Lunisolar Hindu Calendar

 In the previous video, we explored events associated with the movement of Sun, Earth and Moon. 

Let us understand how months of the Hindu Calendar are decided with the help of this model.  Though Hindu Calendar is based on the cycles of the Moon, it tries to accommodate solar year as well in single framework. This is done by adding 'Adhik Maas' or extra month every 33 months.

Months familiar to us are as per Gregorian Calendar which is based on Solar Cycle. 

Earth takes 365 days to complete one revolution around the Sun.

These are divided into 12 parts and each part is called Month. 

Some months have 31 days while some have 30 except February which has 28 or 29 days.

Position of Earth along the orbit is also decided like 21st March, 22nd June, 22nd September and 22 December.

Months in Hindu calendar are based on the cycles of the Moon.  

Time taken by the Moon to complete one revolution from New Moon phase to next New Moon is considered as one month in Hindu Calendar. Also known as ChandraMaas .

On this dial, Zodiac signs as per the Hindu Calendar are named like this.  Mesh, Rishabh, Mithun, Karka,... popularly known as Rashi as well. 

Just like Gregorian Calendar, there are 12 months, Chaitra, Vaishakh, Jeshtya, Aashadh.......

While months are named as Chaitra, Vaishakh, Jeshtya, Aaashadh, Shravan ....

Let us start with Gudhipadva - Festival which marks start of New Year.

Let us take help of the calendar to learn about the same. 

Month is April and Year 2021.

There is New Moon or Amavasya on 12th April. Let us position the moon accordingly.

When Sun is in MEEN Rashi , First Month Chaitra starts from the new Moon phase that is amavasya.

13th April is the first day of Chaitra also known as Chaitra Pratipada.

There is a full moon or Purnima on 27th April and Amavasya or New Moon on 11th May, marking the end of first month Chaitra. 

Each Month of the hindu calendar has 30 days. Each day is also called as Tithi.

But how duration of a day is decided ? 

Moon orbits at a greater speed around Earth. Angle between Sun and Moon continues to increase from 0 degree to 360 degrees from new moon to next new moon. If we divide 360 degrees in 30 equal parts, each part will be of 12 degrees. 

Time moon takes to cover these 12 degrees is considered as one day or Tithi.

Like if it travels 12 degress, Pratipada - First day , after 24 degrees, Dwitiya - second day and so on ...

Due to elliptical orbits of moon as well as earth, speed is different at different locations. Sometimes it takes more time to cover 12 degrees while at other times it takes less time. That is the reason duration of a single day or tithi varies in Hindu Calendar . It fluctuates between 20 to 27 hours. In gregorian calendar each day is fixed as 24 hours. 

From New moon phase, 180 degree travel marks Full Moon and 360 degrees marks the next new moon phase.

This part is also the waxing phase of the moon and is known as shukla paksha. 

This part is also waning phase of the moon also known as Krishna paksh. 

Tithi in Shukla Paksha is prefixed with shuddha while Tithi in Krishna paksh is prefixed with Vadya.

Shudh Pratipada

Shudha Dwitiya

Shudha Ashtami and so on

Vadya Pratipada

Vadya Dwitiya

Vadya Ashtami and so on

Lets move ahead

Next month Vaishakh starts from 12th May 

26th May Purnima

10th June is new moon day , Amavasyya

Start of another month, Jeshtha

In every month, Sun transits from one raashi to another . 

Like in the month of Chaitra, from Meen rashi to Mesh, In Vaishakh , to Vrishabh rashi and in Jeshtha Mithun Rashi.

If this transition does not take place in a particular month, that month is considered as extra month or adhik maas for that year.

12 revolutions of moon mark the completion of 1 year in Hindu Calendar

First month of next year, Chaitra starts from this position again.

In year 2022, Chaitra starts on 2nd April, almost 11 days in advance than the previous year. This is because each month is only 29.5 days approximately.

Moving on, in the year 2023, Chaitra month starts on 22nd March, 22 days earlier than 2021. 

If same sequence is followed, we may have to celebrate hole in monsoon or Diwali in Summer.

This is where extra month or adhik maas comes handy.

Lets us move on.

Vaishakh, jeshtha, aashadh

17th July is amavasya or new moon day and Sun is in Kark Rashi. 

Moon completes one cycle on 17th August but Sun is still in Kark Rashi.

There is no transition of Sun to another Rashi during this period. This month is considered as Extra Month or Adhik Maas.

Adhik Shravan

Month after is considered as regular Shravan as per earlier sequence.

Now sun has transitioned to Sinha rashi from Kark Rashi

Other months follow the sequence as usual.

In 2024, gudhipadva will be on 9th April , somewhat closer to 2nd April in 2021.

Introduction of extra-month or Adhik Maas enables synchronization of Solar and Lunar cycles in Hindu Calendar.

If one considers the start of Chaitra Month from 2000 to 2010, Sun is always in Meen rashi. 

Just like transition of sun through rashis, transition of Moon through Nakshatra is also worth exploring.

We will learn more about this in the next video.

Thank you.

 

Model - Sun, Earth and Moon

  Let us understand various events associated with Sun, Earth and moon with the help of a model.

