The celebrated sage Agastya comes and gives Aditya Hridayam to Sri Rama for his victory.
Several ill-portents indicate to Ravana his imminent defeat.
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Given the sanctity of Aditya Hridayam, I have decided to share the entire stotram here as an embedded PDF. I have taken the text and translation from Indiadivine.org
The key words of benediction from the sage Agastya are:
राम राम महाबाहो शृणु गुह्यं सनातनम् ।
येन सर्वानरीन् वत्स समरे विजयिष्यसे ॥
आदित्यहृदयं पुण्यं.......
सर्वमङ्गलमान्गल्यम् ।
पूजयस्व विवस्वन्तं भास्करं भुवनेश्वरम् ॥
"Oh dear Sri Rama! The mighty warrior with broad shoulders! Listen to this instruction from me of the sacred, esoteric, ancient, Aditya Hridayam. With this, you shall conquer all enemies. It is auspicious and brings welfare to all. Worship the glorious lord Sun! He is the primordial source of all life on earth, he is the nourisher, protector, and illuminator of body, mind, and soul."
Remember that Sri Rama belongs to the Solar Dynasty, descended through the Sun from Brahma himself. Even Hanuman is the blessed disciple of the Sun-god. At every step, the Sun-god has guided Sri Rama's steps.
Praying to the most obvious, all-time, manifestation of Godhood in the form of the Sun-god is the most direct, intuitive, empowering worship one can undertake before any great task. Surya is the manifestation of Vishnu, Brahma, and Shiva, all in one.
It is a great poetic moment in the Ramayana that the glorious sage Agastya, revered as one of the most benevolent divine masters to have blessed India (especially south India), who had long ago blessed Sri Rama in the Dandaka forest and given him divine weapons, should come in person into the battlefield, witnessed by all the gods and rishis and celestials showering their blessings on Sri Rama.
Sage Agastya does not give Sri Rama any new weapons. He simply teaches him to pray to Aditya or Surya or Bhaskara. This is one of the best examples of how a guru helps his disciple. Not by giving any magical bullets but by giving spiritual instruction.
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The concluding verse of Aditya Hridayam is
अथ रविरवदन्निरीक्ष्य रामं मुदितमनाः परमं प्रहृष्यमाणः ।
निशिचरपतिसंक्षयं विदित्वा सुरागाणामाध्यागातो वचस्त्वरेति ॥
"Then, the Sun-god, surrounded by all the gods and celestials and sages, beamed on Sri Rama, full of delight at the way Sri Rama had been instructed by the sage and accordingly propitiated him. He foresaw clearly that Sri Rama was going to end the menace called Ravana, the lord of rakshasas. Smilingly he spoke, giving only one pointed advice to Sri Rama, "Oh, dear Sri Rama! Make haste!""
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Ravana's able charioteer now brought him into the battle in a grand way. The chariot was weaving a mesmerizing web in its movement, speed, and splendour. It gave much confidence to the rakshasas and pretty much shook up all the directions. Its rumble was loud enough to shatter mountains. Ravana's bow was radiant like a divine rainbow, showering a great deluge of arrows.
Sri Rama gave a terrific twang to his bow. He addressed Matali, his divine charioteer:
"Oh, Matali! Witness how rapidly Ravana is advancing on the left flank. He seems to be in a hurry to die. Therefore you should advance in a counter direction. You shall see me destroy the enemy like a whirlwind dispels clouds.
अविक्लवमसंभ्रान्तमव्यग्रहृदयेक्षणम् ।
रश्मिसञ्चारनियतं प्रचोदय रथं द्रुतम् ॥
युयुत्सुरहमेकाग्रः स्मारये त्वां न शिक्षये ॥
"Oh Matali! You are a most capable charioteer, having served Indra himself in great battles. I do not have to tell you anything. I am simply reminding you that you may steer the chariot holding the reins tightly, without any fear, confusion, or indecisiveness. Move at the speed of light, and carry me strategically. I am going to concentrate all my attention on the fighting, and I shall not give you any more instructions."
Matali was most delighted at Sri Rama's confidence in him and his motivating words. He now spun the chariot in counter moves circling Ravana's chariot in such a way that he raised a dust storm that completely clouded Ravana's vision and bearings.
Ravana was enraged and attacked Sri Rama. Sri Rama picked up the special bow from Indra in Matali's chariot and, using powerful arrows, struck Ravana fiercely. The sight of the two great warriors engaged thus was most gripping.
Many gods, celestials, ascetics, other divine beings, had all assembled to witness the destruction of their inglorious tormentor Ravana. They were all praying for his defeat.
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Valmiki describes how several terrifying portents of Ravana's destruction and Lanka's fall manifested now. The sky darkened into a red colour, many scarifying showers from the sky bathed Ravana's chariot, scavenger eagles circled menacingly in the sky, and many fiery objects plunged to earth from above.
एवं प्रकारा बहवः समुत्पाता भयावहाः ।
रावणस्य विनाशाय दारुणा संप्रजज्ञिरे ॥
रामस्यापि निमित्तानि सौम्यानि च शिवानि च ।
बभूवुर्जयशंसीनि प्रादुर्भूतानि सर्वशः ॥
"Thus did several obvious omens of ill-boding manifest frighteningly for Ravana, signifying his death in a terrible way.
At the same time, all around Sri Rama were omens auguring success and prosperity and good. They all signified his impending victory."
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॥ श्रीरामजयम् ॥