Question

Arth and Sun are 8.33 light-minutes apart. Event A occurs on Earth at time t = 0, and event B on the Sun at time t = 2.45 min, as measured in the Earth-Sun frame. Find the time order and time difference between A and B for observers

a) moving on a line from Earth to Sun at 0.75c
b) moving on a line from Sun to Earth at 0.75
c) moving on a line from Earth to Sun at 0.294c.

Answer 1

For observers moving from Earth to Sun or Sun to Earth at different velocities, the time order of events will remain the same as observed from the Earth-Sun frame, but the time difference between events will vary due to time dilation.

Step-by-step explanation:

a) For observers moving on a line from Earth to Sun at 0.75c, the time order of events A and B will be the same as observed from the Earth-Sun frame. The time difference between A and B will be the same as measured in the Earth-Sun frame, which is 2.45 minutes.

b) For observers moving on a line from Sun to Earth at 0.75c, the time order of events A and B will also be the same as observed from the Earth-Sun frame. The time difference between A and B will be the same as measured in the Earth-Sun frame, which is 2.45 minutes.

c) For observers moving on a line from Earth to Sun at 0.294c, the time order of events A and B will still be the same as observed from the Earth-Sun frame. However, the time difference between A and B will be different due to time dilation.

To calculate the time difference, we can use the equation for time dilation: Δt' = Δt / sqrt(1 - v^2/c^2), where v is the velocity of the observer.

Plugging in the values, Δt' = 2.45 minutes / sqrt(1 - 0.294^2) = 2.56 minutes.