The righteousness and wrath of God

Paul was eager to preach the gospel which he personally received from Jesus on his way to Damascus. He claimed that this gospel did not come from men, but came directly from the Lord.
For I would have you know, brethren, that the gospel which was preached by me is not man's gospel.
For I did not receive it from man, nor was I taught it, but it came through a revelation of Jesus Christ (Galatians 1:11-12).
Paul had personally experienced the power of this gospel. He was converted from a persecutor to a persecuted. He had been a Pharisee for many years, yet it was incomparable to the life as a Christian. Unlike the other apostles, Paul was "forced" to receive this revelation while the others were gently invited by Jesus. The experience was powerful. Therefore for Paul, the gospel was the power of God.
For I am not ashamed of the gospel: it is the power of God for salvation to every one who has faith, to the Jew first and also to the Greek (Romans 1:16).
Immediately, Paul switched to another concept --- the righteousness of God.
For in it the righteousness of God is revealed through faith for faith; as it is written, "He who through faith is righteous shall live." (Romans 1:17)
What did Paul mean by the righteousness of God?
How does the Habakkuk quotation prove his point? I think this quotation was Paul's favourite. It summarizes neatly the theology of Paul. Through faith in the risen Lord, man becomes justified and righteous. Then man can gain eternal life. Of course, our righteousness is different from the righteousness of God. But Paul did not continue to develop the concept of the righteousness of God. He simply stated that the gospel revealed God's righteousness and he quotedHabakkuk to support this statement. Immediately, he turned his attention to more urgent problems. I am sure Paul will return to treat the topic more thoroughly in the future.

For Paul, not believing in God was illogical. God revealed Himself in the Creation. Therefore, God is approachable and understandable. Man has enough intelligence to discern God. Even though God is undetectable through human senses, man can still apply his rationality to make sense of the existence of God. There were no more excuses for not knowing and acknowledging God (Romans 1:20b).
But for Paul, the worse sin is not a disbelief in God but idolatry.
and [they] exchanged the glory of the immortal God for images resembling mortal man or birds or animals or reptiles (Romans 1:23).
The consequences were terrible. God would give them up to Satan. Giving them up was the wrath of God.
Delivering the sinful brethren up to Satan was a familiar theme of Paul's theology (1 Corinthians 5:5, 1 Timothy 1:20). Here in Romans, Paul concretized Satan by claiming that God would give those idolaters up to lustful passions. Paul equated idolatry with lust. Then Paul strongly condemned homosexual acts between women and women, men and men. Probably, this was a serious threat the Roman culture posed upon Christians. Probably, this was a result of the Pharisaic background of Paul. He was harsh towards homosexuals.
And since they did not see fit to acknowledge God, God gave them up to a base mind and to improper conduct (Romans 1:28).
This image of God is very righteous and is not quite compatible with the merciful God portrayed in the gospels. Therefore, while we are reading the Romans, we must keep in mind the mercy of God as well so as not to become onesided, making God one-dimensional.  

Dear Lord, we thank You for giving us intelligence and rationality. We further thank You that the Original Sin has not completely wiped out the function of our rationality. May we make good use of our intellect to discern You more. Amen.

Appendix:
ὁ δὲ δίκαιος ἐκ πίστεως ζήσεται.
He who through faith is righteous shall live (Romans 1:17b RSV).
ὁ δὲ δίκαιος ἐκ πίστεώς μου ζήσεται (Habakkuk 2:4b LXX)