Proper Time earth to Pluto

In summary: So when you compute the speed as distance/time, you'll get an answer like 0.5. Then you can just say that the speed is 0.5 times the speed of light, since I'm assuming you're working in units where c=1.In summary, the conversation discusses a spaceship traveling from Earth to Pluto and back in a total of 11 hours, assuming a constant speed and that Earth and Pluto are at rest relative to each other. The speed of the ship during each part of the journey is calculated using the equation speed=distance/time, and the time measured by the ship's clock during the entire trip can be found using the equation (1-v)^1/2 (change in t from a to b
  • #1
sarahaha288
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Homework Statement



A spaceship leaves earth, travels to Pluto (which os 5 hours of distance away at the time), and then returns to Earth in exactyly 11 hours later. assume the spaceships acceleration time is very short so it is always traveling at a constant speed. also assume that Earth and pluto are approximately at rest to each other and the sun during the journey.

a- what is the speed of the ship during each part of the journey?
b- calculate the time measured by the ships clock during the entire trip.

Homework Equations


speed= distance / time

(1-v)^1/2 (change in t from a to b)= proper time

The Attempt at a Solution



I'm not sure what to do because i don't understand how the spaceshp can travel at a constant speed and take 5 hours to get there and 5 hours to get back. I am missing something.
 
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  • #2
Since you wrote sqrt(1-v^2) it looks like you are working in units where the speed of light c=1. Then to say Pluto is 5 hrs away really means that it's (5hrs)*c away or 5 hours traveling at the speed of light. When working in units where c=1, you are sort of allowed to be sloppy and drop factors of c.
 
  • #3


I would first clarify some details about the scenario to fully understand it. For example, is the 5 hours of distance referring to the time it takes for the spaceship to travel from Earth to Pluto or the distance between Earth and Pluto? Also, is the acceleration time during the journey negligible or do we need to consider it in our calculations?

Assuming that the distance between Earth and Pluto is 5 hours of travel time for the spaceship and the acceleration time is negligible, we can approach the problem as follows:

a) The speed of the spaceship during the journey can be calculated using the equation speed = distance / time. Since the distance is 5 hours and the time is 5 hours for each leg of the journey (Earth to Pluto and Pluto to Earth), the speed during each part of the journey would be 1 hour per hour, or simply 1.

b) The proper time, or the time measured by the ship's clock, can be calculated using the time dilation equation (1-v)^1/2 (change in t from a to b) = proper time. Since the speed of the spaceship is 1 during each part of the journey, the time dilation factor would be (1-1)^1/2 = 0. This means that there would be no time dilation and the time measured by the ship's clock would be the same as the time experienced on Earth. Therefore, the total time measured by the ship's clock during the entire trip would be 11 hours (5 hours to Pluto + 5 hours back to Earth + 1 hour for the spaceship's clock to catch up with Earth's clock).

In conclusion, the speed of the spaceship during each part of the journey would be 1 hour per hour and the time measured by the ship's clock during the entire trip would be 11 hours. However, if any of the assumptions made (such as the negligible acceleration time) are not accurate, the results would differ. Further clarification of the scenario would be needed to provide a more accurate solution.
 

What is the proper time it takes for earth to reach Pluto?

The proper time it takes for earth to reach Pluto varies depending on the speed and trajectory of the spacecraft. The fastest spacecraft to reach Pluto was the New Horizons mission, which took 9.5 years to reach the planet. However, the average time it takes for a spacecraft to reach Pluto is around 12-13 years.

How far is the distance between earth and Pluto?

The distance between earth and Pluto varies due to the elliptical orbits of the planets. On average, the distance between earth and Pluto is about 3.7 billion miles (5.9 billion kilometers). However, at its closest approach, the distance can be as little as 2.66 billion miles (4.28 billion kilometers).

What is the proper time for a round-trip journey from earth to Pluto and back?

The proper time for a round-trip journey from earth to Pluto and back also depends on the speed and trajectory of the spacecraft. On average, the round-trip journey can take around 25 years. However, with the current technology, it would take much longer for a spacecraft to make a round-trip journey to Pluto.

How does the distance between earth and Pluto affect the proper time?

The distance between earth and Pluto does not significantly affect the proper time for a spacecraft to reach the planet. The main factors that affect the proper time are the speed and trajectory of the spacecraft, as well as any gravitational assists from other planets along the way.

What is the significance of proper time in space travel?

Proper time is an important concept in space travel as it allows us to calculate the most efficient and effective routes for spacecraft to reach their destinations. It also helps us understand the effects of time dilation and how time can pass differently for objects traveling at different speeds. Proper time calculations are crucial for the success of space missions and the safety of astronauts.

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