A spacecraft of mass M = 12 tons moves around the Moon in a circular orbit at an altitude of h = 100 km. To transfer to the lunar landing orbit, the engine is turned on for a short time. The speed of gases escaping from the rocket nozzle is u=104 m/s. The radius of the Moon and the acceleration of gravity at its surface Rл=1.7•106, gл=1.7 m/s2. 1. How much fuel must be consumed so that when the braking engine is turned on at point A of the trajectory, the ship descends to the Moon at point B (Fig. 4.4)? 2. In the second variant of lunar landing, the ship at point A is given an impulse in the direction of the center of the Moon in order to transfer the ship into an orbit touching the Moon at point C (Fig. 4.5). How much fuel should be consumed in this case?
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