Shani Trayodashe (as Somvatee Amaavasyaa) is not a festival as such but many people observe it to protect themseles from Shani's rage. Shani Trayodasee falls on any Trayodashee when it falls on Saturday. In 2009 it fell on January 24th. It is even more powerful when it falls  in Krishn Paksh - "Krishna Shani Trayodashee". This is the first Shani Trayodashee after Saturn's entry into Cancer. Normally Shani Trayodashee comes twice a year.

"Om Preeng Preeng Prong Sah Shange Namah" recite this Mantra 21 times on this day.

Bhagavaan Shani, also known as Shanaishchar, Shaneeshwar, Saneeswar, Shaneeshwaran or Shani Dev, is one of the Nava Graha. Navagraha are the nine primary celestial beings according to Sanaatan Dharm. According to Sanaatan Astrology, Shani (Saturn) represents the planet Saturn. Since Bhagavaan Shani is a god and son of Sun and Chhaayaa, he is also known as Chhaayaa-Putra (Son of Shadow).

Offer Tail Abhishekam, a bath with Til oil while chanting the Shani Gaaytree or Shani Stotra. Offer Shani Dev black cloth and perform Abhishek with black Til, Kumkum and turmeric powder. Depending on time one can recite
1- Shani's Ashtottar Shat Naamaavalee (108 names),
2- Recite Shani Gaayatri 108 time,
3- Shani Chaaleesaa, Shani Kavach, Shani Mantra (Ushnik) and
4- Shani Stotram recited by Dasharath in Vaalmeeki Raamaayan (11 times).

Coconut and other fruits such as banana and mangoes are offered as Naivedya. Some offer Rice with Sesame seeds, Jaggery and sesame seed oil. You can also perform Navagraha Havan. Finish your Poojaa with Shani Aaratee.

Pauranik Mantra:
Neelaanjan Samaabhaasham Raviputram Yamaagrajam
Chhaayaa Maartand Sambhootam Tam Namaami Shanaishcharam

Vaidik Mantra:
Om Shanno Devee Rabhishtraye, Aapo Bhavantu Peetaye, Shanyorabhi Sravantu Nah

Shani Gaayatree Mantra
Shanaishcharaaya vidhmahe, Chhaayaa Putraaya Dheemahi, Tanno Mandah Prachodayaat

Shani Gaayatree (recite 8 times in the morning)
Kaak Dhwajaaya Vidhmahe, Khadg Hastaaya Dheemahi, Tanno Mandah Prachodayaat

You can also worship Lord Hanumaan since Hanumaan Jee freed Shani Dev from Raavan. So any one who worships Hanumaan will not have ill effects of Shani. I come across people who do not wish to pray Hanumaan because he is Brahmachaaree (celibate) and if they worship him they will be celibate too. People say they do not want to worship Raam because then he will suffer like Shree Raam. Similarly is the fate for Bhagavaan Shree Krishn. Shambhoo Sadaa Shiv is Aghoree so one should not touch Shiv Ling or keep it in the house. But everyone prays Maa Lakshmee, the reality is that you must pray to all her three Swaroop - Kriyaa (Durgaa), Ichchhaa (Lakshmee) and Gyaan (Saraswatee).

Vaalmeeki Raamaayan explains through Dasharath and Vishwaamitra Samvaad (discussion) why Bhagavaan Shree Raam sleeps (retires) at sunset. He tells that there is a connection between planets and body especially around Shani Trayodashee. Vishwaamitra Jee says that we should not be afraid of Shani Dev. Shani is a Yog Purush. Shani gives energy to Indriyaan. One gets different vibrations by reciting Shani Stotra and Mantra.

Shani's 12 Names
Konah Shaniascharah Mandah Chaayaa hridaya nandanah
Maartandajo Yam bhraataa Matangah Graha naayaakaah
Brahmanyah Kroor Karm cha Neelavastronjan Dyutihi

(1) Konah, (2) Shanishcharah (3) Mandah (4) Chhaayaa Hridaya Nandanah (5) Maartandajah (6) Yam Bhraataa (7) Matangah (8) Graha Naayakaah (9) Brahmanyah (10) Kroor Karm (11) Neel Vastram (12) Anjan Dyutih.

These are the twelve famous names of Lord Shanischar. These names are capable to eliminate the bad effects caused by Lord Shanaishchar specially in three parts such as Dwaadash Sthaan (12th House),
Ashtam Sthaan (8th House) and Janma Sthaan (1st House, or Lagna) of the Jaatak. Hence daily rendering of above names shall be very helpful for the persons who are suffering from Shani Peedaa.
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Navagraha Gaayatree
Soorya Gaayatree
Om ashwa dhwajaaya vidmahae,  paash hastaaya dheemahi,  tanno soorya: prachodayaat

Chandra Gaayatree
Om padma dhwajaaya vidmahe,  hem roopaaya dheemahi,  tanno soma: prachodayaat

Angaarak Gaayatree (chevvaai)
Om veeradhwajaaya vidmahe,  vighna hastaaya dheemahi,  tanno bhouma: prachodayaat

Budh Gaayatree
Om gaja dhwajaaya vidmahe,  sukha hastaaya dheemahi,  tanno budha: prachodayaat

Guru Gaayatree
Om vrishabh dhwajaaya vidmahe,  kruni hastaaya dheemahi,  tanno guru: prachodayaat

Shukra Gaayatree
Om ashwa dhwajaaya vidmahe,  dhanur hastaaya dheemahi,  tanno shukra: prachodayaat

Shaneeshwar Gaayatree
Om kaakadhwajaaya vidmahe,  khadg hastaaya dheemahi, tanno mandah: prachodayaat

Raahu Gaayatree
Om naak dhwajaaya vidmahe,  padma hastaaya dheemahi,  tanno raahu: prachodayaat

Ketu Gaayatree
Om ashwa dhwajaaya vidmahe,  shool hastaaya dheemahi,  tanno ketu: prachodayaat