Model is built with small balls, beads and lots of gears. Let us assume that we are way up in the sky and observing these objects from a pole star. Earth revolves around the Sun, not in clockwise direction but in anti clockwise direction.

During this journey around the Sun, it also rotates around its own axis. This axis is not straight but slightly tilted at an angle of 23.5 degrees like this. This tilt is the reason we have seasons on Earth.

Just like it's revolutions around the Sun, Earth also rotates in anti-clockwise direction around it-self. One complete rotation around itself takes 24 hours while one complete revolution around Sun is finished in 365 days or 1 year. Let's take help of this dial so that position of Earth can be referenced as it revolves.

There are numerous stars around our solar system. These were grouped by our ancestors for easier identification. Also know as constellations. There are many but 12 are most important. These constellations mark out the path that Sun appears to take throughout the year.

Mostly known to us as Zodiac signs. Circle is divided into 12 equal parts. One part per zodiac sign.

This outer ring has months marked on it as per Gregorian calendar. Useful while discussing Seasons.

Zodiac signs are arranged like this… Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces.

And months as January, February, March, April, May….

Let's move Earth by hand in steps and study orientation of axis as it revolves around the Sun. Front view is better for this instead of top view

This imaginary line represents Equator. It divides Earth in two equal parts. Northern hemisphere and Southern hemisphere.

Let us start with 21st June.

21st June is the longest day in Northern hemisphere. North pole is at its nearest point towards Sun on this day. Hence this part gets more sunlight. Longest day and shortest night.

Exactly opposite situation is there in the southern hemisphere. Longest night and shortest day .

It's also known as summer solstice.

22nd September

On this day Sun is exactly above the Equator, which makes day and night of equal length. Marking the start of Autumn. During the autumnal equinox, the sun shines directly on the equator, and the northern and southern hemispheres get the same amount of rays.

22nd December

On this day North Pole is farther from the Sun. Northern hemisphere receives less Sunlight.

Days are shorter and nights longer. It's also known as winter solstice. Exactly opposite situation is there in Southern hemisphere.

21 March

Earth’s two hemispheres are receiving the sun’s rays equally. Night and day are often said to be equal in length. Also known as spring equinox or vernal equinox.

Sun rises southward every day starting 21st June till 21st December in Northern hemisphere. And starts rising northward again from 22nd December. These two periods are Popularly known as Uttarayan and Daxhinayan in India.

Moon

This small plastic bead is our Moon.

While the Moon revolves around the Earth, Moon and the Earth revolves around the Sun.

It takes approximately 27.3 days for Moon to complete one revolution around the Earth.  But Earth is also moving constantly. Moon takes more time to reach the same spot. 29.5 days.

The Moon itself does not generate light; it is lit up by the Sun. As the Moon orbits the Earth, the portion of illuminated Moon that we see changes – giving rise to the phases of the Moon.

The Moon does not produce its own light. There is only one source of light in our solar system, and that is the Su. “moonlight” is actually just sunlight reflecting off of the Moon’s surface. The Sun’s light comes from one direction, and it always illuminates, or lights up, one half of the Moon – the side of the Moon that is facing the Sun. The other side of the Moon is dark.

On Earth, our view of the illuminated part of the Moon changes each night, depending on where the Moon is in its orbit, or path, around Earth. When we have a full view of the completely illuminated side of the Moon, that phase is known as a full moon.

In this video, I short recently on a full moon day, moon is seen rising in the east while sun sets in the west. But following the night of each full moon, as the Moon orbits around Earth, we start to see less of the Moon lit by the Sun. Eventually, the Moon reaches a point in its orbit when we don’t see any of the Moon illuminated. At that point, the far side of the Moon is facing the Sun. This phase is called a new moon. During the new moon, the side facing Earth is dark.

We have a “new Moon” when our Moon's orbit around Earth moves it between Earth and the Sun. From Earth, the Moon's surface looks dark because the illuminated side is facing away from Earth. As our Moon continues its orbit counterclockwise around Earth (viewed from above the north pole), more and more of the illuminated part of the Moon becomes visible to us, until it reaches the “full Moon” stage. A full Moon occurs when the Moon has moved in its orbit so that Earth is “between” the Moon and the Sun.

When the Sun and Moon are aligned on the same side of the Earth, the Moon is "new", and the side of the Moon facing Earth is not illuminated by the Sun.

A waxing moon is a moon that gets more sunlight on it as the days go by. It is after we experience a new moon up to a full moon. A waning moon is after the full moon and will remain waning until we again experience a new moon.

Eclipse is another event familiar to us.

A lunar eclipse occurs when the Moon moves into the Earth's shadow.

A solar eclipse occurs when a portion of the Earth is engulfed in a shadow cast by the Moon which fully or partially blocks sunlight. This occurs when the Sun, Moon and Earth are aligned. Such alignment coincides with a new moon

If the Moon were in a perfectly circular orbit, a little closer to the Earth, and in the same orbital plane, there would be total solar eclipses every new moon. However, since the Moon's orbit is tilted at more than 5 degrees to the Earth's orbit around the Sun, its shadow usually misses Earth. A solar eclipse can occur only when the Moon is close enough to the ecliptic plane during a new moon.

