righteous judgment...

"But if Christ is in you, your body is dead because of sin, yet your spirit is alive because of righteousness." - Romans 8:10
As I read this, a question came to mind: so does this mean that righteousness is the channel for an eternal life? What does it mean to be righteous? Can someone who does not believe in God be righteous?

"For God does not show favoritism. All who sin apart form the law will also perish apart from the law, and all who sin under the law will be judged by the law. For it is not those who hear the law who are righteous in God's sight, but it is those who obey the law who will be declared righteous. (Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law, since they show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts now accusing, now even defending them.)" - Romans 2:11-15

"The law" is in reference to that of Jewish descent. This passage is a very good reminder that God isn't only the God of Jews but the One and Only God. Which means, come judgment day, Chrsitans and non-Christians alike will be asked to account for every act before Him alone. According to this passage, those who obey the law are deemed righteous before God and that people who don't know the Jewish law have consciences as their law. So it is reasonable to think that those who obey their conscience are righteous. However, who can say that they've lead a flawless life? We are imperfect beings (this is different from saying we are imperfect creations because God is a perfect God and created us in His image.) Ever since the fall of Adam and Eve, we have been engulfed in the sinful nature that Satan introduced. Thus, no one can be deemed righteous as we all break one law or another be it intentionally or unintentionally. If we have not been baptized by the Holy Spirit, then our conscience will condemn us of our wrong doing on judgment day.

"There is no difference, for all have sinned and fall short of the glory of God, and are justified freely by his grace through the redemption that came by Christ Jesus." - Romans 3:22-23

Indeed, all is equal before God and He does not show favouritism. The only reason Christians (fewer than you'd think) can be deemed righteous is through the justification of a righteous being who paid the price for our unrighteous acts, that being eternal death. Like a bridge raised for a ship to pass, it needs both sides to be lowered for anyone to cross over. Jesus let down his side, what about ours?

 "Now when a man works, his wages are not credited to him as a gift, but as an obligation. However, to the man who does not work but trusts God who justifies the wicked, his faith is credited as righteousness." - Romans 4:4-5

It is by faith that we can be considered righteous, not by any faith but by faith in God. This is considered gift of salvation because God is not obligated to give us salvation.

"...where there is no law there is no transgression." - Romans 4:15

 But there will always be laws, and so there will always be transgression. Because there will always be transgression, there will not be righteousness... unless...