Question

8) What is the distance to a particular star system measured by an observer in a rocket ship traveling to the star system with a speed of 0.95c? (The distance is 37 trillion km as measured by an observer on Earth.)
____ km

9) A spacecraft has a velocity of 20 m/s and an acceleration of 40 m/s² and is descending to land on planet Y and slows down by 4 m/s every second. The strength of the planet's gravitational field is 7 N/kg. If the passengers in the spacecraft account for the forces they feel in terms of a single gravitational field, how strong would this field have to be?
____ N/kg

Answer 1

(8) Solution :-

The distance star from the observer on Earth L = 37 trillion km
                                                                         =37× 10 ⁹km

                                                                         =37× 10 ¹²m

Speed v = 0.95 c

we know from length contraction L ' = L √[ 1 - ( v² / c ² ) ]

                                                        = 1.155 ×10^13 km