MadSci Network: Physics
Query:

Re: A space rocket is moving at 80% of light speed, I m moving at 70% of light

Date: Wed Oct 15 11:53:08 2008
Posted By: Jim Guinn, Staff, Science, Georgia Perimeter College
Area of science: Physics
ID: 1223778192.Ph
Message:

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 youre 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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