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.