An unsettling refreshment

You are an astronaut, it is a few hours before you are scheduled to launch for an intergalactic space mission, and you're sitting on the shore of the Atlantic Ocean near Cape Canaveral, savoring the view one last time. This mission is especially trying; because of the relativistic speed of your spaceship, Earth will be one billion years into the future upon your return.

Depressed beyond words, you decide, in one of your weaker moments, to pee into the Atlantic Ocean.

Flash forward: 1 billion years.

You return to Earth, expecting a hero's welcome, but instead you find that all of humanity has vanished. Instead, the Earth is run by a peaceful clan of telekinetic dolphins who made off with the lion's share of Bitcoins that were abandoned by the last humans as they uploaded their souls to the singularity server. In a disillusioned haze, you bend down and fill your astronaut survival cup with refreshing lake water, hoping for some clarity. After drinking the glass, you realize that this far into the future, all the Earth's water has been thoroughly well mixed since the time you took off on your mission.

Approximately how many molecules of your billion year old urine did you just consume?

Assumptions and details

  • You released \(\textrm{1 L}\) of urine into the Atlantic Ocean.
  • Approximate your urine as consisting of pure water.

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