# Relatvitiy - Spaceship traveling into Galaxy

• Nitric
In summary: The other length should be the time it would take for the spaceship to travel that distance in the galaxy's frame, or 31712.47 * (1-v^2/c^2) = 25 years. In summary, the spaceship would need to travel at a uniform speed of v=d/t in order to make the trip in 25 years.
Nitric
1.The radius of our galaxy is approx. 3x10^20 m. A spaceship sets out to cross the galaxy in 25 years, as measured on board the ship. With what uniform speed does the spaceship need to travel? How long wold the trip take, as measured by a timepiece stationed on Earth?
2. v=d/t
3. So far I have converted the 25 years into seconds using proportions of 1 yr = 31556952 to get 788923800 seconds in 25 years. I found the velocity using v=d/t. d = radius of galaxy and t = 788923800 seconds

I am not sure if I am doing this right, and what do I have to do find out how long this trip would take? I don't think my distance is correct

thanks

Nitric said:
1.The radius of our galaxy is approx. 3x10^20 m. A spaceship sets out to cross the galaxy in 25 years, as measured on board the ship. With what uniform speed does the spaceship need to travel? How long wold the trip take, as measured by a timepiece stationed on Earth?

2. v=d/t
You can't use that equation with the values given since the "d" is given in the frame of the galaxy and the "t" is in the frame of the spaceship. You need to use all values in one frame. You could express the time it takes in the frame of the galaxy in terms of the time in the frame of the spaceship. If it takes 25 yrs in the frame of the ship, how long does it take in the frame of the galaxy? (you can't get a number but you can find an expression in terms of the 25 years and of the speed). Once you have that time "t'", then you may use v = d/t'. And you will be able to solve for the speed v.

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Oops, nrgd has given a far better answer! I fear I missed something - not surprising with relativity.

nrqed said:
You can't use that equation with the values given since the "d" is given in the frame of the galaxy and the "t" is in the frame of the spaceship. You need to use all values in one frame. You could express the time it takes in the frame of the galaxy in terms of the time in the frame of the spaceship. If it takes 25 yrs in the frame of the ship, how long does it take in the frame of the galaxy? (you can't get a number but you can find an expression in terms of the 25 years and of the speed). Once you have that time "t'", then you may use v = d/t'. And you will be able to solve for the speed v.
I knew there was something wrong with using the radius as my d. thanks for that, but I'm still unsure of how to attack the problem

Nitric said:
I knew there was something wrong with using the radius as my d. thanks for that, but I'm still unsure of how to attack the problem

If it takes 25 years in the ship's frame, it will take (gamma times 25) years as measured in the galaxy's frame.

I got through a little bi t of the problem. I learned that I had to convert the radius of the galaxy into light years and use it as the length.

Converting 3x10^20m to lights years is -> 31712.47 light years. I have to use the formula L(v) = L_0 * sqrt(1-v^2/c^2) Now I have two lengths in this equation, I have one of the length (31712.47 lt yrs) what should be the other length? I am trying to solve for velocity from that equation ( L(v) = L_0 * sqrt(1-v^2/c^2) )

## 1. What is the theory of relativity and how does it relate to spaceship traveling into a galaxy?

The theory of relativity, developed by Albert Einstein, is a fundamental principle in physics that explains how objects move and interact with each other in relation to space and time. This theory is crucial in understanding the behavior of a spaceship traveling into a galaxy because it takes into account the effects of gravity and the curvature of space-time.

## 2. How does the theory of relativity affect the speed of a spaceship traveling into a galaxy?

The theory of relativity states that the speed of light is the maximum speed at which any object can travel. This means that no matter how fast a spaceship is traveling, it can never exceed the speed of light. As the spaceship approaches the speed of light, time dilation and length contraction occur, making it more difficult for the spaceship to reach its destination.

## 3. Can a spaceship travel faster than the speed of light?

No, according to the theory of relativity, nothing can travel faster than the speed of light. This is a fundamental principle in physics and has been proven through numerous experiments and observations. The speed of light is approximately 299,792,458 meters per second, which is incredibly fast, but it is still the maximum speed that any object can travel.

## 4. How does the theory of relativity impact the perception of time during spaceship travel into a galaxy?

The theory of relativity states that time is relative and can be affected by the speed and gravitational pull of an object. As a spaceship travels closer to the speed of light, time dilation occurs, causing time to slow down for the astronauts on board. This means that while they may only experience a few months of time, years may have passed on Earth.

## 5. Can the theory of relativity be applied to all forms of space travel?

Yes, the theory of relativity is a fundamental principle in physics and applies to all forms of space travel. Whether it is a spaceship traveling to a nearby planet or a mission to a distant galaxy, the theory of relativity must be taken into consideration to accurately predict the behavior and movement of objects in space.

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