Question #122970
Problem A.1: Interstellar Mission (4 Points)

approximated density of

(a) Calculate the (b)

1

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 hydrogen atom/m

time it takes

your spaceship to reach Sirius.

Determine the mass of interstellar gas that collides with your spaceship during the mission.

Note: Use 1.673 x 10-27 kg as proton mass.
1
Expert's answer
2020-06-23T13:00:27-0400

Solution.

Earth to Sirius=8.7=8.7  light-years;

70%70\% of c;

d=6m;d=6m;

l=25m;l=25m;

mp=1.6731027kg;m_p=1.673\sdot10^{-27} kg ;

a)t=dv;t=\dfrac{d}{v};


t=8.70.7=12.43years;t=\dfrac{8.7}{0.7}=12.43 years;


b) S=πr2+2πrl;S=\pi r^2+2\pi rl;

S=π(3m)2+2π3m25m=159πm2=499.26m2;S=\pi\sdot (3m)^2+2\sdot\pi\sdot3m\sdot25m=159\pi m^2=499.26m^2;

h=8.79.461015m=8.231016m;h=8.7\sdot9.46\sdot10^{15}m=8.23\sdot10^{16}m;

V=499.26m28.231016m=4.1081019m3;V=499.26m^2\sdot8.23\sdot10^{16}m=4.108\sdot10^{19}m^3;

m=DV;D\sdot V;

m=1.6731027kg/m34.1081019m3=6.87108kg;m=1.673\sdot10^{-27}kg/m^3\sdot4.108\sdot10^{19}m^3=6.87\sdot10^{-8}kg;

Answer: a)t=12.43years;a) t=12.43years;

b)m=6.87108kg.b)m=6.87\sdot10^{-8}kg.




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