Flashing light beacon from Earth reaching spaceship moving away at 0.75c

In summary, a flashing light beacon emitted from Earth will have its signal affected by the relativistic effects as it reaches a spaceship moving away at 0.75 times the speed of light (0.75c). Due to the Doppler effect, the frequency of the light will appear redshifted for the spaceship, meaning the intervals between flashes will be longer than if the spaceship were at rest. This scenario illustrates the principles of special relativity, including time dilation and the impact of relative motion on the perception of light signals.
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neelbansal123
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New user has been reminded to please always show their work on schoolwork problems.
Homework Statement
You are on a spacecraft traveling away from the earth at 0.75 c. A beacon on earth flashes exactly once per second.

From the point of view of a person on earth, what is the time between one flash reaching your ship and the next?
Answer- 4 seconds
From your point of view, what is the time between one flash reaching your ship and the next?
Answer 2.6 seconds

No matter how I solve it I do not get the answers mastering physics says are correct. Any ideas?
Relevant Equations
Speed of light constant 3x10^8
Below
IMG_2838.jpeg
 
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You must share your effort in order to receive help via forum rules.
 
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IMG_2841.jpeg
 
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IMG_2841.jpeg
 
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neelbansal123 said:
View attachment 343142
Part A asks about the earth time of the flashes reaching your ship.
You don't need relativity to answer it. Just kinematics.
 
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Hill said:
You don't need relativity to answer it. Just kinematics.
What might help is a diagram (see Minkowski diagram) like this:

1712831602606.png

(everything in seconds):
Flash emitted at earth t=0 has ##x = ct##,
Flash emitted at earth t=1 reaches ship at t=4,
Flash emitted at earth t=2 arrives at t=8 etc.

##\ ##
 
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FAQ: Flashing light beacon from Earth reaching spaceship moving away at 0.75c

1. What happens to the frequency of the flashing light beacon as the spaceship moves away from Earth at 0.75c?

As the spaceship moves away from Earth at 0.75 times the speed of light (0.75c), the frequency of the flashing light beacon will be observed to decrease due to the Doppler effect. Specifically, the light will be redshifted, meaning that the wavelength of the light increases, and the frequency decreases as perceived by the crew on the spaceship.

2. How does the speed of the spaceship affect the perceived brightness of the beacon?

The perceived brightness of the flashing light beacon will decrease as the spaceship moves away from Earth. This is due to the inverse square law of light, which states that the intensity of light decreases with the square of the distance from the source. Additionally, the redshift will also play a role in reducing the perceived brightness, as the energy of the photons is lower when they reach the spaceship.

3. Can the crew on the spaceship still see the beacon if it is moving away at 0.75c?

Yes, the crew on the spaceship can still see the beacon, but the light will be redshifted and appear dimmer. Depending on the intensity of the beacon and the distance, it may be more difficult to see, but as long as the beacon emits enough light, it should still be detectable.

4. What is the time dilation effect on the flashing light beacon as observed from the spaceship?

Due to time dilation, the crew on the spaceship will perceive the flashing of the light beacon to be slower than it actually is. This is a consequence of the relativistic effects of traveling at a significant fraction of the speed of light. The time intervals between flashes will appear longer to the observers on the spaceship compared to how frequently the beacon flashes as seen from Earth.

5. How would the situation change if the spaceship were moving towards the beacon instead of away?

If the spaceship were moving towards the flashing light beacon instead of away, the frequency of the light would be blue-shifted, meaning that the wavelength would decrease and the frequency would increase. The crew would perceive the flashes to occur more frequently, and the beacon would appear brighter due to the Doppler effect, as they are moving into the wavefronts of the light emitted by the beacon.

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