Question

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 × 10⁸ km; G = 6.6 7 × 10^-11 N m² kg^-2 .

Answer 1

Mass of Spaceship, m_s = 1000 kg

Mass of mars M_s = 6.4 × 10²³ kg;

Radius of mars r_m = 3.395 × 10⁶ m

Radius of the orbit of Mars

= 2.28 × 10⁸ km = 2.28 × 10¹¹ m

Initial velocity of spaceship is = 0

So, the Total Initial Energy is only potential energy.

= – 6.67 × 10^-8 [1.88 × 10¹⁷ + 8.772 × 10¹⁸]

= – 6.67 × 8.96 × 10¹⁰

= – 5.976 × 10¹¹ = – 6 × 10¹¹ J.