Due to tile in the orbital planes of Moon and Earth, eclipses do not occur every 15 days.

Lets use this small dial to help is identify various phases of moon as it revolves around the Earth.

Same side of the moon

As speed of rotation of moon around its own axis and time it takes for one revolution around Earth is same, we always see same side of the moon. Let us mark a red line here. It is always facing the earth.

Makar Sankranti

We celebrate Makar Sankrant every year around 14th or 15th Jan. On this day, Sun enters from Dhanu rashi to Makar Rashi. But what does enter a zodiac means. ?

Sun is stationary just like many constellations around us. When observed from Earth, Sun appears to be in particular constellation in the background. This keeps on changing as Earth revolves around the sun. When these imaginary boundaries are crossed, we refer to it as SUN entering a particular constellation/ or zodiac sign or Rashi.

Most of the hindu festivals are celebrated as per Lunar calendar but Makar Sankrati is based on the transition of SUN. This is why it normally comes around 14th or 15th Jan of Gregorian calendar.

In the next video, we will discuss about Hindu calendar which considers lunar as well as solar position while deciding months.

Thank you.

Making of Sun, Earth, Moon model.

I wanted to build a model of Sun , Earth and Moon to capture key events.

To keep it portable I decided to ignore scale for size and distance between Sun, Moon and Earth but focus more on number of rotations of moon around earth in a year as well as alignment of Earth's axis with respect to Sun. 

I used 2.2 mm MDF sheet for gears as well as frame which is is laser cut as required. MDF is cheaper than acrylic. 

Software

• Geargenerator.com
• FreeCad
• Inkscape

With lots of inputs from existing Orrey built on the net, I used geargenerator.com to come up with the desired ratio 12.37 ( close to 12.368 ) for rotations of the Moon around Earth in one year. 

I could manage it with just three gears 33, 24, 8  with module 2.5

To ensure that Earth as well as Moon rotate in anti-clockwise direction, additional idler gears were added. 

Once number and sequence for the gears was finalized, I used FreeCad's Gear workbench to model gears with 1 mm hole in the center and exported SVG file for gears.

This SVG file was then opened in Inkscape, which was used to decided alignment for proper meshing.

Sharing assembly sequence here. Some captures are from different versions.  

Assembly

Base plate is used for correct placement of gears during assembly.  Four 3mm Screw/Nut holds the assembly in place. Pins are used as an axle for the gears. Middle plate separates the  two layers of gear train and ensures smooth rotations. 

Central first gear is fixed in place to the table with the help of two 3 mm screws placed 10 mm apart.

Circular disc enables assembly to freely move around the central first gear. 

Last driven gear has equal number of teeth as that of first gear. This results in exact one rotation of the gear when one year is complete. This gear will drive Earth's axis orientation. Hexagonal pencil profile ensures that axis assembly, circular disc are locked in place with the gear movement without any additional tooling.

Pencil also acts as an axle for outer gear with 8 teeth, This gear has a diameter of 8 mm. 

Axial tilt is achieved with the help of angular slot between to plates. Part of the cycle spoke is used to mount the Earth. Small wheel at the end rests on the lower disc which rotates the moon. Resulting friction rotates the Earth. But this interaction resulted in clockwise rotation of the Earth. To rotate it in anti-clockwise direction, I had to introduce pulley like mechanism .

Two discs were used to mount moon. One is attached to the 8 teeth gear while other one rests on the it.

Top disc enable us to adjust position of the Moon as needed. This can be fixed in place with cello tape to the bottom disc. 

Circular ring is placed on the Earth's disc which will ensure axial tilt of the Moon's orbit as it rotates. 

Sliding of the moon is achieved with the help of rectangular box assembly made from MDF itself.

Circular base disc is also free to rotate in case we need to adjust the position of Constellations as per our viewing angle. 

Small outer ring will be used to label the English months on one side and 'Nakshtra' - subset of constellations on the other side. 

All dials were designed in Inkscape. Clone tool was handy to work with angles and divisions.

This was 7th version which finally made it to the script. 

Do suggest if there are any improvements needed in the current model. 

I plan to make to more sturdier by replacing MDF with 3 mm Acrylic and make it more portable for lab use.

Limitations:

1. Earth does not rotate around itself exactly 365 days in a year
2. Tilt of Moon's Orbit with Earth's Orbit is not 5 degree but much more. This is only to show the up and down movement of the Moon as it rotates around the Earth.
3. Size as well as distance of all the three objects is not as per scale.
4. Moon is fixed in one place. It does not rotate around itself.

Artifacts

Important files used for this project are available for use at this link. This may help other tinkerers.

Note that only gears, disc and support frames are available in the design. You will have to explore axles and other fitments to keep everything in one place.

सूर्य,पृथ्वी व चंद्र - मॉडेल

 सूर्य,पृथ्वी व चंद्रामुळे होणाऱ्या वेगवेगळ्या घटना मॉडेलच्या मदतीने समजावून घेऊया  

त्यासाठी वापरले आहेत वेगवेगळ्या आकाराचे चेंडू, मणी आणि आणि खूप सारे gears. 

