The nearest star to Earth is Proxima Centauri, 4.3 light-years away. Part A At w

Question

The nearest star to Earth is Proxima Centauri, 4.3 light-years away.

Part A

At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 5.3 years, as measured by travelers on the spacecraft?

Express your answer using two significant figures.

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Part B

How long does the trip take according to Earth observers?

Express your answer using two significant figures.

The nearest star to Earth is Proxima Centauri, 4.3 light-years away.

Part A

At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 5.3 years, as measured by travelers on the spacecraft?

Express your answer using two significant figures.

vc =

SubmitRequest Answer

Part B

How long does the trip take according to Earth observers?

Express your answer using two significant figures.

?tEarth =   y  

Explanation / Answer

a) v = d / t = 4.3 ly / 5.3 gamma = 0.811 ly / gamma

gamma = 1 / sqrt [1 - v2/c2]

(v / c)2 = (0.811 / gamma)2

(v / c)2 = 0.658 (1 - v2/c2)

v = 0.629 c = 0.629 * 3 * 108

= 1.89 * 108 m/s

b) delta t = delta t0 * (1 - v2/c2)

delta t0 = 4.3 / 0.629 = 6.83 yr

delta t = 6.83 * sqrt [1 - 0.6292]

= 5.3 years

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