Question

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.
​

Answer 1

Answer:

A.  8.87 years

Explanation:

given that

distance from earth to sirius is 8.7 light-years

speed of the space ship (v) = 70%

                                        0.7 x ( 3 X 10^8)

                                       = 2.1 X 10^8 m/s

Density of interstellar medium (s) = 1 hyd atom/m^3

The diameter of the spaceship is (l) =25 m

so we know that 1 day = 9.461 x 10^15 m

                            S= 8.23107 x 10^16

Therefore the time taken by a person on earth to reach Sirius is given by

t = s/v

    8.23107 x 10^15 / 2.1 x 10^8

t= 391955714.3 sec (s)    12.428 years

time  by someone on the spaceship is given as

T = ($(\sqrt{1-\frac{v^2}{c^2} } } )+$

T = $(\sqrt{1-(0.7)^2)} (391955714.3) sec$

T=279912368.1 sec (s)    8.87 years

Therefore the time elapsed by someone on the space ship is 8.87 years