A spaceship makes the long trip from earth to the nearest star system, Alpha Cen

Question

A spaceship makes the long trip from earth to the nearest star system, Alpha Centauri, at a speed of 0.925 c. The star is about 4.37 light-years from earth, as measured in earth’s frame of reference (1 light-year is the distance light travels in a year.

Part A

How many years does the trip take according to an observer on earth?

Express your answer, with the appropriate units, to three significant figures.

Part B

How many years does the trip take according to a passenger on the spaceship?

Express your answer, with the appropriate units, to three significant figures.

Part C

How many light-years distant is Alpha Centauri from earth, as measured by a passenger on the speeding spacecraft?

Express your answer, with the appropriate units, to three significant figures.

Part D

Use your answer from part C along with the speed of the spacecraft to calculate another answer for part B.

Express your answer, with the appropriate units, to three significant figures.

Part E

Do your two answers for that part agree? Should they?

Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

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Explanation / Answer

Part A) years does the trip take according to an observer on earth = 4.37 /0.925

                                                                                                           = 4.724 years

Part B) years does the trip take according to a passenger on the spaceship = 4.724 * sqrt(1 - 0.9252)

                                                                                                          = 1.795 years

Part C) Alpha Centauri from earth, as measured by a passenger =   4.37 * sqrt(1 - 0.9252)

                                                                                                        = 1.66 light years

Part D) another answer for part B =   1.66/0.925

                                                           = 1.795 years

Part E)    Yes, two answers for that part agree . This is because of the lorentz contraction .

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