Exercise 6.9.9

Answers

1.

The distance from earth to the star is

b

as measured on

C

2.

At time

t

, the space-time coordinates of the star relative to

S^{'}

and

C^{'}

are

B_{v} (\begin{matrix} b \\ 0 \\ 0 \\ t \end{matrix}) = \frac{1}{\sqrt{1 - v^{2}}} (\begin{matrix} b - vt \\ 0 \\ 0 \\ t - bv \end{matrix}) .

3.

Compute

x^{'} + t^{'} v

to eliminate the parameter

t

x^{'} - t^{'} v = \frac{1}{\sqrt{1 - v^{2}}} b (1 - v^{2}) = b \sqrt{1 - v^{2}} .

Hence we get the result.

4.

(a)

The speed that the star comes to the astronaut should be

\frac{d x^{'}}{d t^{'}} = - v .

Hence the astronaut feel that he travels with the speed $v$ .

(b)

In the astronaut’s mind, he leave earth at

t^{'} = 0

. Hence in

S

the earth is at

b \sqrt{1 - v^{2}}

jephianlin

2011-06-27 00:00