Step-by-step explanation:
We can use the Lorentz transformation to calculate the distance to the star system as measured by an observer in the rocket ship.
The Lorentz transformation for length is:
L = L0 / sqrt(1 - v^2/c^2)
where L0 is the proper length (the distance as measured by an observer at rest with respect to the distance), v is the velocity of the rocket ship, c is the speed of light, and L is the length as measured by the observer in the rocket ship.
In this case, L0 = 38 trillion km, v = 0.68c, and c = 299,792.458 km/s.
Plugging these values into the equation, we get:
L = 38 trillion km / sqrt(1 - (0.68c)^2/c^2)
= 38 trillion km / sqrt(1 - 0.68^2)
= 38 trillion km / 0.748331
= 50.8 trillion km
Therefore, the distance to the star system as measured by an observer in the rocket ship is approximately 50.8 trillion km.