Relativity of simultaneity (astronaut and simultaneous explosions.)

In summary: Start by drawing a straight line (world line) from the center of planet X to the center of planet Y. That line represents the astronaut's path, and it's 2 light-hours long.Draw a vertical line at the mid-point. That represents the event when the astronaut is midway between the planets.Draw two diagonal lines, one from the top of the vertical line to the beginning of the path (planet X) and one from the bottom of the vertical line to the end of the path (planet Y). Those two lines represent the two light-hours.Now draw two horizontal lines, one from the beginning of the path to the first diagonal line and one from the second diagonal line to the end of the path. Those lines represent the
  • #1
Gator93
1
0

Homework Statement



An astronaut is space-traveling from planet X to planet Y at a speed of 0.17c. When he is precisely halfway between the planets, a distance of 1 light-hour from each, nuclear devices are detonated. The explosions are simultaneous in the astronaut's frame. What is the difference in time of arrival of the flashes from the explosions as observed by the astronaut?

v = 0.17c = 51000000 m/s
x = 2(1.079E12)
t' = 0 is simultaneous?
t = ?

Homework Equations



t = (gamma)(t' + (vx'/c^2))

gamma = 1/(sqrt (1-B^2))

The Attempt at a Solution



1/(sqrt (1-0.17^2))
1/sqrt(0.9711)
= 1.014770943

(1.014770943)(0 + (51000000*2.158505698E12)/(9E16)
= 20.687 min?

Now I'm not seeing how the units follow through on this without taking it from sec to min, but I've arrived at this answer a few other ways... namely multple equations and setting them equal to see when the first flash would encounter the ship and also when the second flash would catch up to the ship, and taking the difference.

So, I was giving this as a multiple choice problem.
A) 14 min B) 0 min C) 56 min D) 28 min

There is not an E) other... but wouldn't put it past him... then again I'm not confident I'm doing it correctly.
 
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  • #2
Welcome to PF!

Hi Gator93! Welcome to PF! :smile:
Gator93 said:
An astronaut is space-traveling from planet X to planet Y at a speed of 0.17c. When he is precisely halfway between the planets, a distance of 1 light-hour from each, nuclear devices are detonated. The explosions are simultaneous in the astronaut's frame. What is the difference in time of arrival of the flashes from the explosions as observed by the astronaut?

You're making this too complicated :redface: …

first rewrite the question in the astronaut's frame …

what does it say? :smile:​
 
  • #3
You might try drawing a space-time diagram...
 

What is the relativity of simultaneity?

The relativity of simultaneity is a principle in Einstein's theory of special relativity, which states that the concept of simultaneity is relative and depends on the observer's frame of reference. This means that events that are simultaneous for one observer may not be simultaneous for another observer in a different frame of reference.

How does this principle apply to astronauts and simultaneous explosions?

In the context of astronauts and simultaneous explosions, the relativity of simultaneity means that the astronauts may observe the explosions as happening at the same time, but an observer on Earth may see them happening at different times. This is because the astronauts are in a different frame of reference, moving at high speeds relative to the Earth.

Why is the relativity of simultaneity important?

The relativity of simultaneity is important because it is a fundamental principle of special relativity and helps to explain the concept of time dilation. It also has significant implications for our understanding of space and time, and has been experimentally verified through various experiments and observations.

Can the relativity of simultaneity be observed in everyday life?

Yes, the relativity of simultaneity can be observed in everyday life. For example, if you are sitting on a train and someone outside the train is watching you, they may see you and the train as moving at different speeds. This means that events that appear simultaneous to you on the train may not appear simultaneous to someone outside the train.

How does the relativity of simultaneity affect our perception of time?

The relativity of simultaneity challenges the traditional concept of absolute time, and suggests that time is relative and can be experienced differently by different observers. This means that our perception of time may be influenced by our frame of reference and the relative motion between ourselves and other objects or observers.

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