Answer to Question #123007 in Astronomy | Astrophysics for Alok

Question

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

Answer 1

(a) The time in the spaceship's frame of reference will be

$$t=\frac{L}{v}=\frac{8.7c}{0.7c}=12.43\text{ years}.$$

(b) The mass of hydrogen "collected" by the spaceship's cross-sectional area along path 8.7 light years long will be

$$m=\rho V=\rho\frac{\pi d^2L}{4},\\\space\\ m=1.673\cdot10^{-27}\cdot\frac{3.142\cdot6^2\cdot8.7\cdot3\cdot10^8\cdot(365\cdot24\cdot3600)}{4}=\\\space\\=3.893\cdot10^{-9}\text{ kg}.$$