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

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

1.	A space -ship is stationed on Mars. How much energy must be expended onthe spaceship to rocket it out of the solar system ? Mass of the spaceship = 1000 kg , Mass of the sun =2xx10^30 kg . Mass of the Mars = 6.4xx10^23 kg , Radius of Mars= 3395 km. Radiusof the orbit of Mars =2.28xx10^11 m, G=6.67xx10^(-11) Nm^2 kg^(-2)
Answer» Solution :LET R, be the radius of orbit of Mars and R. be theradius 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 gravititional attraction of the Sun = -GMm/R Potential energy of space-ship due to gravititional 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.))` `=6.67xx10^(-11)xx1000xx[(2xx10^30)/(2.28xx10^11)+(6.4xx10^23)/(3395xx10^3)]` `=6.67xx10^(-8) [20/(2.28)+6.4/33.95]xx10^18` J = `5.98xx10^11` J