In a common rest frame,event A happens on planet A and event B occurs on planet B 100 y later.If the space time interval between these two events is 90 ly,how far apart are the 2 planets in their common rest frame?
A)44 ly
B)35 ly
C)49 ly
D)54 ly

Question

Quizplus · Accepted Answer

The space-time interval between the two events is given by:$$s^2=c^2t^2-d^2$$where c is the speed of light, t is the time interval between the two events, and d is the distance between the two planets.We are given that the space-time interval is 90 ly and the time interval is 100 y. Substituting these values into the equation, we get:$$90^2=c^2(100)^2-d^2$$$$d^2=c^2(100)^2-90^2$$$$d^2=90000^2-8100$$$$d^2=8190000$$$$d=9044.51	ext{ ly}$$Therefore, the two planets are 9044.51 ly apart in their common rest frame.

In a Common Rest Frame,event a Happens on Planet a and Event