How Does High-Speed Travel Affect Time Perception?

[xquarky]

Hello guys,

I have a problem solving these two questions, anybody come up with any idea will be appreciated...

1. A jet plane circles the Earth at the equator with a speed of Mach 4. By how much time is the pilot’s watch slow when it lands?

2. A spaceship leaves Earth for a distant star. It has an acceleration g in its rest system for five Earth years, and then it decelerates at g, coming to rest. It then reverses the process to return to Earth. (Do this problem using light years (LY). Calculate c and g in those units.)

a. How far from Earch does it come to rest?
b. The trip takes 20 Earth years. How many years have passed on Earth?

 

[tiny-tim]

Welcome to PF!

anybody come up with any idea will be appreciated...

1. A jet plane circles the Earth at the equator with a speed of Mach 4. By how much time is the pilot’s watch slow when it lands?

Hi xquarky! Welcome to PF!

Idea: what is Mach4 as a fraction of the speed of light?

and how long is the equator?

and what is the formula for time dilation?

 

[Moetasim]

I would approach these questions using the principles of relativity and time dilation. In the first question, since the jet plane is traveling at a high speed of Mach 4, it is experiencing time dilation due to its velocity. This means that time on the plane is passing slower compared to someone on the ground. Therefore, when the pilot lands, their watch will be slow by a small amount, but it would depend on the duration of the flight and the exact speed of the plane.

In the second question, we are dealing with both acceleration and deceleration, which also affect time dilation. The spaceship's acceleration of g in its rest system means that it is experiencing time dilation as well. This would cause time to pass slower on the spaceship compared to Earth. When it reaches its destination and decelerates, it will experience time dilation in the opposite direction, causing time to pass faster on the spaceship compared to Earth.

To answer part a, we would need to know the exact speed and acceleration of the spaceship. However, using the concept of time dilation, we can calculate the distance traveled by the spaceship in Earth's reference frame. This would be 5 light years for the first leg of the journey and 5 light years for the return journey, making a total distance of 10 light years.

For part b, since the trip takes 20 Earth years, we can use the concept of time dilation to calculate the time passed on Earth. This would be 20/γ, where γ is the time dilation factor, which can be calculated using the speed and acceleration of the spaceship in Earth's reference frame. This would give us the number of years that have passed on Earth.

Overall, these questions highlight the fascinating phenomenon of time dilation in relativity and how it affects our perception of time. Further calculations and assumptions would be needed to provide more precise answers, but the principles of relativity and time dilation would be key in solving these problems.