Spaceship Orbit

How fast ((in m/s)\text{m/s}) does a spaceship need to orbit around Earth to not spiral down or fly away from it?

Details and Assumptions:

  • The spaceship is 400 km\SI{400}{\kilo\meter} above the surface of Earth.
  • Earth's radius is 6371 km.\SI{6371}{\kilo\meter}.
  • Gravitational acceleration on the spaceship is 8.69 m/s2\SI[per-mode=symbol]{8.69}{\meter\per\second\squared} towards the center of Earth.

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