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 × 10−27 kg as proton mass.

Answer 1

Time = 12.42 light years.

Mass of inter-stellar gas that collides with the spaceship = 471.43 kg

Explanation:

A) Speed = distance / time

Time = distance / speed.

Distance = 8.7 light years.

Speed = 70% of light = 70/100 * 1 light year = 0.70

Time = 12.42 light years.

B) Mass of inter-stellar gas that collides with the spaceship = surface area * mass of proton

 = 2πrh +πr^2 * 1.673 * 10^-27

 = (2 * 22/7 * 3 * 25) + (22/7 * 9 * 1.673 * 10^-27)

 = 471.43 + 47.32 * 10^-27

 = 471.43 kg approximately.