I Webb Launch Mechanics: Tangential Speed Benefits?

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The French Guiana launch site was selected for its proximity to the equator, providing a higher initial tangential speed for the launch of the James Webb Space Telescope (JWST). However, calculations indicate that this advantage translates to only a minimal increase in tangential speed at L2, raising questions about the necessity of the launch site choice. The Ariane rocket, used for the launch, has a larger payload capacity than any US rocket and is operated by the European Space Agency, a partner in the JWST project. The Ariane successfully placed JWST on a precise trajectory, leading to an extended fuel lifespan estimate of 20 years instead of the anticipated 10 years. Overall, the launch's success highlights the effectiveness of the chosen launch vehicle and site.
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Why was Webb launched from French Guiana?
When I read about the launch location, it is explained that the French Guiana launch site was chosen because it is close to the equator, which means it started with a larger tangential speed than if it were launched from a US location. However, doing the numbers, I find that an initial tangential speed of 460 m/s only gives you about 2 m/s tangential speed at L2, while the orbital speed needed is 500 m/s. So the difference between 2 m/s tangential speed and 88% of that (from a US launch site) seems completely negligible, compared to the difficulty/danger of moving Webb to French Guiana. Is there something I'm missing here?
 
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The Ariane rocket from the European Space Agency has a larger diameter for payload than any US rocket, and ESA is one of the partners in the JWST project. Ariane is launched from the ESA facility in French Guiana.

The Ariane performed admirably putting JWST into an unexpectedly precise trajectory. Because of that, estimates say that JWST's fuel will last for 20 years instead of 10 years.
 
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