A satellite orbits the earth close to its surface. A particle is to be projected from the satellite such that it just escapes the earth. If the escape speed from the earth is v_e , the particle's speed relative to the satellite

Step-by-step solution

Let the orbital speed of the satellite be v_s . For a satellite orbiting close to the earth's surface, v_s = v_e 2 . Let the velocity of the particle relative to the satellite be v _ ps . The velocity of the particle relative to the earth is given by v _p = v _ ps + v _s . For the particle to just escape the earth, its speed relative to the earth must be equal to the escape speed v_e . Thus, | v _p| = v_e . Using vector addition, we have: | v _ ps + v _s|^2 = v_e^2 v_ ps ^2 + v_s^2 + 2v_ ps v_s = v_e^2 Substituting