Question

How long will it take a spacecraft travelling at 99% the speed of light (gamma = 7) to reach

the star Sirius which is 8.6 light-years away according to people on Earth ? How long will it

take according to the crew of the ship?

Answer 1

The time taken is
`t = 2.739 *10^(8) \ s`

Step-by-step explanation:

From the question we are told that

The speed of the spacecraft is
`v = 0.99c`

where c is the speed of light with value
`c = 3.0*10^(8) \ m/s`

=>
`v = 0.99 * 3.0 *10^(8 ) = 2.97*10^(8)\ m/s`

The distance of Sirius is
`d = 8.6 \ light-years = 8.6 * 9.461*10^(15)= 8.135*10^(16) \ m`

Generally the time taken is mathematically represented as

`t = (d)/(v)`

substituting values

`t = (8.136 *10^(16))/(2.97 *10^(8))`

`t = 2.739 *10^(8) \ s`