Final answer:
The inquiry is about using the formula for length contraction in special relativity to calculate the length of a spaceship moving at high speed relative to an Earth-bound observer.
Step-by-step explanation:
The question you've asked pertains to the concept of length contraction in the field of physics, specifically in the context of special relativity. Length contraction is a phenomenon predicted by the Lorentz transformation equations, which describe how measurements of time, length, and other physical quantities differ for observers in different inertial frames of reference that are moving relative to each other at high velocities close to the speed of light (c).
To find the length of an object, such as a spaceship, as observed from a different frame of reference, one could use the Lorentz contraction formula:
L' = L * sqrt(1 - (v^2/c^2)), where L is the proper length (the length of the object as measured in the frame where it is at rest), v is the relative velocity between the observer and the moving object, and c is the speed of light.
In the example provided, the spaceship is 200 m long in its own frame of reference (board the spaceship) and is moving at 0.970c relative to Earth. Using the formula, we can calculate the observed length (L') from the Earth frame:
L' = 200 m * sqrt(1 - (0.970c)^2/c^2)
Calculating this will provide the length of the spaceship as seen by an Earth-bound observer, demonstrating the effect of length contraction.