are from Mesha (Aries) to Meena (Pisces). The 12 Indian Lunar month names are from Chaitra to Phaalguna. These month names are derived from a Nakshatra name in such a way that the Fullmoon happens on that particular Nakshatra. For example, In Chaitra, the full moon is on Chitra Nakshatra and in Phaalguna, the full moon is on Uttara Phaalguni Nakshatra.

On the contrary, the Gregorian calendar or the common calendar we use now internationally is a Tropical Calendar where the Vernal Equinox is generally fixed on March 21 itself.

6. Types of Zodiac

The Zodiac is the portion of the sky through which the Ecliptic passes through. All the 12 Zodiac Signs or Rashis are present in this portion of the sky. Both Sidereal and Tropical year are explained in the previous section, considering the revolution of the Earth. As we observe the Zodiac, the Sidereal year means the Sun completing one full cycle and re-entering the same Sign back. Whereas the full cycle time taken for the Sun to cross the Celestial equator back is called the Tropical year. We have also seen that these are not the same because of the Precession of the Equinox. There is an inevitable drift of 1 degree happening in every 72 years.

In our Indian tradition, the North-South movement of the Sun is named as Ayana. There are two namely Uttarayana and Dakshinayana corresponding to the North and the South movement respectively.  Uttarayana starts at the peak of the winter and Dakshinayana starts at the peak of the summer.

The Zodiac could be divided into the 12 Signs considering either of the two types of year. In the first method, a well known Constellation had been selected as the beginning Sign, that is Aries or Mesha Rashi.   In the second method, the point where the Sun crosses the Celestial Equator towards North is considered as the beginning. The first method is known as the Nirayana system meaning “Without Motion” and the second method is known as the Sayana system meaning “With Motion”.

In India, we follow the Nirayana system with the fixed zodiac and the related Sidereal year, whereas Europeans follow Sayana system with moving zodiac and the Tropical year.

7. Effect of the Precession of the Equinox

As explained before, the Precession of the Equinox causes two types of years and zodiacs. Because of these two types, certain confusions also could arise.  The Vernal Equinox is taking place always on March 21. Currently, that is when the Sun is aligned to Uttara Bhadrapada (Uthrattathi) Nakshatra in Meena Rashi (Pisces). In another 500 years, that would get drifted to Aquarius, that means at the time of the Equinox the Sun would be in Kumbha Rashi. Around 1800 years before, when all the Calendars got synchronized the Vernal Equinox was aligned to Ashwini Nakshatra in Mesha Rashi (Aries).  Currently, the North Celestial Pole is very near to the star Polaris (Alpha Ursa Minoris) or Dhruva.  In another 12500 years from now or 12500 years before, the North Celestial Pole would be near the star Vega (Alpha Lyrae) or Abhijit.  Even the axial tilt of 23.5 degrees is not fixed.  It oscillates between 22.1 and 24.5 degrees on a cycle of 41000 years.

Following the Sidereal year and fixed Nirayana zodiac – The seasonal nature of our important days could drift away.

Most of the new years celebrated in India are just after the Vernal Equinox. In another 12500 years from now or 12500 years before, these new years would get so much drifted away so that it would be in the month of September where Autumnal equinox happens. Festivals like Makara Sankranti and Pongal would take place in June and they would no longer be aligned with the beginning of Uttarayana.  Even now itself, the actual Uttarayana starts on the Winter Solstice day, 23 days earlier to Makara Sankranti and in another 500 years, it would be aligned to Dhanu Sankranti day.

Similarly, Deepavali is celebrated on Kartika Amavasya, in Tula Rashi now, at the beginning of the winter.  Considering precession, 12500 years before or after, Deepavali would be at the beginning of the summer.

Following the Tropical year and moving Sayana Zodiac – The names of the Zodiac signs would really lose their meaning.

As per the Tropical European system, Aries sign starts always on March 21, the day of the Equinox.  Now itself due to the moving zodiac, the Sun is really in Pisces when the Aries sign starts. In another 12500 years from now or 12500 years before, the Vernal Equinox would happen when the Sun is actually in Libra. As per the Tropical system that would mark the beginning of the Aries sign.

Similarly, Christmas and New Year (January 1) is celebrated at the peak of the winter when the Sun is in Sagittarius.  This also would get shifted back to Libra and so on.

Some of the Indian calendars like the official Shaka calendar has been recalibrated to follow the Tropical year, but the month names remain the same as Chaitra to Phaalguna.  These months also would lose their actual meaning.  Chaitra month of Shaka calendar would not be aligned to having the full moon on Chitra Nakshatra day.

Basically, the astronomical meaning of these important days would get changed.  After all, Astronomy and Astrology originated from the Greek word Astron meaning star.  The corresponding Sanskrit word Jyotisha also originated from the light from the stars.  Anything to do with stars automatically gets aligned to the Sidereal than the Tropical method.

8. To sum it all up

If fixed zodiac is followed, then the seasonal nature of festivals would go away.  Similarly, if moving zodiac is followed astronomical nature of festivals also would go away.  These are inevitable because of the difference between the Sidereal and the Tropical year. We could only follow one system and there are a few effects associated with that.



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Both ffmpeg and vlc are two of the important applications in free software media processing. I wanted to compile both to incorporate latest codecs, x264 and libvpx for video along with aac and libopus for audio. This is what I have done on Debian unstable.

