|MadSci Network: Physics|
Dear Iyappan, These are very interesting questions that involve two important results from Special Relativity, time dilation and the velocity addition law. In the first part of your question I think you are asking that if you are moving from the Earth at 70% of the speed of light, how much time has passed on your clock as measured by the Earth, after one hour has passed on the Earth. The answer for this comes from the time dilation equation t’ = t / (1 – v^2 / c^2)^(1/2) , where “t” is the time that has passed for you and t’ is the time as measured by the Earth. With v=0.7c and t’=1 hour we find t = 0.71hours or about 43 minutes. For the rocket at v=0.8c we find t = 0.60hours or 36 minutes. For the second part of your question, I think you’re asking about how you would measure the time passing on the rocket. To determine that, we first need to figure out how fast you would measure the speed of the rocket. To do this, we need to use the velocity addition law which states Vry = (Vre + Vey) / (1 + Vre Vey / c^2), where Vry is the velocity of the rocket with respect to (w.r.t.) you, Vre = 0.80c is the velocity of the rocket w.r.t. the Earth, and Vey=-0.70c is the velocity of the Earth w.r.t. you. This yields Vry = 0.23c , so you measure the rocket as moving at 23% the speed of light. This means that after 1 hour has passed for you, (using the above equation, again) you think that only 0.97hours, or about 58 minutes and 23 seconds have passed on the rocket. Well, I hope this answers your questions, Iyappan. If you would like some more information, please let us know. Sincerely, Jim Guinn
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