Spaceship Orbit

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

Details and Assumptions:

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