You are on an interstellar mission from Earth to the distant star Sirius, which is 8.7 light years away. Your spaceship can travel with 70% the speed of light and has a cylinder shape with a diameter of 6 meters at the front surface and a length of 25 meters. You have to cross the interstellar medium with an approximated density of 1 hydrogen atom/m^3. (a) How long does it take for your spaceship to reach Sirius? (b) What is the mass of interstellar gas that collides with your spaceship during the mission? Note: Use 1.673 x 10^27 kilograms as proton mass.

(a). 12.43 years.

(b). 3.89 × 10^ -9 kg.

Explanation:

So, we are given the following data or parameters or information which is going to assist us in solving this question;

=> " mission from Earth to the distant star Sirius has a light year = 8.7 light years away. "

=> "The spaceship can travel with 70% the speed of light"

=> " The spaceship's cylinder shape has a diameter of 6 meters at the front surface and a length of 25 meters. "

=> density = 1 hydrogen atom/m^3.

Step one: convert light year to metres.

J = 8.7 × 9.461 × 10^15 = 8.23 × 10^16 m.

Step two: convert percentage speed of light to metre per seconds;

70% = 70/100 = 0.7.

U = 0.7 × speed of light = 0.7 × 3.0 × 10^8 = 2.1 × 10^8 m/s.

(a).

Step three: determine the time taken(convert to years);

J / U = time taken; = 8.23 × 10^16 m/ 2.1 × 10^8 m/s = 12.43 years.

(b). The mass of interstellar gas that collides with your spaceship during the mission;

Volume= {(6m)^2 × 22/7}/ 4 × ( 8.23 × 10^16 m). = 2.33 × 10^18 m^3..

Density = mass/volume .

Mass= [24 × 365 × 3600 × 3 × 10^8 × 8.7 × 1.673 × 10^-27 × 6^2 × 22/7]/4 = 3.89 × 10^ -9 kg.