Where does this soul go after death? Its description is found in detail in the Chandogya Upanishad of the Tandya Mahabrahman of Samaveda. There are three movements of the Jeeva described there, out of which we will talk about the movement towards the chandraloka (चंद्रलोक) in which the Shraddh (श्राद्ध) of the ancestors is done. All our ancestors are called pitaras (पितर). It is self-understood that the corporeal body of the deceased does not come or go anywhere, there is no movement in the soulless unconscious dead body, but the soul is omnipresent, and there is no movement even in the omnipresent. Therefore, only the subtle body composed of the five karma senses (कर्मेन्द्रिय), the five gyana senses (ज्ञानेन्द्रिय), the five pranas (प्राण), the mana/mind (मन), and the buddhi/intellect (बुद्धि), leave the body and go to other worlds and births.
Among these 17 elements, the mind is the dominant one and it is the reason for the attraction of the angelic body towards the moon. But why? It is a law of science that homogeneous substances have attraction. Each object gets attracted towards its alike object. The lump of soil comes to the earth because of attraction. In physics, the law of gravitation is taught, which is nothing but the attraction between masses, G.m1.m2/r.r. In the same way, the mind is a form of the moon(chandrama), “Chandrama manaso jatah” (The moon (chandrama) manifested from the mind of Virat Purusha, –Purusha Sukta, Rigveda), the mind dominant subtle body has an attraction towards its alike, the Moon.
How do these parts come into our subtle body? So the answer is that, as when air flows through the flower, it takes some fragrant fraction of flower with it and becomes fragrant; like even after removing water from a bowl, some part of the water still remains in the bowl i.e. the substances which are together, even if they are separated, some fraction of each other remains on them, in the same way, the subtle body which has lived for a long time in the corporeal body, when comes out of it, some part of that remains attached on it.
This article can be read in Hindi here,
आधुनिक विज्ञान और पितर श्राद्ध
The main relation of Shraddh is with the movement of the subtle body towards Chandraloka (moon) because the consumers of Shraddha are the ancestors who live in Chandralok. It is the law of nature that in the process of movement from one point to another, every substance of the world becomes weak. You ate food, then lost the energy gained, you started getting hungry again at night. Plants were watered today and due to attenuation, they had to be re-watered tomorrow. And to understand more deeply, Rutherford gave a model of an atom in which the electron revolves around the nucleus at a very high speed, but there was a flaw in the theory that according to Planck Maxwell’s theory the electrons necessarily have acceleration (Factor of movement) that causes the emission of continuous electromagnetic radiation (this emission is attenuation) due to which it will ultimately fall into the nucleus causing an explosion, which is impossible for stability.
We are able to fulfill our attenuation, but the souls who are going to different lokas (worlds), do not have the power to compensate for the attenuation that comes in their subtle body. We fulfill that through Shraddh. What will happen if we do not perform Shraddh? According to the Vedas, the mind is part of the Moon and intellect is part of the Sun. Therefore, the moon and the sun may have an attraction on the mind and the intellect part of the subtle body respectively, but they cannot have any attraction on the air. If the movement of those sun-oriented and moon oriented souls gets stopped, they would not be able to move towards respective worlds and would continue to wander in the air. The ghosts, sprites, phantom’s body is made up of air, so the wandering souls will also be considered as phantoms. That is why it is famous among the followers of Sanatana Dharma that – “The shraddh of that man has not been done, so he flies in the air.”
That’s why Vedas command sons to save the subtle bodies of father and mother. – “When you were body-less, at that time the parents had made your body with their parts. Today they(parents) are becoming bodiless, so it is your karma to make their bodies now.” So according to the Vedas, the object of the shraddha is to confirm the subtle body by the Soma part (Soma is chandrama) of the pindas of rice (rice balls), etc. Even by modern science, Shraddh proves to be completely scientific. The only difference remains that modern science does not believe in spirituality whereas Shraddha is spiritual along with scientific.
The ascetics, sages, etc. go through the path of devayana, they do not need the confirmation of this body by Soma, they themselves are fiery, no one can stop the attraction of the sun on them, hence the shraddh of the ascetics is not necessary.
Those whose forefathers get Arghya-Kavya from them, their ancestors gets satisfied and they bless them. Their blessings are beneficial. The ancestors of those who do not perform Shraddh, leave their breaths filled with damnation. In this way, we have tried to throw light on Shraddh in a nutshell, there is a lot of detail about it in the Shastras.
Shraddh: Pitru Sooktam from Rigveda
Pitru Sukta is in Sanskrit. 14 Richas or Mantras of 15th Sukta from Tenth Mandal of the Rigveda are called as Pitru Sukta. In the first 8, Richas Pitras from different places are called for accepting Havi (in short it is the food offered to Pitras (ancestors) as Naivedayam). Remaining 6 Richas are the prayer made to Agni to bring all the Pitrus for accepting Havi. Shankha Yamayan is the Rishi of the Pitru Sukta and Pitras are devata, Chhanda is Tristup (1-10, 12-14) and Jagati (13).
May they ascend, the lowest, highest, midmost, the Fathers who deserve a share of Soma,
May they who have attained the life of spirits, gentle and righteous, aid us when we call them. 
Now let us pay this homage to the Fathers, to those who passed of old and those who followed,
Those who have rested in the earthly region, and those who dwell among the Mighty Races. 
I have attained the gracious-minded Fathers, I have gained son and progeny from Viṣṇu.
They who enjoy pressed juices with oblation seated on sacred grass, come oftenest hither. 
Fathers who sit on sacred grass, come, help us: these offerings have we made for you; accept them.
So come to us with most auspicious favor, and give us health and strength without trouble. 
May they, the Fathers, worthy of the Soma, invited to their favorite oblations.
Laid on the sacred grass, come nigh and listen: may they be gracious unto us and bless us. 
Bowing your bended knees and seated southward, accept this sacrifice of ours with favor.
Punish us not for any sin, O Fathers, which we through human frailty have committed. 
Lapped in the bosom of the purple Mornings, give riches to the man who brings oblations.
Grant to your sons a portion of that treasure, and, present, give them energy, ye Fathers. 
Our ancient Fathers who deserve the Soma, who came, most noble, to our Soma banquet,—
With these let Yama, yearning with the yearning, rejoicing eat our offerings at his pleasure. 
Come to us, Agni, with the gracious Fathers who dwell in glowing light, the very Kavyas,
Who thirsted mid the Gods, who hasten hither, oblation winners, the theme of singers’ praises. 
Come, Agni, come with countless ancient Fathers, dwellers in light, primeval, God-adorers,
Eaters and drinkers of oblations, truthful, who travel with the Deities and Indra. 
Fathers whom Agni’s flames have tasted, come ye nigh: ye kindly leaders, take ye each your proper place.
Eat sacrificial food presented on the grass: grant riches with a multitude of hero sons. 
Thou, Agni Jātavedas, when entreated, didst bear the offerings which thou madest fragrant,
And give them to the Fathers who did cat them with Svadha. Eat, thou God, the gifts we bring thee. 
Thou, Jātavedas, knowest well the number of Fathers who are here and who are absent,
Of Fathers whom we know and whom we know not: accept the sacrifice well-prepared with portions. 
They who, consumed by fire or not cremated, joy in their offering in the midst of heaven,—
Grant them, O Sovran Lord, the world of spirits and their own body, as thy pleasure wills it.