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 120 ly from our solar system. Consider an interstellar spaceship leaving Earth to travel to Boralis. The ship can reach 0.70c almost instantly and can also decelerate almost instantly. The ship is 175 m long in its reference frame. (a) What is the length of the moving ship (in m) as measured by observers on Earth? m (b) How much time (in years) will it take for the spaceship to travel from Earth to Boralis, as measured by an observer on Earth? years (c) How much time (in years) will it take for the spaceship to travel from Earth to Boralis, as measured by astronauts in the spaceship? years

Answer 1

al From special thorey of relativity, length contraction which states that moving object's length is shorter than its proper length. Grisen, proper length to 175m. Length of the moving ship when measured by Observers in earth LoL. LE L = 95.85 m dry. from time-diration theorey time masured from stationary frame of a clock in a clock in moring frame is slower than the clock at stationary fame, 1758 1- 0.76 be T- 1/ --202 120x9.461x10' 0.7 X 3x108 0.76 - T = 312.99 year Wren masured by astronauts in the spaceship 120x9.461 x 1015 = 171.43 s year. 0.7x3x108