Question

Interstellar Mission:
You are on an interstellar mission from the Earth to the 8.7 light-years distant star Sirius. Your spaceship can travel with 70% the speed of light and has a cylindrical shape with a diameter of 6 m at the front surface and a length of 25 m. You have to cross the interstellar medium with an approximated density of 1 hydrogen atom/m3.

(a) Calculate the time it takes your spaceship to reach Sirius.
(b) Determine the mass of interstellar gas that collides with your spaceship during the mission.

Note: Use 1.673 × 10−27 kg as proton mass.

Answer 1

(a) Calculate the time it takes your spaceship to reach Sirius:

$$t=\frac{D}{v}=\frac{D}{0.7c}=\frac{8.7c}{0.7c}=12.4\text{ years}.$$

(b) Determine the mass of interstellar gas that collides with the spaceship during the mission. The density of gas is 1 atom per cubic meter. The area of the front is

$$A=\frac{\pi d^2}{4}.$$

The volume of space passed by the spaceship is

$$V=AD=\frac{\pi d^2D}{4}.$$

The mass of the gas "eaten" by the spaceship's front is

$$m=\rho V=\frac{\rho\pi d^2D}{4},\\\space\\ m=\frac{1.673 \cdot 10^{−27}\pi 6^2\cdot8.7\cdot3\cdot10^8\cdot365\cdot24\cdot3600}{4}=3.89\cdot10^{-9}\text{ kg}.$$