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 x 10^27 kg as proton mass.
Answers
Given that,
Distance = 8.7 lye
Speed = 70%
Diameter = 6 m
Length = 25 m
(a). We need to calculate the time
Using formula of speed
Where, d = distance
v = velocity
Put the value into the formula
We need to calculate the time dilation
Using formula of time dilation
Put the value into the formula
We need to calculate the value of Lorentz factor
Using formula of Lorentz factor
Put the value into the formula
(b). According to relativity,
Suppose the spaceship moves along x- axis
The spaceship's length will be change
The volume of spaceships is
The original volume of spaceships is
The mass of hydrogen atom is
The original mass is
We need to calculate the mass of interstellar gas
Due to length transformation mass will be change
Put the value of l'
Put the value into the formula
Hence, (a). The time takes your spaceship to reach Sirius in 12.4 years.
(b). The mass of interstellar gas is