Question

the speed of a spacecraft moving between Earth and Mars at an instant when earth and mars are 2.4into10^11 m apart is v=0.8c. the distance between them measured from the frame where they are at rest.what is the distance between E and M in the spacecraft frame.and what time elapses betewen crossing E and reaching M.

Answer 1

Answer on Question #67703, Physics / Mechanics | Relativity

the speed of a spacecraft moving between Earth and Mars at an instant when earth and mars are 2.4into10^11 m apart is v=0.8c. the distance between them measured from the frame where they are at rest.what is the distance between E and M in the spacecraft frame.and what time elapses between crossing E and reaching M.

Find: L – ? t – ?

Given:

$$L_0 = 2.4 \times 10^{11} \text{ m}$$ $$v = 0.8 \text{ c}$$ $$c = 3 \times 10^8 \text{ m/s}$$

Solution:

Length contraction: $L = L_0 \sqrt{1 - \frac{v^2}{c^2}}$ (1)

Of (1) $\Rightarrow$ $L = 1.44 \times 10^{11} \text{ m}$

Time: $t = \frac{L_0}{v}$ (2)

Of (2) $\Rightarrow$ $t = 10^3 \text{ s}$

Answer:

$1.44 \times 10^{11} \text{ m}$

$10^3 \text{ s}$

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