Q: 8.24 A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the space ship \small =1000\hspace{1mm}kg ; mass of the sun \small =2 \times 10^3^0\hspace{1mm}kg; mass of  mars \small =6.4 \times 10^2^3\hspace{1mm}kg ; radius of mars\small =3395\hspace{1mm}km;radius of the orbit of mars \small =2.28 \times 10^8\hspace{1mm}km;    \small G=6.67 \times 10^-^1^1\hspace{1mm}Nm^2kg^-^2

Answers (1)

Firstly, the potential energy of spaceship due to the sun is given by :

                                                                      =\ \frac{-GMm_s}{r}

and the potential energy of spaceship due to mars is given by :

                                                                      =\ \frac{-GMm_m}{R}

It is given that the spaceship is stationary so its kinetic energy is zero.

Thus the total energy of spaceship is :

                                                               =\ \frac{-GMm_s}{r}\ +\ \frac{-GMm_m}{R}

Thus the energy needed to launch the spaceship is :

                                                                =\ \frac{GMm_s}{r}\ +\ \frac{GMm_m}{R}

or                                                              =\ 6.67\times 10^{-11}\times 10^3 \left ( \frac{2\times 10^{30}}{2.28\times 10^{11}}\ +\ \frac{6.4\times 10^{23}}{3.395\times 10^6} \right )

or                                                             =\ 596.97\times 10^9\ J

or                                                             =\ 6\times 10^{11}\ J