सुरवात अर्थातच पृथ्वीपासून.  पृथ्वी सूर्य व चंद्राकडे आपण आकाशातून खाली बघत आहोत असे समजूया 

पृथ्वी सूर्याभोवती प्रदक्षिणा घालते. पण घडाळ्याच्या काट्यांप्रमाणे म्हणजेच clockwise नाही तर उलट दिशेने म्हणजे anticlockwise .

परिभ्रमण करता करता पृथ्वी स्वतःच्या अक्षाभोवती गोल फिरते,. ह्या अक्षाला पृथ्वीचा आस असे म्हणतात. 

पृथ्वीचा आस हा सरळ नसून थोडा तिरका आहे म्हणजे आस दक्षिणोत्तर असून उत्तरेकडे तो साधारणपणे ध्रुव ताऱ्याकडे रोखलेला आहे.  तिच्या कक्षाकडे २३.५ अंशातून 

पृथ्वी पण स्वतःभोवती  anti-clockwise फिरते म्हणजे पश्चिमेकडून पूर्वेकडे. 

पृथ्वी स्वतःभोवती पश्चिमेकडून पूर्वेकडे फिरण्याऐवजी पूर्वे कडून पश्चिमेकडे फिरली तर काय होईल ? विचार करा . 

स्वतःभोवती एक प्रदक्षिणा पूर्ण करण्यास पृथ्वीला जवळपास २४ तास लागतात. 

तर सूर्याभोवती प्रदक्षिणा पूर्ण करण्यास ३६५ दिवस लागतात. यालाच आपण एक वर्ष म्हणतो.  

या सगळ्याचा एकत्रित परिणाम म्हणूनच पृथ्वीवर उन्हाळा, पावसाळा व हिवाळा हे ऋतू क्रम सुरू असतात.

या वेगवेगळ्या घटना समजावून घ्यायच्या तर नुसतेच आकाश काय कामाचे. ? चला एक वर्तुळ ठेवूया.  

सूर्यमालेच्या चहूबाजूस असंख्य तारकापुंज आहेत. आपलय पूर्वजांनी यातील काही ठराविक तारे निवडले व त्यांना नावे दिली. यालाच आपण कॉन्स्टिल्लाशन्स म्हणतो . पण सूर्य आणि चंद्र यांच्या भ्रमण मार्गातील १२ च विचारात घेतली जातात. जशा कि आपल्या बारा राशी. वर्तुळाचे १२ भाग  पाडले. एक भाग एक राशी. आपल्या रोजच्या वापरातील इंग्रजी महिने या छोट्याश्या चकती वर काढले आहेत. हे ऋतूंचा अभ्यास करताना उपयोगी पडतील 

राशींची मांडणी या क्रमाने केली आहे. मेष वृषभ मिथुन कर्क ....  

आणि महिने जानेवारी , फेब्रुवारी .... 

पृथ्वीला हाताने टप्प्या टप्प्यात फिरवत तिचा आस कसा झुकलेला आहे ते बघूया 

.

आसाची स्थिती वरून बघण्यापेक्षा बाजूने बघितल्यास जास्त चांगली कळते. 

सुरु करूया २१ जून पासून 

21 june.

हे विषुववृत्त , पृथ्वीला दोन भागात विभागणारी काल्पनिक रेषा , वरचा भाग उत्तर गोलार्ध तर खालचा दक्षिण गोलार्ध 

उत्तर गोलार्धात 21 जून हा वर्षातील सर्वात मोठा दिवस.  पृथ्वीचा उत्तर धृव हा 21 जूनच्या दिवशी सूर्याच्या दिशेने सर्वाधिक कोनामध्ये कललेला असतो. यामुळेच  उत्तर गोलार्धात पृथ्वीवर या दिवशी सर्वाधिक प्रकाश पडतो.दिवस सर्वात मोठा आणि रात्र सर्वात लहान असते. 

या विरुद्ध परिस्थिती दक्षिण गोलार्धात असते, दिवस लहान तर रात्र मोठी.  यादिवशी ग्रीष्म ऋतूस सुरवात होते. समर  solistice असेही म्हणतात 

22 september

 या स्थितीत  कोणताही गोलार्ध सूर्यकड़े कललेला नसतो.  या दिवशी सूर्य खगोलीय विषुववृत्तावर असल्याने पृथ्वीवरील कोणत्याही ठिकाणी १२ तासांचा दिवस व १२ तासांची रात्र असते. म्हणून या दिवसांना विषुव-दिन असेही म्हणतात. या दिवशी सूर्य बरोबर पूर्वेस उगवतो व पश्र्चिमेस मावळतो. यालाच शरद संपात / Winter Equinox असेही म्हणतात  या दिवशी शरद ऋतूस सुरवात होते 

22 December

पृथ्वीचा उत्तर धृव सूर्याच्या सूर्याच्या विरुद्ध  दिशेने  कललेला असतो. उत्तर गोलार्धात रात्र मोठी व दिवस लहान असतो.  या दिवशी शिशिर ऋतूस प्रारंभ होतो. याउलट दक्षिण गोलार्धात सगळ्यात मोठा दिवस व सगळ्यात छोटी रात्र असते. Yalach winter solistice pan mhantaat  

