Question

You are a junior space cadet on an interstellar space station. Your job is to launch a long distance spacecraft. The mass of the spacecraft without any fuel is 1217 kg. This mass is often called dry mass. The rocket engine of the craft can exhaust hot gas at a speed of 2.26 km/s relative to the space craft. How much rocket propellant does the craft need, if you want the craft to reach a final speed of 5.51 km/s relative to the station? In interstellar space the gravitational pull of the stars is negligible.

Answer 1

The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket:

Where, is the maximum change of velocity of the vehicle (with no external forces acting), m₀ is the initial total mass, including propellant, also known as wet mass, m_f is the final total mass without propellant, also known as dry mass, v_e is the effective exhaust velocity and M is mass of rocket propellant.

Here in this problem, v_e = 2.26 Km/s, = change in velocity from rest = 5.51 Km/s, m_f = mass of the spacecraft without any fuel = 1217 kg,

If you want the craft to reach a final speed of 5.51 km/s relative to the station, you need 12718.5 Kg of rocket propellant.