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Interesting in the article it says:
I think at the equator, the rocket would benefit the most from the earth's rotation speed to gain acceleration and gravity escape. Thus, then can have a heavier load with the same effort.
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That's essentially correct. Of course, the satellite does not achieve escape velocity, or we'd never see it again. When a satellite launches from a non-equatorial location, it will end up in an inclined orbit if it takes full advantage of the earth's rotational assist. It takes fuel to alter the orbit into a geosynchronous equatorial orbit. By launching from the equator you can loft more, and use less fuel thus saving the satellite's on-board fuel and lengthening it's usable life.
This is one of the on-going issues with the ISS. Since the most southern Russian launch facility is at Baikonur at 47 degrees N the ISS is in an orbit that is inclined to reach that latitude (51.59 degrees inclination). Cape Canaveral is at 28 degrees North, so when we launch a Shuttle to the ISS, we have to waste fuel (giving up payload) launching more northerly to go into the same inclined orbit. The most efficient launch trajectory is directly east, so most US shuttle orbits not going to the ISS only incline 28 degrees or so.