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

Answer:

A)3750 days

I did the rule of 3

v= d/t or t=d/v

B)7,267,940 x 10^-11

I don´t know with its right

Does someone arrive in other value?

I would like to know

In the second exercise

A) 20 years and 300 days

b) august 2047

Answer 2

Answer:

(a) The time taken by the spaceship to reach Sirius is 12.4 years.

(b) The mass of the interstellar gas that collides with your spaceship during the mission is $3.89 * 10^{-9} kg$.

Step-by-step explanation:

Given:

Distance (D) = 8.7 light years = 8.7c

Speed (v) = 70% the speed of light = 0.7c

Diameter (d) = 6m

Length (l) = 25m

To find:

Time taken by the spaceship to reach Sirius (t)

Mass of the interstellar gas collided (m)

Step 1: To find the time taken by the spaceship to reach Sirius

We know that, speed = distance/time

Therefore,

$time= \frac{distance}{speed}$ or $t = \frac{D}{v}$

Substituting the given values, we get

$t=\frac{8.7c}{0.7c}$

$t=12.4$

Therefore, the time taken is 12.4 years.

Step 2: To determine the mass of interstellar gas that collides with the spaceship

The density of the gas is given to be 1 hydrogen atom per cubic meter. The area of the front is

$A=\frac{\pi d^{2} }{4}$

The volume of space passed by the spaceship is

$V=AD$

$V=\frac{\pi d^{2}D }{4}$

Therefore, the mass of the gas that collided with the spaceship is given by

m = ρV

$m=(\frac{\pi d^{2}D }{4})$ * ρ

$m=\frac{1.673*10^{-27}\pi (6^{2})(8.7)(3*10^{8})(365)(24)(3600) }{4}$

$m=3.89*10^{-9}$

Therefore, the mass of the interstellar gas is 3.89×(10^-9) kg.

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