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 = 1000 kg; mass of the Sun = 2 × 10³⁰ kg; mass of mars = 6.4 × 10²³ kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28 × 10⁸kg; G= 6.67 × 10^–11 m²kg^–2.

Mass of the spaceship, m_s = 1000 kg
Mass of the Sun, M = 2 × 10³⁰ kg 
Mass of Mars, m_m = 6.4 × 10 ²³ kg 
Orbital radius of Mars, R = 2.28 × 10⁸ kg
                                    =2.28 × 10¹¹m 
Radius of Mars, r = 3395 km
                          = 3.395 × 10⁶ m 
Universal gravitational constant, G = 6.67 × 10^–11 m²kg^–2 

Potential energy of the spaceship due to the gravitational attraction of the Sun =

Potential energy of the spaceship due to the gravitational attraction of Mars = - 

Since the spaceship is stationed on Mars, its velocity and hence, its kinetic energy will be zero. 
Total energy of the spaceship = 
                                            =  
The negative sign indicates that the system is in bound state. 
Energy required for launching the spaceship out of the solar system, 
= – (Total energy of the spaceship) 
=  
= 6.67 × 10¹¹ × 10³ ×
= 596.97 × 10⁹ 
=  6 × 10¹¹ J.