# Solving for the Speed to Reach a Star 240 Light Years Away

• MHB
• MermaidWonders
In summary, to reach a star 240 light years away in an 85-year human lifetime, the person on the spaceship would need to travel at a speed of 240 light years divided by 85 years, or approximately 2.82 times the speed of light. This would result in a time dilation of 240 years for the person on the spaceship, while only 85 years would pass for a person at rest on Earth. The equation used to calculate this is $\Delta t' = \frac{\Delta t}{\sqrt{1 - \frac{v^2}{c^2}}}$, where $\Delta t'$ is the time measured by the person on board the spaceship, $\Delta t$ is the time measured by
MermaidWonders
How fast would you have to go to reach a star 240 light years away in an 85-year human lifetime?

Here, I know that I'm supposed to find $v$, but I'm having a hard time setting up my equation(s) in order to reach the final answer. :(

MermaidWonders said:
How fast would you have to go to reach a star 240 light years away in an 85-year human lifetime?

Here, I know that I'm supposed to find $v$, but I'm having a hard time setting up my equation(s) in order to reach the final answer. :(

Let's start with a question. You do know that you can go 85 light years in 85 years at 1x Speed of Light, right?

MermaidWonders said:
How fast would you have to go to reach a star 240 light years away in an 85-year human lifetime?

Here, I know that I'm supposed to find $v$, but I'm having a hard time setting up my equation(s) in order to reach the final answer. :(
There is a wrinkle here. If we are talking about an observer on Earth then as tkhunny points out there must be some kind of misprint... It can't be done.

If you are talking about an observer on the flight we can do it. What do you know about time dilation? (See the section "Simple Inference of Velocity Time Dilation.")

Can you finish from here? If not just let us know.

-Dan

tkhunny said:
Let's start with a question. You do know that you can go 85 light years in 85 years at 1x Speed of Light, right?

Yes.

topsquark said:
There is a wrinkle here. If we are talking about an observer on Earth then as tkhunny points out there must be some kind of misprint... It can't be done.

If you are talking about an observer on the flight we can do it. What do you know about time dilation? (See the section "Simple Inference of Velocity Time Dilation.")

Can you finish from here? If not just let us know.

-Dan

I know that the time measured in the frame in which the clock is at rest is called the proper time, and so a moving clock runs slower (hence dilated).

MermaidWonders said:
I know that the time measured in the frame in which the clock is at rest is called the proper time, and so a moving clock runs slower (hence dilated).
So what we have here is
$$\displaystyle \Delta t' = \frac{\Delta t}{\sqrt{1 - \frac{v^2}{c^2}}}$$

where $$\displaystyle \Delta t'$$ is measured by the observer's clock and $$\displaystyle \Delta t$$ is the time in the moving frame, aka "proper time."

So one possibility is if we wish the moving frame to experience 85 years and the observer's frame to be 240 years, then $$\displaystyle \Delta t' = 240$$ and $$\displaystyle \Delta t = 85$$. Solve for v.

-Dan

topsquark said:
So what we have here is
$$\displaystyle \Delta t' = \frac{\Delta t}{\sqrt{1 - \frac{v^2}{c^2}}}$$

where $$\displaystyle \Delta t'$$ is measured by the observer's clock and $$\displaystyle \Delta t$$ is the time in the moving frame, aka "proper time."

So one possibility is if we wish the moving frame to experience 85 years and the observer's frame to be 240 years, then $$\displaystyle \Delta t' = 240$$ and $$\displaystyle \Delta t = 85$$. Solve for v.

-Dan

But isn't the light year a unit of distance? For instance, the 240 light years in this question would represent a certain distance?

topsquark said:

-Dan

What do you mean? It says "240 light years away"... I'm confused.

MermaidWonders said:
What do you mean? It says "240 light years away"... I'm confused.

Indeed, the distance traveled is $v\Delta t' = 240\text{ lightyear}$.
So we have $\Delta t' = \frac{240\text{ lightyear}}{v}$ and $\Delta t = 85\text{ year}$.

I like Serena said:
Indeed, the distance traveled is $v\Delta t' = 240\text{ lightyear}$.
So we have $\Delta t' = \frac{240\text{ lightyear}}{v}$ and $\Delta t = 85\text{ year}$.

Ah, OK, that makes sense. So is $\Delta t'$ the time measured by the person on board the spaceship, and 85 years measured by a person at rest on Earth?

MermaidWonders said:
Ah, OK, that makes sense. So is $\Delta t'$ the time measured by the person on board the spaceship, and 85 years measured by a person at rest on Earth?

It's the other way around.

I like Serena said:
It's the other way around.

## 1. How long would it take to reach a star that is 240 light years away?

The speed required to reach a star 240 light years away would depend on the type of spacecraft and propulsion system being used. However, assuming a constant speed of 30,000 kilometers per second, it would take approximately 800,000 years to reach the star.

## 2. Is it possible to travel at the speed of light to reach the star?

According to the theory of relativity, it is not possible for any object with mass to travel at the speed of light. Therefore, it is not possible to reach the star 240 light years away at the speed of light.

## 3. How does the distance to the star affect the speed required to reach it?

The distance to the star has a direct impact on the speed required to reach it. The farther the distance, the higher the speed required to cover that distance in a reasonable amount of time.

## 4. What are some potential challenges in solving for the speed to reach a star 240 light years away?

Some potential challenges in solving for the speed to reach a star 240 light years away include the limitations of current propulsion systems, the effects of relativity on time and space, and the potential hazards of traveling through interstellar space.

## 5. Can the speed to reach a star 240 light years away be calculated accurately?

Yes, the speed required to reach a star 240 light years away can be calculated accurately using mathematical equations and scientific principles. However, as mentioned before, the actual speed required may vary depending on various factors such as the spacecraft and propulsion system used.

Replies
6
Views
2K
Replies
1
Views
1K
Replies
9
Views
2K
Replies
15
Views
2K
Replies
5
Views
2K
Replies
5
Views
3K
Replies
27
Views
2K
Replies
2
Views
1K
Replies
130
Views
9K
Replies
5
Views
5K