Gayatri

 I may never cause harm to the ultimate truth. May mother's blessings always be with me and the whole world feel the grace of divine mother.

I bow before Mother Vindhyabasini, Guru Gorakhnath and all Godheads. May Sandhya bandana and Sandhya Diyo always shine like ages before. May Pasupatinath always bless us.

It will be more than amazing to explain any mantra with the help of Jyotish. Jyotish explains how the shining stars, their deities and Graha who owns Griha guides the life of a child, help to grow and finally the lights set in the west. 

Gayatri mantra with its Vyāhṛtis and Shanti Mantra provided by sage Yagyavalkya is like this

ॐ भूः ।  ॐ भुवः ।  ॐ स्वः ।  ॐ महः ।  ॐ जनः ।  ॐ तपः ।  ॐ सत्यं ।  

ॐ तत्सवितुर्वरेण्यं  

भर्गो देवस्य धीमहि  

धियो यो नः प्रचोदयात् ॥

ॐ आपो ज्योती रसोऽमृतं  

ब्रह्म भूर्भुवः स्वरोम् ॥

ॐ भूः ।  ॐ भुवः ।  ॐ स्वः ।  ॐ महः ।  ॐ जनः ।  ॐ तपः ।  ॐ सत्यं । 

The Vyahartis can be explained by help of Jyotish. Satyam is the world of the Ultimate truth, Tapa is the world of Sun, Jana is the world of Moon, Maha is the world of Budha (Mercury) [Bipin Behari- Myths and Symbols of Vedic Astrology p. 66 only about Mercury] , Swa is the swarga lok of Guru Brihaspati and Shukracharya, Vubha is the world of Mars or the earth in its fullest sense above the surface and Bhu is the base of the earth or inner earth, we may say the world of Shani. 

I may be totally wrong but the book above mentioned systematically explained how the life evolved with the help of planets in sequence of planets. In case of Mercury the writer was explicit. And to see the Gayatri to give its full meaning, the Vyahartis is perfect to remember how many worlds we have and how many worlds we must cross to know the Ultimate world of Satyam. 

Now let us turn towards the main mantra in Rig Veda, which is explained by Sage Yagayavalkaya in Gayatri Hridayam (being illiterate in Sanskrit I can't fully comprehend it so far). 

It is neither intuitive nor can be known from text by word to word translation of Mantra. Whatever little understanding I can have with the help of useless translation of Google Translate and other site, tried to gather meaning as much as can be for my own satisfaction.

ॐ तत्सवितुर्वरेण्यं  

Taat is param padam (also tanmaheshwor is recalled which I couldn't make any sense of), which refers to Vishnu's 3 famous steps (explained in Purana in relation to Bali Maharaj and mantra is in Rig Veda that he has 3 steps in 3 Lokas which are below Maharloka ruled by Mercury). Savitur is Agni and also Aditya or the Sun in its particular form or benevolent form. Varanyam as the sage said is Anna or food or Prajapati. Upanishads clearly stated the whole creation is food etc. So, the line of Upanishads about Prajapati who is in the form of food and also within a golden rob in every heart shinning like a Sun. [I don't know if I can extend it to the fact that light is the only source of energy and it carries food required for every being and also non-beings.]

भर्गो देवस्य धीमहि  

Bharga is said to be Water or Aapa by the sage. Water is also associated with the moon. Or the latent form of unconsciousness (by Carl Jung). 2nd principle of life formation as said earlier is here recalled by water or Moon. Devasya is then explained as Savitu or Purusha or Vishnu whose 3 steps earlier recalled. It is interesting to note that Puranic details depict Vishnu to reside in an Ocean. Varuna is also the deity of water and in one line Yajurveda said Varuna and Vishnu are same. Lastly Dhimahi is associated with Aishwarya, and variations of Adhaytma. So, the line is about the unconscious which holds all life principles and is based on the Truth of first line or the Ultimate is life principle of Vishnu.

धियो यो नः प्रचोदयात्

Now Dhiya is recalled as Mahiti or Prithivi we may say Dhahrani who can hold the Dharma. Our base of life, bodily life which is the ultimate manifestation of divine principles. A purpose of all stars and planets and deities. Playground of all energies. 

Yo na Prachodayat is Kaam or desire or will in its nearest sense of translation. From which the worlds (or our worlds which are within grasp of senses) emerges. It is inimical and it is not which can be said as balanced and neutral even being cause of everything. 

I don't have any thoughts on Shanti Mantra part. 

[All of this may be incorrect, as I do not know Sanskrit and am just a beginner in Jyotish. Yet, with a spirit of inquiry and a desire to understand this great mantra for myself, I dare to write.]