A question about sepcial relativity

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In summary, an astronaut on the Helios satellite travels to Jupiter and back in 75 days, with an average speed of a quarter of a million km/h relative to Earth. The time difference between the clock on Earth and the one on the satellite can be calculated by finding the speed of the satellite as a multiple of c, and multiplying it by 75 days converted into seconds.
  • #1
wowolala
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An astronaut traveling on the Helios satellite (the fastest human made craft) goes on a trip to Jupiter and back in 75 days as measured by an observer on the Earth. If the average speed of the satellite is a quarter of a million km/h with respect to the Earth , what is the time difference ( in seconds) between the time recorded by the clock on the Earth and the one on board the satellite?



honestly, i am really confused on this part , can somebody help me?

thx so much
 
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  • #2
Hi wowolala! :smile:

Find the speed, v (as a multiple of c).

Then the clock on the satellite will go slow by … ?

Then multiply by the time (75 days converted into seconds). :smile:
 
  • #3
for your question! I can help explain this concept for you. Special relativity is a theory that explains how time and space are affected by the motion of objects. In this scenario, the astronaut on the Helios satellite is traveling at a very high speed (a quarter of a million km/h) compared to the observer on Earth. According to special relativity, time will pass slower for the astronaut on the satellite compared to the observer on Earth.

To calculate the time difference between the clocks on Earth and the satellite, we can use the formula t' = t / √(1 - v^2/c^2), where t' is the time experienced by the astronaut, t is the time experienced by the observer on Earth, v is the relative speed between the two objects, and c is the speed of light.

In this case, we know that the average speed of the satellite (v) is a quarter of a million km/h, which is equivalent to 69,444.4 m/s. The speed of light (c) is approximately 299,792,458 m/s. Plugging these values into the formula, we get t' = t / √(1 - (69,444.4)^2 / (299,792,458)^2).

Solving for t', we get t' = t / √(1 - 0.0000000000000000000232) = t / 0.9999999999999999999768.

This means that for every 1 second that passes on Earth, only 0.9999999999999999999768 seconds will pass on the satellite. To find the time difference, we can subtract the two values: t' - t = t / 0.9999999999999999999768 - t = 0.0000000000000000000232t.

Since we know that the astronaut traveled for 75 days, or 6,480,000 seconds, we can multiply this value by the time difference to get the actual time difference in seconds: 6,480,000 x 0.0000000000000000000232 = 0.00000000000000014976 seconds.

In conclusion, the time difference between the clocks on Earth and the satellite is approximately 0.00000000000000014976 seconds. This may seem like a very small amount, but it is a significant effect
 

1. What is special relativity?

Special relativity is a theory in physics that describes how time and space are affected by the motion of objects in a non-accelerated (inertial) frame of reference.

2. Who developed the theory of special relativity?

The theory of special relativity was first developed by Albert Einstein in 1905.

3. What are the key principles of special relativity?

The key principles of special relativity are the principle of relativity, which states that the laws of physics are the same for all observers in uniform motion, and the principle of the constancy of the speed of light, which states that the speed of light is the same for all observers regardless of their relative motion.

4. How is special relativity different from general relativity?

Special relativity deals with objects in a non-accelerated frame of reference, while general relativity also includes the effects of gravity and acceleration. Special relativity is a special case of general relativity.

5. What are some real-world applications of special relativity?

Special relativity has led to the development of technologies such as GPS and particle accelerators, and has also played a crucial role in the development of nuclear energy. Additionally, special relativity has greatly contributed to our understanding of the universe and the behavior of objects at high speeds.

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