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.
Answers
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.
Explanation:
Calculate the time it takes your spaceship to reach Sirius:
t= D/v = 0.7c
D/0.7c = 8.7c / 0.7c =12.4 years.
(b) Determine the mass of interstellar gas that collides with the spaceship during the mission. The density of gas is 1 atom per cubic meter. The area of the front is
A= πd ² /4
The volume of space passed by the spaceship is
V=AD= πd ² D /4
The mass of the gas "eaten" by the spaceship's front is
m=ρV= ρπd² D/4
m= 4
1.673⋅10 ⁻ ²⁷π6² ⋅8.7⋅3⋅10 ⁸⋅365⋅24⋅3600
=3.89⋅10 ⁻⁹kg.