How Far Did Astronaut Sarah Travel During Her Trip?

Question:

If Astronaut Sarah leaves Earth in a spaceship at a speed of 0.280c relative to Earth and her destination is a star-system 12.5 light-years away, how far did she travel during the trip?

Answer:

Sarah traveled a distance of 12 light years during her trip.

When determining the distance Sarah traveled during her trip, we can apply the concept of length dilation. The formula for length dilation is:

L = L₀√(1 - v²/c²)

First, we calculate the original distance L₀ in meters:

L₀ = 12.5 light-years × 365 days/year × 24 hours/day × 3600 seconds/hour × 3 × 10^8 m/s

L₀ = 1.183 × 10^17 meters

Substitute the given values of v (0.28c) and L₀ into the formula:

L = 1.183 × 10^17 meters √(1 - (0.28c)²/c²)

L = 1.136 × 10^17 meters

Converting the distance L from meters to light years:

L = 1.136 × 10^17 meters / (365 days/year × 24 hours/day × 3600 seconds/hour × 3 × 10^8 m/s) light years

As a result, Sarah traveled a distance of 12 light years during her trip to the star-system.