21 March

 या स्थितीत  कोणताही गोलार्ध सूर्यकड़े कललेला नसतो.  या दिवशी सूर्य खगोलीय विषुववृत्तावर असल्याने पृथ्वीवरील कोणत्याही ठिकाणी १२ तासांचा दिवस व १२ तासांची रात्र असते. यालाच वसंत संपात दिन असेही म्हणतात. vernal equinox . या दिवशी वसंत ऋतूस सुरवात होते  

२१ जूनपासून २२ डिसेंबरपर्यंत तो दररोज आदल्या दिवसापेक्षा अधिकाधिक दक्षिणेस गेलेला दिसतो; तर २२ डिसेंबरपासून २१ जूनपर्यंत तो दररोज आदल्या दिवसापेक्षा अधिकाधिक उत्तरेस गेलेला दिसतो. सूर्याच्या या उत्तरेकडून दक्षिणेकडे (२१ जून ते २२ डिसेंबर) आणि दक्षिणेकडून उत्तरेकडे (२२ डिसेंबर ते २१ जून) होणाऱ्या भासमान भ्रमणाला अनुक्रमे दक्षिणायन व उत्तरायण म्हणतात. 

चंद्र

हा छोटा मणी म्हणजे आपला आवडता चंद्र .

चंद्र पृथ्वीभोवती परिभ्रमण करीत असतो. पृथ्वी आणि चंद्र हे दोघेही एकमेकांसोबत सूर्याभोवती फिरतात. 

चंद्र पृथ्वीभोवतीची एक प्रदक्षिणा सुमारे २७.३ दिवसात पूर्ण करतो. पण पृथ्वीसुद्धा सूर्याभोवती फिरत असल्यामुळे पृथ्वीच्या आकाशात त्याच ठिकाणी यायला चंद्राला जवळजवळ २९.५ दिवस लागतात.

चंद्र हा स्वयंप्रकाशित वस्तू नाही. चंद्रावर सूर्याचा जो प्रकाश पडतो, तो परावर्तित होतो, त्यामुळे चंद्राचा तेवढाच प्रकाशित झालेला भाग आपल्याला दिसतो. चंद्राच्या परिभ्रमणा मुळे हे प्रकाशित चंद्रबिंब वेगवेगळ्या आकारात आपल्याला दिसते, त्यालाच आपण चंद्राच्या कला असे म्हणतो.

अमावस्या आणि पौर्णिमा 

सूर्य आणि चंद्र हे जेव्हा पृथ्वीच्या संदर्भात एकमेकांच्या विरुद्ध दिशेला येतात, तेव्हा पृथ्वी ही सूर्य आणि चंद्राच्या मध्ये असते. त्यामुळे या स्थितीत आपल्याला चंद्राचे बिंब १००%  प्रकाशित दिसते. याला आपण पौर्णिमा म्हणतो. 

अमावास्येला  चंद्राचा प्रकाशित भाग हा आपल्या विरुद्ध बाजूला असतो. तर अंधाराचा भाग आपल्याकडे. अर्थात तेव्हा चंद्रबिंब अंधारलेले असते. या स्थितीमध्ये सूर्य आणि पृथ्वी  यांच्यामध्ये चंद्र असतो.

आणखीन एक महत्वाची घटना म्हणजे ग्रहण 

 अमावास्येच्या स्थितीमध्ये सूर्य, चंद्र आणि पृथ्वी अशी सरळ रेषेत स्थिती असते.  जर ते एकाच प्रतलात आले, तर अशा वेळी चंद्राची सावली पृथ्वीवर पडते. जिथे ती सावली पडते, त्या सावलीच्या भागातून सूर्यग्रहण दिसते.

या स्थितीमध्ये जर सूर्य, पृथ्वी आणि चंद्र एका समान प्रतलात आले, एका रेषेत आले, तर पृथ्वीची सावली चंद्रावर पडल्याने चंद्रग्रहण होते.

हे प्रतल एकसमान असते तर दर अमावस्या आणि पौर्णिमेला ग्रहणं झाली असती. पण चंद्राची कक्षा ही पृथ्वीच्या कक्षेशी जवळजवळ ५ अंशाचा कोन करते. यामुळे काही वेळा चंद्र, सूर्य आणि पृथ्वीच्या प्रतलांपेक्षा कधी वरती तर कधी खालती असतो . त्यामुळेच प्रत्येक पौर्णिमा अथवा अमावास्येला ग्रहण होत नाही.

सूर्यग्रहण अमावास्येच्या आसपास होते जेव्हा चंद्र, पृथ्वी व सूर्याच्या मध्ये येतो. याउलट चंद्रग्रहण पौर्णिमेच्या आसपास होते जेव्हा पृथ्वी, चंद्र व सूर्य यांच्यामध्ये येते. 

शुक्ल पक्ष / कृष्णपक्ष 

चंद्राच्या बदलत्या कला ओळखणे सोपे जावे म्हणून हि एक गोलाकार चकती लावूया. 

