# Escape Orbit is On

**Classical Mechanics**Level 4

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.