Worship Sri Sri Radha-Damodara
Radharani is especially keen to hear Krishna's pastimes, but She is particularly attracted to the Damodara pastime. Charmed by Damodara's mood of surrender in agreeing to be bound by Mother Yasoda's love, Sri Radha longs to have that same exchange with Krishna. She desires to express such intense love for Krishna that He will also agree to be bound by Her love.
Appreciating this mood of Mother Yasoda to enhance Her own feelings for Krishna, She resolves to experience this same reciprocation of love." (Srimad Bhagavatam 10.9.20 Purport) Radha-Damodara thus refers to Radharani's mood of intense attraction for this pastime between Damodara and Mother Yasoda.
In the Sixteenth Vilasa, Volume One of Hari-bhakti-vilasa by Srila Gopal Bhatta Goswami, we find this description of "The Way to Worship Sri Sri Radha-Damodara":
tatah priyatama vishno
radhika gopikasu ca
karttike pujaniya ca
In the Padma Purana it is said: "Because She is the gopi most dear to Lord Vishnu, Sri Radha' should be worshiped along with Lord Damodara during the month of Karttika.
dvijam damodaram kritva
tat-patnim radhikam tatha
karttike pujaniyau tau
"Dressing Lord Damodara as a brahmana and Sri Radha' as His wife, one should worship them with nice garments, ornaments, and foods during the month of Karttika.
pujayet karttike tu yah
tasya tushyati tat-prityai
sriman damodaro harih. iti.
"O brahmanas, during the month of Karttika one should worship the Deity of Sri Radha. To please Sri Radha, Lord Damodara, the Supreme Personality of Godhead, will be pleased with that worshiper."
One should regularly recite the prayer called Damodarashtaka, which was spoken by Satyavrata, which attracts Lord Damodara, and which describes the worship of Lord Damodara.
Sri Sri Radha Damodar, Vrindaban
Relationship between Sri Krishna and Srimati Radharani
The relationship between Sri Krishna and Srimati Radharani (maya-mrgam) indicates yogamaya in this context since Radharani is Krishna's hladini-sakti, His original internal pleasure potency. Because Krishna is Madana-mohana and Radharani is Madana-mohana-mohini, therefore mrgam means Krishna is like a deer that is controlled by the beautiful Radharani. Sri Radha always performs puja to bind Krishna because She cannot live without Him. Due to Radharani's aradhana, or worship, Krishna never leaves Vrndavana. He runs through the forests of Vrndavana (anvadhavat), playing with His friends and cows and engaging in amorous pastimes with His most desired object (ipsitam), Srimati Radharani.
All the gopis love to hear Mother Yasoda sing about the glories of Krishna. Radharani is especially keen to hear Krishna's pastimes, but She is particularly attracted to the Damodara pastime. Charmed by Damodara's mood of surrender in agreeing to be bound by Mother Yasoda's love, Sri Radha longs to have that same exchange with Krishna. She desires to express such intense love for Krishna that He will also agree to be bound by Her love. Appreciating this mood of Mother Yasoda to enhance Her own feelings for Krishna, She resolves to experience this same reciprocation of love. "(Srimad-Bhagavatam 10.9.20, purport.)
Radha-Damodara thus refers to Radharani's mood of intense attraction for this pastime between Damodara and Mother Yasoda. In celebration of this mood of love, She performs Katyayani vrata in the month of Kartik to receive the benediction to enter into this intimate relationship of loving exchange. By performing this vrata, Sri Radha is willing to undergo any austerities so that Krishna will agree to be bound by Her love.
According to Vedic civilization, during the month of Kartik unmarried girls are required to worship goddess Durga and perform austerities in order to get a good husband. In KRSNA book, the unmarried gopis perform Katyayani vrata to get Krishna as their husband. They eat only havisyanna—a bland kichari prepared by boiling mung dahl and rice together without any spices—to purify the body before enacting a ritualistic ceremony. After taking bath in the Yamuna River, they worship a deity of goddess Durga with sandalwood pulp, garlands, incense, lamps, fruits, grains, and twigs of plants. After worship, they pray for the benediction to become the wives of Krishna. (KRSNA, the Supreme Personality of Godhead, chapter 22)
Jiva Goswami has written that Srimati Radharani always performs austerities simply to bind Krishna more and more with Her love. Because without Krishna She cannot even bear to live. It is due to Sri Radha's aradhana, or worship, that Krishna never leaves Vrndavana. Gaudiya Vaisnavas consider Radharani to be the presiding Deity for the month of Kartik, which, significantly, is also called Damodara. Srila Rupa Goswami, in his Sri Utkalika-vallari, proclaims Radharani as Kartik-devi, the goddess of Kartik.
The Hari-bhakti-vilasa proclaims, "O learned brahmanas! Lord Damodara becomes very pleased if during the month of Kartik one worships a Deity of Radhika solely for Her pleasure." (Hari-bhakti-vilasa 16.95) For this reason, Vaisnavas perform austerities in the month of Kartik to please Sri Radha. They consider Kartik as the month of Radha-Damodara because of the following pastime in the Uttara-khanda of the Bhavisya Purana.
"Once in the auspicious month of Kartik, Krishna came late for a rendezvous with Radharani in Her kunja. In loving anger, Sri Radha looked at Krishna with frowning eyebrows. Using some golden vines, Radha then tied a rope around Sri Krishna's belly to punish Him for not showing up as promised. Krishna said He was late because Mother Yasoda kept Him home for a festival. Seeing Her mistake, Radha quickly untied Her beloved Damodara." (Radha Kunda Mahima Madhuri, by Mahanidhi Swami, page 50)
Radharani's desire to bind Krishna with Her love is fulfilled in this pastime. Therefore, Vraja Vaisnavas worship this Damodara who is bound by Radharani's love. Of course, Krishna is already famous as Damodara from His childhood. In fact, just as Krishna is eternal, so is His Holy Name. He is always known as Damodara, although it appears that His name comes into being as a result of the pastime with Mother Yasoda. Damodar also means one who is bound with ropes of love by his mother. (Isvara.org, Manonatha dasa)