A space - ship is stationed on Mars. How much energy must be expended on the spaceship to rocket it out of the solar system? Mass of the spaceship = 1000 kg. Mass of thesun=2xx10^(30)kg. Mass of the Mars =6.4 xx10^(23) kg. Radius of Mars =3395Radius of the orbit of Mars = =2.28 xx10^(11)m, G = 6.67xx10^(-11)Nm^(2)kg^(-2).

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

1.	A space - ship is stationed on Mars. How much energy must be expended on the spaceship to rocket it out of the solar system? Mass of the spaceship = 1000 kg. Mass of thesun=2xx10^(30)kg. Mass of the Mars =6.4 xx10^(23) kg. Radius of Mars =3395Radius of the orbit of Mars = =2.28 xx10^(11)m, G = 6.67xx10^(-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. 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 to gravitational attraction of Mass - `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.))` `:.`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 xx10^(-11) xx1000 xx[(2xx10^(30))/(2.28xx10^(11))+(6.4xx10^(23))/(3395xx10^3)]` `=6.67 xx10^(-8)[(20)/(2.28)+(6.4)/(33.95)]xx10^(18)J=5.98xx10^(11)J`