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From the conditions of the foregoing problem determine the boost time tau_0 in the reference frame fixed to the rocket. Remember tau_0=int_(0)^(tau)sqrt(1-(v//c)^2)dt, where dt is the time in the geocentric reference frame. |
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Answer» SOLUTION :The boost time `tau_0` in the reference frame fixed to the rocket is related to the time `tau` elapsed on the EARTH by `tau_0=underset(0)overset(tau)intsqrt(1-v^2/c^2)dt=underset(0)overset(tau)INT[1-(((w^'t)/(c))^2)/(1+((w^'t)/(c) )^2)]^(1//2)dt` `=underset(0)overset(tau)int(dt)/(sqrt(1+((w^'t)/(c))^2))=c/wunderset(0)overset((w^'tau)//c)int (DXI)/(sqrt(1+xi^2))=c/w1n[(w^'tau)/(c)+sqrt(1+((w^'tau)/(c))^2)]` |
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