27-28 Sri Saunaka said: Please describe to us, who have great faith
in your words, the different sets of seven personal features and
associates the sun-god exhibits during each month, along with their
names and activities. The associates of the sun-god, who serve their
lord, are personal expansions of the Supreme Personality of Godhead
Hari in His feature as the presiding deity of the sun.
29 Suta Gosvami said: The sun travels among all the planets and thus regulates their movements. It has been created by Lord Visnu, the
Supreme Soul of all embodied beings, through His beginningless
30 The sun-god, being nondifferent from Lord Hari, is the one soul of all the worlds and their original creator. He is the source of all the
ritualistic activities prescribed in the Vedas and has been given many
names by the Vedic sages.
31 Being the source of the material energy, the Personality of Godhead Lord Hari in His expansion as the sun-god is described in nine
aspects, O Saunaka: the time, the place, the endeavor, the performer,
the instrument, the specific ritual, the scripture, the paraphernalia
of worship and the result to be achieved.
32 The Supreme Personality of Godhead, manifesting His potency of time as the sun-god, travels about in each of the twelve months,
beginning with Madhu, to regulate planetary motion within the
universe. Traveling with the sun-god in each of the twelve months is a
different set of six associates.
33 My dear sage, Dhata as the sun-god, Krtasthali as the Apsara, Heti as the Raksasa, Vasuki as the Naga, Rathakrt as the Yaksa, Pulastya as
the sage and Tumburu as the Gandharva rule the month of Madhu.
34 Aryama as the sun-god, Pulaha as the sage, Athauja as the Yaksa, Praheti as the Raksasa, Punjikasthali as the Apsara, Narada as the
Gandharva and Kacchanira as the Naga rule the month of Madhava.
35 Mitra as the sun-god, Atri as the sage, Pauruseya as the Raksasa, Taksaka as the Naga, Menaka as the Apsara, Haha as the Gandharva and
Rathasvana as the Yaksa rule the month of Sukra.
36 Vasistha as the sage, Varuna as the sun-god, Rambha as the Apsara, Sahajanya as the Raksasa, Huhu as the Gandharva, Sukra as the Naga and
Citrasvana as the Yaksa rule the month of Suci.
37 Indra as the sun-god, Visvavasu as the Gandharva, Srota as the Yaksa, Elapatra as the Naga, Angira as the sage, Pramloca as the
Apsara and Varya as the Raksasa rule the month of Nabhas.
38 Vivasvan as the sun-god, Ugrasena as the Gandharva, Vyaghra as the Raksasa, Asarana as the Yaksa, Bhrgu as the sage, Anumloca as the
Apsara and Sankhapala as the Naga rule the month of Nabhasya.
39 Pusha as the sun-god, Dhananjaya as the Naga, Vata as the Raksasa, Susena as the Gandharva, Suruci as the Yaksa, Ghrtaci as the Apsara
and Gautama as the sage rule the month of Tapas.
40 Ritu as the Yaksa, Varca as the Raksasa, Bharadvaja as the sage, Parjanya as the sun-god, Senajit as the Apsara, Visva as the Gandharva
and Airavata as the Naga rule the month known as Tapasya.
41 Amshu as the sun-god, Kasyapa as the sage, Tarksya as the Yaksa, Rtasena as the Gandharva, Urvasi as the Apsara, Vidyucchatru as the
Raksasa and Mahasa“kha as the Naga rule the month of Sahas.
42 Bhaga as the sun-god, Sphurja as the Raksasa, Aristanemi as the Gandharva, Uma as the Yaksa, Ayur as the sage, Karkotaka as the Naga
and Purvacitti as the Apsara rule the month of Pusya.
43 Tvashtha as the sun-god; Jamadagni, the son of Rcika, as the sage; Kambalasva as the Naga; Tilottama as the Apsara; Brahmapeta as the
Raksasa; Satajit as the Yaksa; and Dhrtarastra as the Gandharva
maintain the month of Isa.
44 Vishnu as the sun-god, Asvatara as the Naga, Rambha as the Apsara, Suryavarca as the Gandharva, Satyajit as the Yaksa, Visvamitra as the
sage and Makhapeta as the Raksasa rule the month of Urja.
45 All these personalities are the opulent expansions of the Supreme Personality of Godhead, Visnu, in the form of the sun-god. These
deities take away all the sinful reactions of those who remember them
each day at dawn and sunset.
46 Thus, throughout the twelve months, the lord of the sun travels in all directions with his six types of associates, disseminating among
the inhabitants of this universe purity of consciousness for both this
life and the next.
In the physical realm, the sun sphere is one. Which is called Sol in modern language. But the deities presiding over the sun are 12, corresponding to the months. 12 individual conscious energies all non-different from each other. They basically have the same duties both general, as well as astrological.
The physical planet is not called graha. Graha is termed with respect to astrology. Graha refers to an entity that has the power to "seize, lay hold of, or grasp". The Navagrahas are 9 deities which have a hold on people's destinies, those who are born in Bhuloka. They are just a class of deities, nothing special other than that.
As far as I know Aditya Hridayam Stotra is applicable for any deity that controls the sun. It won't be applicable for the moon god.