अमावास्येपासून परत आमावास्येपर्यंत लागणारा वेळ , हाच आपला एक मराठी महिना , यालाच चांद्रमास असे पण म्हणतात, 

चांद्र मास हा तीस दिवसांचा (प्रत्यक्षात साडे एकोणतीस दिवसांचा) असतो, तर चांद्र वर्ष ३६० दिवसांचे (प्रत्यक्षात ३५४ दिवसांचे). हे सूर्याधारित सौरवर्षापेक्षा ११ दिवसांनी लहान असते. सूर्यवर्षाच्या बरोबर येण्यासाठी साधारणपणे दर (सुमारे) ३३ महिन्यांनी अधिक चांद्रमास येतो.

अमावास्येनंतर चंद्र पूर्वेच्या दिशेने पुढे सरकताना, आपल्याला चंद्राचा अधिकाधिक प्रकाशित भाग चंद्रकोरीच्या स्वरूपात दिसायला लागतो. याला आपण शुक्ल पक्षातील चंद्र असे संबोधतो

पौर्णिमेनंतर चंद्र कक्षेत पुढे गेल्यावर त्यावर पडणारा सूर्यप्रकाश हळूहळू कमी होत गेलेला आपल्याला दिसतो. याला आपण कृष्णपक्ष असे म्हणतो.

सन्मुख बाजू

चंद्राला स्वतःभोवती फिरण्यास लागणारा वेळ हा पृथ्वीच्या भोवती फिरण्यास लागणाऱ्या वेळाएवढाच असल्यामुळे चंद्राची कायम एकच बाजू (सन्मुख बाजू) पृथ्वीच्या दिशेला असते.  या बाजूला एक लाल उभी रेघ काढूया .पृथ्वीभोवती एक प्रदक्षिणा केली तरीही हा बिंदू हालत नाही.

मकर संक्रांति 

मकरसंक्रांतीच्या दिवशी सूर्य धनू राशीतून मकर राशीत प्रवेश करतो .प्रवेश करतो म्हणजे नक्की काय ?

खरं तर सूर्य हा निश्चल आहे. पण पृथ्वीच्या भ्रमणामुळे आपल्याला सूर्य फिरत असल्याच्या भास होतो. दूरवर असणारे अनेक तारकासमूह पण बहुतेक निश्चल आहेत. या तारकासमूहांचा संदर्भ धरून आपण सूर्याची स्थिती ठरवतो.  

मकरसंक्रांतीच्या दिवशी सूर्य धनू राशीतून मकर राशीत असा प्रवेश करतो 

इंग्लिश महिन्यानुसार हा दिवस बहुधा १४ जानेवारी रोजी येतो. परंतु दर काही वर्षांनी ही इंग्रजी तारीख एकएक दिवस पुढे जाते, 

Gear Basics

 Notes on my work on Gears

How many wheels does this toy car have ? 

There are many, not just four. 

These wheels inside are special wheels. These wheels have teeth on the outside also known as Gear.

Most of the machines around us use gears to perform the intended work. [Clock, Cassette Player, Drill machine, Sugarcane ]

Lets understand more about gears. 

I will pin this wheel. It rotates freely around the pin. This motion can be transferred to another wheel If they are in close contact with each other. But this contact may not always work especially for high speeds. Friction may wear the surface as well over time. 

To take care of this, let us attach this pointed profile to the wheels. 

Now the motion of one wheel can be easily transferred at all speeds. 

A wheel with teeth on the outside is called gear. 

Instead of regular plastic gears, we will use gears laser cut from MDF sheet and some pins. 

Normally gears are driven by a motor but for now we will rotate it by hand.

Let us take this gear and pin it in the center.

With little force I can rotate it 

Let us mark a black line like this. 

I moved it by 360 degrees or one rotation in an anti-clockwise direction. 

Or one rotation again in a clockwise direction. 

Another gear can be placed like this on the right side. 

Rotating gear on the left will not have any effect on the gear on the right. 

Let us place the teeth of one gear in between the teeth of the another gear

This is also known as meshing the gear. 

Let us mark gear on the left as A while gear on the right as B. 

We will place push pins next to the markings. That way we can count the number of rotations.

One rotation of A also results in one rotation of B but with one change. B rotates in the opposite direction. 

This is true even if A is rotated multiple times, slower or faster. 

This is also true when I rotate B. A rotates the same number of turns but in opposite directions. 

The gear A is called driver gear while the gear B is called driven gear. 

How about introducing another identical gear in between ? Can you predict how B will move now ?

Gear B turns in the same direction as that of A.  Number of rotations however remains unchanged. 

Now let us replace middle gear with another one, this time with more teeth. How will gear B react ?

Direction and number of rotations for the gear on the right do not change. 

This is also true when we use middle gear with less teeth.

Middle gear is also known as idler gear -  a gear placed between a driving and a driven gear to transfer motion without change of direction .

Idler gear can be placed anywhere as long as it is meshed properly.

How about introducing one more in between A and B ? 

Everything is the same except the direction of rotation. Can you find some relation between number of gears between driven gear and driver and direction of rotation ?

Now let us look at gears of different teeth. 

This one with 20 teeth and this one with 40 teeth. 

