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by fred_is_fred 1919 days ago
The Haber process which you mentioned is really key here. It uses a lot of natural gas - more interesting than cow methane might be using nitrogen fixing bacteria or crop rotation (legumes) to reduce it's usage.
2 comments

From what I've read, you can't grow enough legumes to fix the needed amount of nitrogen for high intensity agriculture. The Haber process sustains a sizable fraction of the world's animal population.
Human urine would be a sufficient source of nitrogen but it ends up in sewage nitrification-denitrification reactors that eventually turn most of the urea back into nitrogen gas so that the effluent can be safely discharged into water bodies.
I guess that makes sense, the nitrogen has to go somewhere.
I'm not sure what it does to their methane output, but can't you feed legumes straight to cows? You definitely can to chickens and pigs.