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 1,673x 10^-27 kg as proton mass

Time = 12.43 years

Mass = 4.71.43kg

Explanation:

Given the following :

Distance = 8.7 light years

Speed = 70% the speed of light

Diameter = 6m

Lengtg = 25m

Density = 1 hydrogen atom/m^3

Mass of proton(Me) = 1.673x 10^-27

A.) time it takes your spaceship to reach Sirius :

From the relation: Speed = (distance / time)

Time = distance / speed

Time = (70/100) × 1 light year

Distance = 8.7 light years

Time = 8.7 / 0.7 = 12.4285 years

Time = 12.43 years

B.) Mass of inter-stellar gas that collides with the spaceship can be calcuted by finding the product of the surface area of the cylindrical space ship and the mass of proton.

That is ;

surface area * mass of proton

Surface area of a cylinder = 2πrh + πr^2×Me

= 2πrh + Me×πr^2)

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

= 2× 235.714 + 28.285) × 1.673 * 10^-27

= 471.428 + 47.31 * 10^-27

= 471.428 + 4.73 × 10^-26

= 4.71.43kg approximately