The body consists of five elements - Prithvi(earth), Jala(water),Agni(fire),vayu(air) and Aakasha(ether). At the time of death the praana attains a new body called aathivaahika which consists of only three elements - fire,air and ether. This new body emerges out leaving behind the 'dead body' which is subjected to funeral rituals. This new body, at the end of the pindapradana rituals during the ten days after death ,converts into what is called a bhogadeha. The bhogadeha travels for 12 months following the movements of moon and attains the chandramandala where pitruloka exists. All throughout these 12 months, its existence is in prethavastha or as a pretha.As a result of the sapindeekarana ritual performed at the end of 12 months (which at present is performed on the 12th day, however, it is like issuing a post dated cheque, its result reaches the atma only at the end of 12 months) the prethavastha is lost and the atma attains pitruloka.
The pitruloka exists on the invisible side of the moon. On amavasya or new moon day, the moon comes exactly between the earth and sun.The sunrays fall directly on this invisible half of moon called pitruloka. It is noon time there, time for lunch. One day of pitrus consists of 30 human days. By offering food to pitrus in the form of amavasya tarpana which repeats every 30 days is like feeding them every day.
In fact, the amavasya is also supposed to be obseved like the yearly sraadham in the annam - homam format. However, it has been simplified to suit the modern day situation. The rishis must have thought, if we insist on the elaborate version, people will altogether stop doing it.
One becomes eligible to perform Amavasya tarpanam only after the demise of one's father. Even if mother is alive, he can perform.
Every form of life, moving and nonmoving desires jala(water) from the hands of brahmin. The tarpana is also performed every day with just water as part of daily bath and brahmayajna. However, amavasya tarpana is performed using water mixed with til.
The three important requirements for tarpana are darbha,water and til. Darbha is considered as equal in purity to Agni and water. Devas reside on the tip of Darbha, middle portion is of manushyas and the base of pitrus. A pavitram worn during amavasya tarpanam should be made of 3 darbhas. Water is considered as praana, energy, essence of all plants, medicine, annam, amruta and somarasa. The oil or tailam in til(gingelly seeds) can satisfy hunger and remove heat.
If tarpanam is performed at home on sapthami/trayodash tithis or Sunday/Tuesday/Friday or Janmanakshatra, til should be mixed with akshata(rice). A silver or copper vessel should be used for tarpanam