For my purpose, I was compiling these codecs from source. To use the development libraries and headers given by Debian, one has to install the following packages, sudo is used to denote usage of root

sudo apt-get install libfaad-dev libfaac-dev libx264-dev libvpx-dev libopus-dev

Instead of using the development pacakges provides by Debian, I was compiling and installing these libraries to /opt. To use proper package config paths for both ffmpeg and vlc, one has to do export PKG_CONFIG_PATH or alternatively supply then to the configure script.

export PKG_CONFIG_PATH=/opt/lib/pkgconfig

Downloading the corresponding source code

# faac
wget -c http://downloads.sourceforge.net/faac/faac-1.28.tar.gz
# faad
wget -c http://downloads.sourceforge.net/faac/faad2-2.7.tar.gz
# x264
git clone git://git.videolan.org/x264.git
# libvpx
git clone https://chromium.googlesource.com/webm/libvpx
# opus
git clone http://git.xiph.org/opus.git
# ffmpeg
git clone git://source.ffmpeg.org/ffmpeg.git
# vlc
git clone git://git.videolan.org/vlc.git

As I mentioned above, I was using /opt as the prefix. These are the compilation commands used. Replace the number of CPU cores with “-jN” option of make.

# faac
./configure --prefix=/opt
# comment out line 126 of faac-1.28/common/mp4v2/mpeg4ip.h
# strcasestr in case of any compilation error
make -jN
sudo make install
# faad
./configure --prefix=/opt
make -jN
sudo make install
# x264
sudo apt-get install yasm # install dependencies
./configure --prefix=/opt --enable-shared
make -jN
sudo make install
# libvpx
sudo apt-get install yasm #install dependencies
./configure --prefix=/opt --enable-vp8 --enable-vp9 --enable-shared
make -jN
sudo make install
# libopus
./configure --prefix=/opt
make -jN
sudo make install


# install these extra package dependencies:
sudo apt-get install libopenjpeg-dev libvorbis-dev libschroedinger-dev libvpx-dev libopus-dev
./configure --prefix=/opt --extra-cflags='-Wall -g -I/opt/include/' --extra-ldflags='-L/opt/lib/' --enable-avfilter --enable-libschroedinger --enable-libvpx --enable-libspeex --enable-libtheora --enable-libopus --enable-libvorbis --enable-pthreads --enable-zlib --disable-stripping --enable-runtime-cpudetect --enable-libfaac --enable-libx264 --enable-postproc --enable-swscale --enable-x11grab --enable-libopenjpeg --enable-shared --enable-gpl --enable-nonfree --disable-static --disable-stripping --disable-altivec --disable-armv5te --disable-armv6 --disable-doc --disable-htmlpages --disable-manpages --disable-podpages --disable-txtpages
make -jN
sudo make install


# package dependencies:
apt-get install libtool gettext cvs libfaad-dev libfaac-dev libswscale-dev libpostproc-dev libqt4-dev libgcrypt20-dev libdbus-1-dev lua5.2 liblua5.2-dev libproxy-dev libdvbpsi-dev liblivemedia-dev libnotify-dev libshout3-dev libdca-dev libflac-dev libmpeg2-4-dev libmpeg3-dev libsdl2-dev libgnutls28-dev libavc1394-dev libsmbclient-dev libtwolame-dev liba52-0.7.4-dev libfribidi-dev libjack-dev libmad0-dev
# a few more extra dependencies:
apt-get install libcdio-dev libvcdinfo-dev libpulse-dev libxml2-dev libmodplug-dev libnotify-dev libcaca-dev libncursesw5-dev libxpm-dev libxcb-shm0-dev libxcb-xv0-dev libxcb-keysyms1-dev libxcb-randr0-dev libx11-xcb-dev libxcb-composite0-dev
./configure --prefix=/opt --disable-update-check --disable-gnome --disable-gtk --disable-familiar --disable-fb --enable-sdl --enable-esd --enable-mad --enable-arts --disable-jack --enable-pulse --enable-lirc --enable-a52 --enable-aa --enable-dvbpsi --without-dv-raw1394 --disable-dc1394 --disable-kde --enable-mp4 --enable-dvb --disable-satellite --enable-ogg --enable-vorbis --enable-shout --enable-qt4 --disable-slp --enable-flac --disable-skins --disable-basic-skins --enable-skins2 --enable-freetype --enable-mkv --enable-speex --enable-caca --enable-live555 --enable-libmpeg2 --enable-fribidi --enable-cdio --enable-mod --enable-theora --enable-modplug --enable-gnutls --enable-ffmpeg --enable-ncurses --enable-smb --disable-gnomevfs --enable-bonjour --enable-mpc --enable-vcd --enable-vcdx --enable-twolame --enable-x264 --enable-faad -enable-faac --enable-vpx --enable-opus --enable-xcb --disable-zvbi --enable-telx --enable-mediacontrol-bindings --disable-atmo --enable-taglib --enable-libass --enable-libdca --enable-alsa --disable-dv --disable-dvdnav --disable-notify --enable-v4l --enable-v4l2 --enable-pvr --enable-dvd --without-dvdcss CPPFLAGS='-I/opt/include' CFLAGS='-g -O2 -I/opt/include' LDFLAGS='-L/opt/lib -Wl,--as-needed' CXXFLAGS='-g -O2' PKG_CONFIG_PATH='/opt/lib/pkgconfig:/usr/lib/pkgconfig'
make -jN
sudo make install

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Hello world!

Welcome to WordPress.com. After you read this, you should delete and write your own post, with a new title above. Or hit Add New on the left (of the admin dashboard) to start a fresh post.

Here are some suggestions for your first post.

  1. You can find new ideas for what to blog about by reading the Daily Post.
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