γ=1/√(1-β^2),β=0.8,γ=5/3.
(1)t=γ*τ=(5/3)*30min=50min,所以是12:50;
(2)x=v*t=0.8c*50min=40min*c;
(3)△t=x/c=40min,12:50+40min=13:30,所以是13:30;
(4)地球上的观察者在接受到信号后发出回答信号按地球上的坐标飞船位置是90min*0.8c=72c,设光信号追上飞船是飞船按地球上的坐标是X,时刻是T。T=72min*c/(c-v)+90min=72min*c/(c-0.8c)+90min=450min,X=v*T=0.8c*450min=360min*c.
T'=γ(T-v/c^2 *X)=270min(洛仑兹变换),
12:00+270min=16:30,所以是16:30。