Escape Orbit is On

At a certain height (\(=3630 \text{ km}\)) from the surface of the earth, a spacecraft Rosetta orbits the earth in circular orbit with \(v_{\text{orb}} (=6326 \text{ ms}^{-1}\)).

Meanwhile, at the surface of the earth, the ground control(for some reason) want to bring Rosetta, escape from its orbit around the earth(somewhere beyond the earth).

Find the approximated minimum impulse in Ns that Rosetta needs to exert to escape from its orbit around the earth!

Details and Assumptions

  • Gravitational constant \(G= 6.67\times {{10}^{-11}} \text{ Nm}^2 \text{kg}^{-2}\).
  • Mass of the earth \(M = 6\times {{10}^{24}}\text{ kg} \).
  • Mass of Rosetta \(m=5\times {{10}^{3}} \text{ kg} \).
  • Radius of the earth \(R = 6370\text{ km} \).
  • Neglect the gravity from other celestial objects.
  • Consider the two objects as two point of masses.
  • Neglect the change of m when Rosetta exerting impulse.

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