The Milky Way galaxy is a part of a group of galaxies calledthe Local Group. The

Question

The Milky Way galaxy is a part of a group of galaxies calledthe Local Group. The proper distance from the Milky Way, on oneside of the Local Group, to the M31 galaxy on the other side isapproximately 2.4 × 106 light-years. How long (inyears) would it take a spaceship traveling at 0.999c totravel this distance according to travelers onboard?

a. 1.1 × 105years
b. 5.6 × 104years
c. 2.0 × 104years
d. 8.4 × 105years
e. 2.4 × 106 years The Milky Way galaxy is a part of a group of galaxies calledthe Local Group. The proper distance from the Milky Way, on oneside of the Local Group, to the M31 galaxy on the other side isapproximately 2.4 × 106 light-years. How long (inyears) would it take a spaceship traveling at 0.999c totravel this distance according to travelers onboard? 1.1 × 105years 5.6 × 104years 2.0 × 104years 8.4 × 105years 2.4 × 106 years

Explanation / Answer

the time taken by the spaceship traveling at 0.999cto travel this distance according to travelers onboard is t = (to/(1 -v2/c2)1/2) to = (do/c) where c is the speed oflight and has a value 3 * 108 m/s do= 2.4 * 106 light years = 2.4 *106 * 9.46 * 1015 m = 22.704 *1021 m v = 0.999c

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