As methane is broken down by light-induced chemical reactions over a timescale of tens of millions of years, it can't just be a remnant of the atmosphere present when Titan itself was formed, and it must be replenished quite regularly.

I was also interested in formulating the path of chemical reactions.

the tens of millions of dollars.

Jupiter instead cooled down below the threshold for fusion, but it maintained enough heat and mass and pressure to cram atoms very close together, to the point they stop behaving like the atoms we recognize on earth. Inside Jupiter, they enter a limbo of possibility between chemical and nuclear reactions, where planet-sized diamonds and oily hydrogen metal seem plausible.

Methane is only around for a short time geologically. The time scale is somewhere between 10 and 100 million years.

This model is in agreement with the observations made so far by both the Huygens probe that landed on Titan on 14 January 2005 and the remote sensing instruments on board the Cassini spacecraft.