A space-ship is stationed on Mars. How much energy must be expanded on the spaceship to rocket it out of the solar system ? Mass of the spaceship = 1000 kg, Mass of the sun =2 xx 10^(30) kg. Mass of the Mars = 6.4 xx 10^(23)kg, Radius of Mars = 3395 km. Radius of the orbit of Mars = 2.28 xx 10^(11)m, G = 6.67 xx 10^(-11) Nm^(2) kg^(-2).

A space-ship is stationed on Mars. How much energy must be expanded on

1.	A space-ship is stationed on Mars. How much energy must be expanded on the spaceship to rocket it out of the solar system ? Mass of the spaceship = 1000 kg, Mass of the sun =2 xx 10^(30) kg. Mass of the Mars = 6.4 xx 10^(23)kg, Radius of Mars = 3395 km. Radius of the orbit of Mars = 2.28 xx 10^(11)m, G = 6.67 xx 10^(-11) Nm^(2) kg^(-2).
Answer» Solution :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 = -GMM/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 `= -(GMm)/(R) -(GM.m)/(R.) = -Gm((M)/(R) +(M.)/(R"))` `therefore` Energy required to rocket out the spaceship from the solar system = -(total energy of spaceship) `=-[-Gm((M)/(R)+(M.)/(R.))] = Gm((M)/(R)+(M.)/(R.))` `= 6.67 XX 10^(-11) xx 1000 xx [(2 xx 10^(30))/(2.28 xx 10^(11)) + (6.4 xx 10^(23))/(3395 xx 10^(3))]` `= 6.67 xx 10^(8)[(20)/(2.28) + (6.4)/(33.95)]xx 10^(18) J = 5.98 xx 10^(11)J`