The Gāyatrī Mantra

It intrigues me that every online blog has a variant interpretation of the mighty गायत्री मन्त्र, as do scholars. Perhaps it's poetics. You're welcome to relate to a text the way you wish, but there is an underlying semantic based on grammar which should be taken into account. The provenance of the verse is the Ṛgveda itself, 3.62.10 and it is prefaced by ॐ and the  mahāvyāhṛtis भूः भुवः and स्वः as described in the Taittareya Āraṇyaka (2.11.1-8)*.

The मन्त्र:

ॐ भूर्भुवः स्वः 

तत्स॑वि॒तुर्वरे॑ण्यं॒ भर्गो॑ दे॒वस्य॑ धीमहि ।

धियो॒ यो नः॑ प्रचो॒दया॑त् ॥

The translation:

We meditate on that most excellent radiance of god Savitā, may he rouse forth/impel our  thoughts/intelligence/prayers

The विग्रह:

ॐ भूः भुवः स्वः 

तत् । सवितुः । वरेण्यम् । भर्गः । देवस्य । धीमहि ।

धियः । यः । नः । प्रऽचोदयात् ॥

The अन्वय:

ॐ भूः भुवः स्वः

देवस्य सवितुः तत् वरेण्यम् भर्गः धीमहि 

यः नः  धियः प्रऽचोदयात् ॥

The analysis:

सवितुः देवस्य - genitive singular of सवितृ/देव - of that god Savitā; genitive, masculine, singular 

तत् - that, the - neuter accusative, singular (agrees with भर्गः)

वरेण्यम् - to be wished for, most excellent, desirable; accusative gerundive √वृ (adjective for भर्गः)

भर्गः - radiance, lustre, splendour, effulgence; accusative, neuter, singular**

धीमहि - may we reflect on, meditate on; optative, 1st person plural of √धी 4Ā

यः -  which/who;  Hindi जो (refers to the god Savitā

प्रचोदयात् - will/shall/may [he] incite, urge, instigate, rouse forth; optative 3rd person singular of प्र√चुद् 1P

(agrees with Sun)

नः - our; genitive plural, personal pronoun

धियः - insights, religious thoughts, prayers, devotion; accusative plural of धी (fem noun)  
[धियः is in the accusative plural because it is the object of the verb प्र√चुद्]

* भूः भुवः स्वः These mantric utterances are given various meanings. The table below from hinduism.about.com elaborates:

**भर्गः - appears in most modern dictionaries as a masculine substantive. However it is not attested as such till the Śatapatha Brāhmaṇa. In the Ṛgvedic context it is a neuter, 'bhargas'. I'd like to thank Dr. Renate Söhnen Thieme for this helpful information.