In the Nirukta (Vedic etymology), Rta and Satya serve as synonyms and at the same time refer to water in the physical plane. Satya literally means truth and reality. It is therefore Holy Speech (the Vedas). It is the Law to be observed. Rta literally is right. It is truth or cosmic order/principle, of karma justice and rain cycle (or Yajña [cosmic weal]). We must faithfully accept whatever befalls us. Satya is what should happen whereas Rta is what actually happens.
However, Rta is also called in the Nirukta as Yajña (cosmic weal or upkeep). We shall discuss it on other pages.
Invocation of triple peace is peace at personal, social and natural levels. We suffer from own negligence or failures (e.g. laziness), others’ acts (e.g. dog and thief) and from nature’s furies (e.g. earthquake, flood and failure of rains).
Now to the Upanishad excerpt ...
The Taittiriya Upanishad (I.11)
After teaching the Veda, teacher (āchārya) exhorts the passing out student:
Speak the truth (satya).
CAUTION: Most of us say ‘yoga is beneficial’ without either practising it or knowing what yoga is! That is, we say something else and practise someting else. Recall the story of Yudhishthira learning lesson on anger where he tests himself in practice alone (this appears in my book Yoga: An Analytical Release.]
Observe/practise the Divine Law (dharma).
Law is mandatory and not your choice. The Vedas form the Eternal Law. In terms of Avidya of the Yoga Sutras (ibid.), understand the nature of the world as impermanent, impure (indeterminate), pain and non-self (or unpossessable).
Never be careless in study of the Veda (Svādhyāya or svadhyaya) [in discharging debt of Rishis].
After bringing acceptable sum for teacher, never break clan succession (i.e. do marry and procreate).
Do not neglect satya. Do not neglect dharma. Do not neglect svadhyaya.
Do not neglect personal welfare (kusala = safety).
Do not neglect prosperity (bhūti).
Do not neglect study and teaching of the Veda [Brahma Yajña, or Tapas]. 
Do not neglect your duties to gods (keepers of universe) and ancestors (or guardians).
Humans have solemn obligations/debts to Rishis, gods and ancestors.
Treat mother as god. Treat father as god.
Treat teacher (āchārya, or role model) as god.
Treat unanticipated guest (atithi) as god.
Whatever blameless deeds there are, those ought to be performed.
Whatever right conduct of ours, that ought to be heeded. 
Make the superior Brahmins (versed in the Veda and ever mindful of Brahman, the supreme reality), comfortable with seat [support].
Give with faith (sraddhā). Do not give without faith.
Give according to your status or prosperity (srī).
Give with courtesy (modesty).
Give fearfully (because tomorrow situation may change).
Give empathatically (or conscientiously).
Now, in case you face doubt about some act or conduct. 
Brahmins who are: competent to counsel; reasonable or mentally settled (or committed in yoga); voluntarily committed (āyukta); not severe [they should not be right alone but also should look right]; seekers of dharma. The way they conduct there. So you conduct there.
Now, in instances involving criticism or accusation.
Brahmins who are: competent to counsel; reasonable or mentally settled (or committed in yoga); voluntarily committed (āyukta); not severe [they should not be right alone but also should look right]; seekers of dharma. The way they conduct in them. So you conduct in them.
This is mandate [and not your choice]. This is counsel.
This is the secret doctrine (upanishad) of the Veda.
This is ruling. Thus it should be adhered.
Like this indeed it should be adhered. 
The Secret Doctrine of the Veda
Works bind; duties assigned by Sruti (Veda) deliver
This is the secret doctrine (upanishad) of the Veda referred to above. We enumerated the Nitya Karmas (solemn daily duties), but we need to discuss their significance.
Generally, we say karma is of two kinds: good and bad, or pious and profane. The world is the result of these two. We do good and bad karma and then per force take births in different life forms to experience their fruits/deserts. We thus remain stuck in the birth-death cycle. From countless past lives, each individual has as if a vast reservior or giant tree of good and bad deeds (and their impressions). According to the Yoga Sutras, at root of the tree or reservoir lies Avidya (ignorance of reality). As long as the root is there, the fruits unceasingly sue us in the form of births, life spans and experiences of pleasure and pain (bhoga). (Quarter II passim.) ... Then how to escape this birth-death cylce!
Here is the way:
The act (karma) of Yogi is neither pious nor profane, whereas of others’ is of three kinds (pious, profane and pious-profane mix). (IV.7 ibid.)
The acts of Yogi, Rishi or Brahma-knower fall ouside the category of good and bad. Though they look to be working like common people, they in reality are not. A simile given for them is that of lotus leaf in the water (untouched, unaffected and undecaying). Let us understand like this:
A sepoy in service of king killed someone with the sword. Spies of the king happened to witness that. They caught him red handed, but sepoy pleaded innocent. They were amused because that meant sword killed and not the sepoy. They took him to the king and reported to king his cruel act that had been witnessed by them. However, on finding the details of murder, king smiled and said, ‘Well done. You carried out my orders well.’ ... Now onus shifted dramatically. ...
Order, duty and mandate in the form of dharmas and nitya karmas prescribed by the Vedas, when faithfully carried out, without personal motive crossing one’s mind, escape the classification of good and bad, enabling the escape from birth-death cyle. The Gita endorses this and refers to duties as assigned by the Vedas and concludes:
Yajña, gift and Tapas (austerity) are not to be given up. These are rather mandatory. These indeed purify mind of the wise. (xviii.5)
According to philosopher Shankara, nitya karmas are even antidote to past bad karma. ...The Gita upholds and celebrates their practice, howsoever small, because that incurs no loss of effort and setback and even saves from horrors of birth-death cycle (ii.40 ibid.).
The Vedic dharmas encompass human life so comprehensively that there is no room to seek or pursue on one’s own. You need not even pray for something in your own words. The Vedic hymns take care of all your needs. The Vedas totally constrict ego and personal will out of you ... in favour of total surrender or let-go. Manu calls Karma Yoga as Vedic in concept and in assigning duties.
If you suffer wavering or hesitation from compliance with Vedic instructions, you simply need to do at least Pranayama (and Yoga exercises) and recite Gayatri Mantra to change the chemistry of your mind.
ॐ भूर्भुवः॒ स्वः । तत्स॑वितुर्वरे॑ण्यं भ॒र्गो॑ दे॒वस्य॑ धीमहि ।
धियो॒ यो नः॑ प्रचो॒दया॑त् ॥
Om bhoor bhuvah svah
~ ~ Earth, Mid-Region and Heaven (Stellar) planes [three worlds]
~ ~ Agni, Vayu/Indra and Surya (Sun) [their respective chief gods]
~ ~ Fire, lightning/electricity and solar (atomic) lights
~ ~ Rik, Sama (sāma) and Yajus (mantras or Vedas), the whole knowledge
~ ~ Prāna, Apāna and Vyāna (diffused breath energising muscles, tissues and joints)
tat savitur varenyam bhargo devasya dheemahi;
dhiyo yo nah prachodayāt. (RV III.62.10)
We meditate god Savitri’s (Creator’s) lovely, bedazzling splendour
[That takes the speech form of the three Vedas and the physical form of three worlds
and is capable of scorching karma seeds from sprouting].