# Relativity: Spaceship travel times and distances

• annalian
In summary, the conversation discusses the time it takes for a cosmic ship traveling at 0.96 c to reach a star located 95.0 light years away from Earth. The equation t=L/v is used to calculate the time it takes for the ship to reach the star from Earth, which is 99 years. The equation Lr=L*sqrt(1-v^2/c^2) is used to calculate the time it takes for the ship to reach the star from its own perspective, which is 26.6 years. The equation tr=Lr/v is used to calculate the time it takes for the ship to reach the star from the perspective of an observer on the ship, which is 27.7 years.
annalian

## Homework Statement

A star is 95.0 year lights away from Earth. How much time does it take to a cosmic ship, which moves with speed 0.96 c, to reach the star, if it is measured from a watcher from a) Earth a)ship c)What si the distance of trip, based on the viewer from the ship?

## Homework Equations

t=L/v
Lr=L*sqrt(1-v^2/c^2)

## The Attempt at a Solution

a) t=L/v=99 years
c) Lr=L*sqrt(1-v^2/c^2)=26.6 years
b) tr=Lr/v=27.7 years.
I'm not sure if for this I should use tr=t/sqrt(1-v^2/c^2). Which one is the best to use because the results are different. But if I use tr=t*sqrt(1-v^2/c^2) it has the exact same result. If 27.7 years is the correct answer, then why should the length contract and time not dilate?

Last edited:
Is your problem description complete ?
In part a) , what do you use for L and what do you use for v to get 99 y ?

BvU said:
Is your problem description complete ?
In part a) , what do you use for L and what do you use for v to get 99 y ?
I had forgotten to put the speed. it is 0.96 c

## 1. What is relativity and how does it apply to spaceship travel?

Relativity is a scientific theory proposed by Albert Einstein that describes the relationship between space and time. It explains that the laws of physics are the same for all non-accelerating observers, and that the speed of light is constant for all observers. This theory applies to spaceship travel because it affects how time and distance are perceived by observers traveling at high speeds.

## 2. How does relativity affect the travel time of a spaceship?

According to the theory of relativity, time is relative and can be affected by the speed of an object. As a spaceship moves at high speeds, time slows down for the passengers on board. This means that the travel time experienced by the passengers will be shorter than the time experienced by an observer on Earth.

## 3. Can relativity also affect the distance traveled by a spaceship?

Yes, relativity also affects the perception of distance for objects traveling at high speeds. As the speed of a spaceship increases, the distance it travels will appear shorter to an observer on Earth. This is known as length contraction, where the length of an object appears shorter when moving at high speeds.

## 4. How does the theory of relativity impact space exploration?

The theory of relativity has a significant impact on space exploration because it explains the effects of traveling at high speeds, such as time dilation and length contraction. These effects must be taken into account when planning missions and calculating travel times and distances. Without the understanding of relativity, our current understanding and capabilities in space exploration would be limited.

## 5. Is there any evidence to support the theory of relativity in regards to space travel?

Yes, there is a significant amount of evidence that supports the theory of relativity in regards to space travel. One of the most famous examples is the Hafele-Keating experiment, where atomic clocks were used to measure the effects of time dilation for objects in motion. The results of this experiment confirmed the predictions of relativity and provided evidence for its validity.

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