Question

A spaceship travels at a constant speed from earth to a planet orbiting another star. When the spacecraft arrives, 12 years have elapsed on earth, and 9.2 years have elapsed on board the ship. How far away (in meters) is the planet, according to observers on earth?

Answer 1

`7.2878*10^(16) m`

Step-by-step explanation:

Time elapsed on Earth
`d_(t)`= 12 years

Time elapsed on board the ship
`d_(t_o)` = 9.2 years

now r=
`(d_(t) )/(d_t_o)`= 12/9.2= 1.3043

`v= c \sqrt{1-(1)/(r^2)}`

`v= 3*10^8 \sqrt{1-(1)/(1.3043^2)}`

v=
`1.9258*10^8`

therefore distance L=
`d_(t)* v`

putting value we get

=
`12**1.9258*10^8`

=
`12**365*24*3600*1.9258*10^8`

=
`7.2878*10^(16) m`