Solving for Time: Paradox Equations for Astronauts Near Light Speed

[NeroBlade]

Hi

Do any of you guys know what equations or formulas I should be using for questions like "If A is on Earth and B is an Astronaut traveling near the speed of light". Calculate the duration of B's journey to A and the duration of B's journey according to B.

I assume that B's time calculation (The proper time) is less than the time calculated in A's frame. I'm puzzled when the equation involving gamma was involved which I think is the Time Factor.

Could you tell me which equations should I be looking at for those 2 situations other than c = s/t

 

[Doc Al]

I assume that B's time calculation (The proper time) is less than the time calculated in A's frame. I'm puzzled when the equation involving gamma was involved which I think is the Time Factor.

Gamma, the Lorentz factor, is involved with both time dilation and length contraction.

Could you tell me which equations should I be looking at for those 2 situations other than c = s/t

That's the big one. Realize that distances are contracted for the moving observer.

 

[kerimek]

Hello!

When dealing with situations involving astronauts traveling near the speed of light, we must take into account the effects of special relativity on time. The equations you will need to use are the time dilation equation, which is t = t0 / √(1 - (v^2 / c^2)), and the length contraction equation, which is L = L0 √(1 - (v^2 / c^2)). Here, t0 represents the time in the stationary frame (in this case, A's frame), t represents the time in the moving frame (B's frame), v represents the velocity of the astronaut, c represents the speed of light, L0 represents the length of an object in the stationary frame, and L represents the length of the same object in the moving frame.

To solve for the duration of B's journey to A, you will need to use the time dilation equation. Plug in the values for t0 and v, and solve for t. This will give you the time in A's frame. To find the duration of B's journey according to B, you will need to use the length contraction equation. Plug in the values for L0 and v, and solve for L. This will give you the length of the journey as perceived by B.

The time factor, gamma, is also important to consider when dealing with time dilation. It is represented by the symbol γ and is equal to 1 / √(1 - (v^2 / c^2)). This factor takes into account the effects of special relativity on time and is used in the time dilation equation.

I hope this helps you in solving for time in these types of situations. Remember to always take into account the effects of special relativity when dealing with astronauts traveling near the speed of light. Good luck!