Traveling to Another Galaxy: Can You Get There Alive?

[esb08]

Homework Statement

You wish to travel to another galaxy, which is 1,000,000 light years away. You'd like to be still alive when you get there. How fast must you travel? Given enough fuel, can you do this?

Homework Equations

t/t(proper)=gamma
v=v'+u/1+(uv'/c^2)

The Attempt at a Solution

my teacher gave us the solutions, and I would really like to know why i need to solve for gamma and what it means...please :(

 

[Fusilli_Jerry89]

as I don't have time to go through the derivation and what exactly gamma does I can tell you this:

Gamma = 1/sqrt(1-(v^2)/(c^2))

This means gamma is always bigger than or equal to 1.

For this question you want time dilation (obviously). You should know that when you travel faster relative to something else, your clock will run slower than the stationary clock, right?

This means that t' (time in rocket's frame) must be less that t (time in universe's frame).

Hence, t' = t/gamma. We need to know gamma in order to solve for velocity..
gamma = t/t'. Now we want t' to equal 50 years (I just chose a random number of years I want you to age).

Next, we must find t (the time it would take for the spaceship to get to the galaxy in the universe's frame). In this frame: t is just the distance in the universe's frame divided by the velocity in the universe's frame. This is just: 1 000 000/v.

Now we have one equation for gamma, and one for v and since both are related to each other, simply convert v to gamma in this equation, or convert the gamma above to v.


Things to remember:

when you move faster than another object, your time moves slower than the object's time. Hence why you will age slower in this question. Just remember, if gamma is 1 or greater, in order to take a time and make it smaller, you have to divide by gamma. If you multiply, then the opposite would happen.

Since the speed of light is c in all reference frames there are certain consequences..
Think of the mirror clock example.. In a stationary frame, the light just goes up and and so the time the light takes to go from one mirror to the other and back again is just the distance btwn the mirrors divided by c multiplied by 2. If a spaceship had one of these mirror clocks and was moving relative to you, you would also measure the speed of light to be c so:

since the ship is moving at some x velocity, there is also an x distance (perpendicular to the mirror clock) that the light has to travel through in order to reach the other mirror. Since the speed is the same, and the distance is more (light has to travel along the hypotenuse of this distance triangle) the time has to be less! Because speed is distance/time.

 

[esb08]

Thanks so much. You were very helpful, and I appreciate it

 

[Thoth]

the distance is 1,000,000 light years. light travels at 3x10^8 m/s (300,000,000 m/s). therefore at 300,000,000 m/s it will take 1,000,000 years to reach your destination.

to get there quicker, you would need to travel faster. let's say you wanted to get there in 10 years, not 1 million years

1 million years divided by 10 equals 100,000. therefore to get to your destination in 10 years, you would need to travel at 100,000 times the speed of light.

so 3x10^8 times by 1 x 10^5 = 3x10^13 or 30, 000, 000, 000, 000 m/s

 

[DaveC426913]

the distance is 1,000,000 light years. light travels at 3x10^8 m/s (300,000,000 m/s). therefore at 300,000,000 m/s it will take 1,000,000 years to reach your destination.

to get there quicker, you would need to travel faster. let's say you wanted to get there in 10 years, not 1 million years

1 million years divided by 10 equals 100,000. therefore to get to your destination in 10 years, you would need to travel at 100,000 times the speed of light.

so 3x10^8 times by 1 x 10^5 = 3x10^13 or 30, 000, 000, 000, 000 m/s

It would be difficult to be more wrong.


The problem doesn't ask how to get there faster than light can travel, the problem merely asks if you could get there within your lifetime. Read up on relativistic time dilation. Or simply read post 2.