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 × 10−27 kg as proton mass.

Answer 1

a) Time taken for the spaceship to reach Sirius, t' = 8.86 years = 9 years(approx)

b) The mass of the interstellar gas that collides with the spaceship, m' = 1.195 * 10^(-27) kg

Explanations:

The calculations are handwritten and attached as files below. However, the following steps were taken to arrive at the solutions

a) to calculate the time taken for the spaceship to reach Sirius

Step 1: calculate the time taken to reach Sirius from the perspective of the earth using time = distance/speed

Step 2: Use lorentz time dilation formula to calculate the equivalent time to reach Sirius from the perspective of the person in the spaceship

b) to calculate the mass of the interstellar gas

Step1: Calculate the new length of the spaceship using special relativity

Step 2 Get the new volume also by using the new length gotten

Step2: Get two equations for the original mass and the new mass using mass = density * volume

Step 3: Write the original mass in terms of the new mass and make necessary substitution.

Note: Check complete solution in the file attached.