Question

One of the primary goals of the Kepler space telescope is to search for Earth-like planets. Data gathered by the telescope indicates the existence of one such planet named Boralis orbiting a star 115 ly from our solar system. Consider an interstellar spaceship leaving Earth to travel to Boralis. The ship can reach 0.96c almost instantly and can also decelerate almost instantly. The ship is 159 m long in its reference frame.(a)What is the length of the moving ship (in m) as measured by observers on Earth

Answer 1

44.52m

Step-by-step explanation:

d = 115 ly

The ship travels at a Velocity, v = 0.96c

The ship is = 159m long

To calculate this we use the formula for length contraction

L = Lo/γ

We have γ = 1/√1-v²/c²

L = Lo√1-(0.96c)²/c²

= 159 x √1-0.9216

= 159 x √0.0784

= 159 x 0.28

= 44.52m is the length of the ship as measured by the observers on earth.