question_answer 24)

A space-ship is stationed on Mars. How much  must be expended on the spaceship to rocket it out of the solar system ? Mass of the spaceship = 1000 kg, Mass of the Sun Mass of the Mars  Radius of Mars = 3395 km. Radius of the orbit of Mars G = 6-67 x 10-11 N m 2 kg-2.  

Answer:

Let R, be the radius of orbit of Mars and R' be the radius of the Mars. M be the mass of the Sun and M' be the mass of Mars. If m is the mass of the space-ship, then Potential energy of space-ship due to gravitational attraction of the Sun = - GM m/R Potential energy of space-ship due to gravitational attraction of Mars = - GM' m/R' Since, the K.E. of space ship is zero, therefore, total energy of space ship  Energy required to rocket out the space   ship from the solar system = - (total energy of space ship)