Final answer:
According to the theory of relativity, when an object moves at high speeds, its length appears shorter to an observer in a different frame of reference. This phenomenon is known as length contraction. The length of the spaceship as measured by the inhabitants of the star system can be calculated using the formula L' = L / γ, where L is the length of the spaceship as measured by the passengers and γ is the Lorentz factor.
Step-by-step explanation:
According to the theory of relativity, when an object moves at high speeds, its length appears shorter to an observer in a different frame of reference. This phenomenon is known as length contraction. The formula for length contraction is given by:
L' = L / γ
Where L' is the length of the spaceship as measured by the inhabitants of the star system, L is the length of the spaceship as measured by the passengers, and γ is the Lorentz factor.
In this case, the length of the spaceship according to its passengers is given as 540 m. Therefore, using the formula for length contraction, we can calculate the length of the spaceship as measured by the inhabitants of the star system:
L' = 540m / γ
Since the spaceship is moving at a sub-light speed, γ can be calculated using the formula:
γ = 1 / √(1 - (v^2/c^2))
Substituting the given values, we can calculate γ and then find the length of the spaceship as measured by the inhabitants of the star system.