Answer to Question #122844 in Astronomy | Astrophysics for annie

Question #122844
Interstellar Mission:
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 × 10−27 kg as proton mass.
1
Expert's answer
2020-06-21T20:13:52-0400

The time it takes your spaceship to reach Sirius from the viewpoint of observers left on the Earth is


t=Dv=8.7c0.7c=12.43y.t=\frac{D}{v}=\frac{8.7c}{0.7c}=12.43^\text{y}.


The mass of interstellar gas that collides with your spaceship during the mission can be found by determining the volume of space that the spaceship passes through:


V=AD=πd24D.V=AD=\frac{\pi d^2}{4}D.

Then the mass of gas will be


m=ρV=ρπd2D4=3.886109 kg.m=\rho V=\frac{\rho\pi d^2D}{4}=3.886\cdot10^{-9}\text{ kg}.

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