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- Homework Statement
- A message is sent via radio wave (λ = 10 m) from Earth to a nearby star, Proxima Centauri, which lies 1.3 parsecs from Earth. A parsec is a unit of length and 1 parsec = 3.1 × 10^16m. How long will it take the message to reach Proxima Centauri traveling through vacuum?

(a) 0 yrs, the message arrives instantly.

(b) 1.38 yrs

(c) 4.26 yrs

(d) 255.0 yrs

(e) 1.38 × 108 yrs

- Relevant Equations
- t = t0/γ (time dilation)

l = γl0 (length contraction)

t0: proper time

l0: proper length

Radio wave travels at the speed of light 3x10^8 (m/s)

Converting the distance to meter: 1.3 x 3.1x 10^16 = 4.03x10^16m

The time it takes in our Earth frame of reference is: 4.03x10^16m/3x10^8 (m/s) = 4.26 years

The answer is B

But wouldn't the time in light's frame of reference be 0 and it's length be infinite?

If it was another particle traveling at near light speed than it it's frame of reference, the time and distance it has to travel are still given by time dilation and length contraction formulas right?

Converting the distance to meter: 1.3 x 3.1x 10^16 = 4.03x10^16m

The time it takes in our Earth frame of reference is: 4.03x10^16m/3x10^8 (m/s) = 4.26 years

The answer is B

But wouldn't the time in light's frame of reference be 0 and it's length be infinite?

If it was another particle traveling at near light speed than it it's frame of reference, the time and distance it has to travel are still given by time dilation and length contraction formulas right?