Our Milky Way galaxy is 100,000 ly in diameter. A spaceship...

Our Milky Way galaxy is 100,000 ly in diameter. A spaceship crossing the galaxy measures the galaxy's diameter to be a mere 1.0 ly.
a. What is the speed of the spaceship relative to the galaxy?
b. How long is the crossing time as measured in the galaxy's reference frame?

Key Concepts

Time Dilation

Time dilation refers to the effect where time passes more slowly for an observer in motion relative to a stationary observer. This means that the duration of events, such as the time it takes for a spaceship to cross the galaxy, will be measured differently in different inertial frames, and is an essential concept for understanding how time intervals transform under high-speed travel.

Length Contraction

Length contraction is a relativistic effect wherein an observer in motion relative to an object measures the object's length to be shorter than the proper length measured in the object’s rest frame. In the problem, the galaxy’s diameter appears contracted from the perspective of the fast-moving spaceship, illustrating this concept.

Inertial Reference Frames

Inertial reference frames are coordinate systems in which objects either remain at rest or move at a constant velocity when no net force is acting on them. The differences in measurements, such as distance and time, between observers in different inertial frames (like a spaceship versus a stationary galaxy) result in phenomena explained by special relativity.

Special Relativity

Special Relativity is the theory that describes the physics of objects moving at significant fractions of the speed of light. It postulates that the laws of physics are the same in all inertial frames and that the speed of light in a vacuum is constant, leading to surprising effects such as time dilation and length contraction when objects travel at relativistic speeds.

Transcript

Please give Ace some feedback