Question

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.

Answer 1

Solution.

Earth to Sirius$=8.7$  light-years;

$70\%$ of c;

$d=6m;$

$l=25m;$

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

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

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

b) $S=\pi r^2+2\pi rl;$

$S=\pi\sdot (3m)^2+2\sdot\pi\sdot3m\sdot25m=159\pi m^2=499.26m^2;$

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

$V=499.26m^2\sdot8.23\sdot10^{16}m=4.108\sdot10^{19}m^3;$

m=$D\sdot V;$

$m=1.673\sdot10^{-27}kg/m^3\sdot4.108\sdot10^{19}m^3=6.87\sdot10^{-8}kg;$

Answer: $a) t=12.43years;$

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