Calculating Speed of Light on a Spaceship: Earth Relative vs. Spaceship Relative

[tymartin]

Homework Statement

You're riding a fast spaceship going 7.52 x 107m/s and you turn on your flashlight. What's the speed of the light ray relative to the spaceship? What is its speed relative to the earth?

Homework Equations

The Attempt at a Solution

Deeply confused

 

[Doc Al]

Hint: Consider the postulates of Special Relativity. (You should be able to answer the questions immediately with no calculation.)

 

[nlightner]

.

I would first clarify the question by asking for more information. Specifically, I would want to know the reference frame for the speeds given - is the spaceship moving at 7.52 x 10^7 m/s relative to the Earth, or is this its speed in its own frame of reference? This is important because the speed of light is constant in all inertial reference frames, so the answer would be different depending on the reference frame being used.

Assuming the spaceship is moving at 7.52 x 10^7 m/s relative to the Earth, then the speed of light relative to the spaceship would also be 3.00 x 10^8 m/s, as measured by an observer on the spaceship. This is because the speed of light is always constant at 3.00 x 10^8 m/s, regardless of the relative motion of the observer.

However, if the spaceship is moving at 7.52 x 10^7 m/s in its own frame of reference, then the speed of light relative to the spaceship would be 3.00 x 10^8 m/s minus the speed of the spaceship (7.52 x 10^7 m/s). In this case, the speed of light relative to the Earth would still be 3.00 x 10^8 m/s, as measured by an observer on Earth.

In summary, the speed of light is always constant at 3.00 x 10^8 m/s, and its relative speed to the Earth or a spaceship would depend on the reference frame being used. It is important to clarify the reference frame when discussing relative speeds and velocities.