One full rotation of gear C results in only half rotation of gear D.

Tried another way, one full rotation of gear D results in two rotations of gear C.

This observation leads to another important concept - Gear ratio.

This is true even if I rotate gear C faster or slower, clockwise or counter-clockwise.

One time, four times or even 10 times. I can even attach motor to gear A and run it much faster. Ratio still remains the same.

Relationship of two meshing gears does not change. 

Gear ratio is the number of rotations of driver gear to the number of rotations of a driven gear.

We use the word ratio to describe this constant relationship between two values. 

A colon is often used to show a gear ratio:

gear ratio = rotations of a driver gear : rotations of a driven gear

The order of the two numbers in a ratio is very important. 

What will be the gear ratio in this scenario ? It will be 1:2 instead of 2:1.

 In terms of the bicycle, the gear ratio is the ratio of pedal rotations to wheel rotations.

Can you find gear ratios for these pairs ? 

Is there a relationship between the gear ratio and the ratio between teeth ?

Teeth can be used to find the gear ratio. This relationship between the tooth ratio and the gear ratio is very important. It allows us to find a gear ratio without actually having to build a gear train and turn the gears. We can find the ratio of any two gears if we know the number of teeth on each of the gears. 

We can rewrite the gear ratio as teeth on driven gear to teeth of driver gear. 

gear ratio = = rotations of driver gear

rotations of driven gear

teeth of driven gear

teeth of driver gear

So far we have used only single gear meshed with another single gear to increase or decrease the speed of rotation. 

There is another way which we can use to achieve larger ratios - compound gears.

Gear Trains

To create large gear ratios, 

A small gear and a larger gear are glued together, one on top of the other. Gear trains often consist of multiple gears in the train.

One full rotation of large gear on the left side results in 8 rotations of smaller gear on the right side. Other way, 8 rotations of small gear results in one rotation of gear on the left side. 

In the next video, we will discuss transfer of motion across planes, torque as well as other ways to create gears from everyday material.

Thank You.

मराठी महिने / अधिक महिना

 पहिल्या भागात सूर्य,पृथ्वी व चंद्रामुळे होणाऱ्या वेगवेगळ्या घटना मॉडेलच्या मदतीने समजावून घेतल्या.

 या भागात जाणून घेउया भारतीय पंचांगातील महिने व साधारणपणे दर पावणेतीन वर्षांनी येणारा अधिक महिना .

आपल्या परिचयाचे  इंग्रजी महिने हे पृथ्वीच्या सूर्याभोवती होणार्‍या प्रदक्षणेवर आधारलेले आहेत. 

पृथ्वीला सूर्याभोवती प्रदक्षिणा पूर्ण करण्यास ३६५ दिवस लागतात. 

या दिवसांना १२ भागांत विभाजन करून १२ महिने ठरविले गेले.  काही ३१ दिवसांचे तर काही ३० . फेब्रुवारीचा फक्त २८ किंवा २९ दिवसांचा.

पृथ्वीचे स्थानपण प्रत्येक महिन्यात त्याच ठिकाणी. जसे २1 मार्च, २२ जुन,  २२ सप्टेंबर आणि २२ डिसेंबर 

भारतीय पंचांगात महिने हे चंद्राच्या पृथ्वीभोवती होणार्‍या प्रदक्षणेवरून ठरतात.

अनेक धर्माचे सण आणि उत्सव चांद्र महिन्याप्रमाणे साजरे केले जातात. या सणांचे नाते विशिष्ट ऋतूंशीही कायम राहावे, यासाठी कालगणनेत ‘अधिक महिना’ आला. 

भारतीय कालगणनेतील महिने व अधिक महिना कसा येतो हे समजावून घेऊया कॅलेंडर च्या मदतीने 

साल आहे २०२१ आणि महिना आहे एप्रिल . 

१२ एप्रिल ला अमावस्या होती. चंद्राची जागा अमावसेच्या ठिकाणी .

अमावास्येपासून परत आमावास्येपर्यंत लागणारा वेळ , हाच आपला एक मराठी महिना , यालाच चांद्रमास असे पण म्हणतात, 

सुरवात करूया गुढीपाडव्यापासून.

मीन राशीत सूर्य असताना ज्या चंद्रमासाचा प्रारंभ होतो त्याला चैत्र म्हणतात. 

१३ एप्रिल पासून चैत्र महिना सुरु झाला.

पहिला दिवस  चैत्र शुक्ल प्रतिपदा 

२७ एप्रिल ला पौर्णिमा आणि ११ मे ला अमावास्या.

एका चांद्र महिन्यात ३० दिवस. एका दिवसाला तिथी असेही म्हणतात . 

पण तिथी कशी ठरवितात. ? 

 चंद्र हा सूर्यापेक्षा जलद गतीने जाणारा,  त्यामुळे या दोघांमघील अंतर एका अमावास्येपासून वाढत वाढत ते दुसऱ्या अमावास्येपर्यंत ३६०° म्हणजेच पुन्हा ०° होते. ३६०° चे ३० समान भाग पाडले म्हणजे प्रत्येक भाग १२° चा झाला.

