Answer to Question #122844 in Astronomy | Astrophysics for annie

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

The time it takes your spaceship to reach Sirius from the viewpoint of observers left on the Earth is

$$t=\frac{D}{v}=\frac{8.7c}{0.7c}=12.43^\text{y}.$$

The mass of interstellar gas that collides with your spaceship during the mission can be found by determining the volume of space that the spaceship passes through:

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

Then the mass of gas will be

$$m=\rho V=\frac{\rho\pi d^2D}{4}=3.886\cdot10^{-9}\text{ kg}.$$