Speed of light and year?

Question

Hi,

Assume that a galaxy is 93000 ly in diameter. A spaceship crossing the galaxy measures the galaxy's diameter to be a mere 8 ly.

(a) What is the speed of the spaceship relative to the galaxy?
1.04999999994c
0.89999999994c
0.59999999994c
0.79999999994c
0.94999999994c
0.99999999994c

(b) How long is the crossing time as measured in the galaxy's reference frame (in years)?


I converted the light years into meters and then took a ratio of the two. Am I on the right track? It also seems like I should be using the equation delta t = delta x / v.


Thanks!

Speed of the vessel.

Thanks!

Answer 1

No you are not on the correct track. In order to determine the speed of the ship, you need to take relativistic effects into account. Since the galaxy has shrunk in the direction of travel as measured in the ship frame, I must assume that the ship is travelling at very near light speed. The difference in length measurement between the two reference frames is easy to calculate using the Lorentz transform method, which can be found in any reasonably good modern physics text. I would recommend Tipler. Once you determine the speed of the ship in the galaxy reference frame, then it is simple to determine the time that it takes to cross the galaxy in the galaxy frame - the answer shouild be in the neighborhood of 10,000 years, I suspect.

Answer 2

not entirly sure what you are trying to calculate here. are you looking for the speed of the vessel or the speed of the galaxy itself. using the model you propose we would have to account for the various constants such as speed at wich teh galaxy movies through the universe, and more importantly how you would maintain your course in a straight line while the galaxy spins and shifts. If you could kindly clarify your question maybe I could answer it hypothetically for you vs trying to give you a rational answer.


if you cross the galaxy in 8 years you would be traveling 11625 times the speed of light. of course that means you did not meaasure the 93000LY galaxy to be 8 LYs since you far exceed the speed of light. takes the concept of the impossible to a whole new level. Remember, light year is a measure of distance, not speed, so if the ship measured the galaxy we would actually be dividing the known distance by the percieved time to calculate the acutal speed. Is that what you are looking for?