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 × 10027 kg as proton mass.
Because you are moving with an enormous speed, your mission from the previous problem
will be influenced by the effect of time dilation described by special relativity: Your spaceship
launches in June 2020 and returns back to Earth directly aer arriving at Sirius.
(a) How many years will have passed from your perspective?
(b) At which Earth date (year and month) will you arrive back to Earth?
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.
Because you are moving with an enormous speed, your mission from the previous problem
will be influenced by the effect of time dilation described by special relativity: Your spaceship
launches in June 2020 and returns back to Earth directly aer arriving at Sirius.
(a) How many years will have passed from your perspective?
(b) At which Earth date (year and month) will you arrive back to Earth?
The time for the astronauts going to space will be :
t= D /v
= 8.7c / 0.7c
=12.42 y (12 y 153 d).
From June 2020 it will be November 2032.
(b) It will take (for people on Earth) :
t e= 1−(v/c) ² t =² 12.42 / √ 1−(0.7) ²
=17.39 y (17 y 142 d).
From June 1, 2020 it will be October 21, 2037.
You will arrive back on earth in October 21, 2037.
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