प्रत्येक १२ अंशांचे अंतर पडण्यास जो कालावधी लागतो, त्याला तिथी म्हणतात. 

१२ अंश अंतर गेल्यावर प्रतिपदा ,  २४ अंश गेल्यावर द्वितीया ….

अंशात्मक अंतराच्या दृष्टीने पाहिल्यास तिथी सारख्याच म्हणजे बारा बारा अंशाच्या असल्या, तरी चंद्राच्या लंबवर्तुळाकार कक्षेमुळे व असमान गतीमुळे तिथींचा कालावधी असमान असतो , म्हणजे २० ते २७ तासांची तिथी असू शकते . या उलट इंग्रजी वर्षात 24 तासांचा दिवस असतो.

180 अंश झाल्यावर पौर्णिमा आणि ३६० अंश झाल्यावर परत अमावस्या . म्हणजेच पुढल्या महिन्याला सुरवात .

अमावास्येनंतर चंद्र पूर्वेच्या दिशेने पुढे सरकताना, आपल्याला चंद्राचा अधिकाधिक प्रकाशित भाग चंद्रकोरीच्या स्वरूपात दिसायला लागतो. याला आपण शुक्ल पक्षातील चंद्र असे संबोधतो.

या काळात येणाऱ्या तिथीच्या आधी शुद्ध हा शब्द लावतात 

या ठिकाणी चंद्र असेल तर शुद्ध प्रतिपदा

या ठिकाणी चंद्र असेल शुद्ध द्वितीया

या ठिकाणी चंद्र असेल शुद्ध अष्टमी 

पौर्णिमेनंतर चंद्र कक्षेत पुढे गेल्यावर त्यावर पडणारा सूर्यप्रकाश हळूहळू कमी होत गेलेला आपल्याला दिसतो. याला आपण कृष्ण पक्ष असे म्हणतो. या काळात येणाऱ्या तिथीच्या आधी वद्य हा शब्द लावतात 

वद्य प्रतिपदा

वद्य द्वितीया

वद्य  अष्टमी 

चला पुढे जाऊया 

१२ मे पासून वैशाख महिना सुरु होतो , या महिन्यात २६ मे ला पौर्णिमा 

१० जून ला अमावस्या - 

जेष्ठ महिना सुरु झाला 

२४ जून ला पौर्णिमा 

प्रत्येक चांद्रमासात सूर्याचे राशी संक्रमण होते. 

जसे चैत्र महिन्यात मीन राशीतून मेष राशीत , वैशाख महिन्यात वृषभ राशीत आणि जेष्ठ महिन्यात मिथुन राशीत , 

हे संक्रमण जर झाले नाही तर त्यावर्षी अधिक महिना येतो. 

चंद्राच्या १२ प्रदक्षिणा पूर्ण झाल्या कि एक चंद्र वर्ष पूर्ण होते व परत चैत्र महिना सुरु होतो 

२०२२ मधे ०२ एप्रिल ला चैत्र महिना सुरु होतो , गुढीपाडवा हा सण या वर्षी १० दिवस आधी आला. याचे कारण मराठी महिना हा २९. ५ दिवसांचाच असतो 

असेच महिने पुढे सरकत गेले तर २०२३ ला गुढीपाडवा म्हणजेच चैत्र महिना २२ मार्च ला येतो. या वर्षी गुढीपाडवा २०२१ च्या पेक्षा अंदाजे २२ दिवस आधी आला . 

असाच क्रम सुरु राहिला तर दरवर्षी गुढीपाडवा अलीकडे येत जाईल. आणि  होळीचा सण पावसाळ्यात साजरा करण्याची वेळ येईल. पण असे होत नाही कारण अधिक महिना …

चला पुढे जाऊया 

वैशाख 

जेष्ठ 

आषाढ 

१७ जुलै ला अमावस्या आणि सूर्य आहे कर्क राशीत  १७ ऑगस्ट २०२३ ला , चंद्राची एक प्रदक्षिणा झाली तरी सूर्य कर्क राशीतच आहे. म्हणून हा अधिक महिना. 

या नंतरचा महिना तोच धरतात . श्रावण - आता सूर्य पुढील राशीत म्हणजे सिंह राशीत आहे 

आणि पुढे बाकीचे महिने त्याच क्रमाने येतात. 

असेच जर आपण पुढे जात राहिलो तर २०२४ मध्ये ०९ एप्रिल ला गुढीपाडवा येईल 

साधारण पणे त्याच वेळेस - २०२१ ला होता तसा

अधिक महिन्यामुळे चांद्र कालगणनासुद्धा सौर कालगणनेशी स्वतःला जुळवून घेते. २००० सालापासून पुढील १० वर्षे जर चैत्र महिना कधी आला हे बघितले तर साधारण या टप्प्यात . म्हणजेच सूर्य कायम मिन राशीत होता . 

आपण सूर्याचे राशी संक्रमण बघितले तसे चंद्राचे नक्षत्र संक्रमण पण महत्वाचे आहे.. कोणत्या राशीमध्ये कोणती नक्षत्रे हे ठरलेले असते. पण यासंबंधी अधिक माहिती पुढल्या भागात ... 

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