நிஷ்க்ரமணா

“निष्क्रमणम् niShkramaNam” means “taking the child outside the house for the first time,  especially to see the sun and the moon. 

Manusmriti 2.34 says:

चतुर्थे मासि कर्तव्यम् शिशॊर्निष्क्रमणं गृह्यात् ।

The “niShkramaNa” samskAra should be performed for the child in the fourth month.

Yama smriti says:

The samskAra for the third month is soorya darshaNam and the samskAra for the fourth month is chandra darshaNam for the new born child.

pAraskara gRuhya sootram of shukla yajur vedA, kaNDa 1, kaNDikA 17 says:

सू.५. चतुर्थे मासि निष्क्रमणिका
सू.६. सूर्यमुदीक्षयति तच्चक्षुरिति

“niShkramaNa” is performed in the 4th month after birth of the child. The father or the uncle takes the child to the courtyard or a clean place and shows the sun for the first time while uttering the following mantra. (vAjasanEyi samhita 36.24)

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Meaning: Oh,  supreme Lord dear to all like the eyes, the benefactor of the dEvas!  Looking at the sun may we pay obeisance for hundred (autumns) long years, May we live for hundred years, May we live with kith and kin for hundred long years, May we live in happiness for hundred years, May we live with name and fame for hundred years, Let us hear only good things for hundred years, Let us talk good things for hundred years, May we live unconquered for hundred years.- likewise looking at the sun let us live a life like this” (Yajur vEdA samhita 36.24)

The VishNu DharmOttara enjoins a shloka for the same:

apramattaM pramattaM vA divA rAtrAchathApi vA |

rakshantu satataM sarvE dEvA: shakrapurOgamA: ||

Whether the child is conscious or unconscious, whether it is day or night, let all the Gods led by Indra protect the child.

Chandra darshanam चन्द्र दर्शणम्

It has been a practice of the “sutra” period to also show the moon to the child in the third month.
drAhyAyana gRuhya sootra, paTala 2, khaNDa 3, says:

सू.१. जननाज्जयौत्स्ने तृतीयॆ तृतीयानाम् प्रात: स्नाप्य कुमारमस्तमितॆ शान्तासु दिक्षु पिता चन्द्रमसमुपतिष्ठॆत् प्राञ्जलि: ।

On the 3rd day of the third bright fortnight (shukla paksha), after the son’s birth, the child should be given a bath in the morning and after sunset in the evening the father should join his hollowed hands up in prayer to the moon.

सू.२. शुचिनाऽऽच्छाद्य माता प्रच्छेदुदक्छिरसम् ।

The mother should dress the son in clean garments and hand him with his face turned to the north to his father.

सू.३. अनुपृष्ठम् गत्वॊत्तरतस्तिष्ठेत् ।

She should then pass behind the husband’s back and face towards north.

सू.४. यत्ते सुसीम इति तिसृभिरुपस्थायॊदंञ्च मात्रे प्रदाय यदद इत्यपामञ्जलिमवसिञ्चेत् ।

1. The husband chants the following mantra from “mantra brAhmaNa, 1.5.10”

यत्तॆ सुसीमी हृदयं हितमन्त: प्रजापतौ वॆदाहं मन्ये तद्ब्रह्म माहं पौत्र मघं निगाम् |

Oh, beautifully-parted-haired one!  The heart that you have rests in Prajapati, I know that, it is brahmaN,  May I not have misfortune with children.

2. He then hands over the son to his mother again with the head facing north. The father then gives prAnjali ( libations of water ) with the following mantra from ” mantra brAhmaNa, 1.5.13.

स्यददश्चन्द्रमसि कृष्णं पृथिव्या हृदयँ श्रितम् ।

तदहँ विद्वाँस्तत्पश्यन् माहँ पौत्र मघं रुदम् ||

3. He does this twice silently. सू. ५. द्विस्तूष्णीम् ।