Question

A spaceship travels at a constant speed from earth to a planet orbiting another star. When the spacecraft arrives, 13 years have elapsed on earth, and 7.9 years have elapsed on board the ship. How far away (in meters) is the planet, according to observers on earth

Answer 1

`L=9.76*10^(16)m`

Step-by-step explanation:

From the question we are told that:

Time on earth
`T_e= 13yrs`

Time on ship
`T_s= 7.9yrs`

Therefore

`r=(t_e)/(t_s)`

`r=(13)/(7.9)`

`r=1.65`

Generally the equation for Constant Velocity is mathematically given by

`V=C\sqrt{1-(1)/(r^2)}`

`V=3*10^8\sqrt{1-(1)/(1.64^2)}`

`V=2.38*10^8m/s`

Therefore

`L=V*t`

Where

`t=(13*365.25*24*3600)s`

`t=4.1*10^8`

`L=2.38*10^8m/s*4.1*10^8`

`L=9.76*10^(16)m`