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Modern Physics A trip is planned to to visit the Alpha Centauri star system 4.3 light...

Modern Physics

A trip is planned to to visit the Alpha Centauri star system 4.3 light years away. Provisions are put in place to allow a trip of 16 years' total duration. How fast must the spacecraft travel if the provisions are to last? Neglect the period of acceleration, turnaround, and visiting times. Express your answer as a multiple of c.

Expert Solution

Let,

: be the distance to the Alpha centauri.
: be the speed of spacecraft
: be the time or total duration.
: be the speed of light.

One must know that, "light years" is a unit of length or distance used to defined astronomical distances.

Given,

We must convert given quantities in SI unit,

The distance D therefore 4.3 light years is equal to,

Time in seconds is

Velocity or the speed of the spacecraft is given as,

Now in terms of c i.e. speed of light.

We know that speed of light is ,

Now multiply and divide by 3 on RHS,

This should be the speed of the spacecraft in terms of c.

genius_generous answered 4 hours ago

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