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 × 10⁸kg; G= 6.67 × 10^–11 m²kg^–2.

Answer 1

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)