Question

In astronomy, distances are often expressed in light-years. One light-year is the distance traveled by light in one year. If the distance to a star is 3.6 light-years, what is this distance in meters? (There are 365.25 days in one year.)

Answer 1

Answer:

The distance of the star is $3.40x10^{16}$ meters

Explanation:

It is known that the speed of light has a value of $3x10^{8}m/s$ in vacuum. That is, it travels $3x10^{8]m$ in one second, according with the following equation:    

$v = \frac{x}{t}$

Where v is the speed, x is the distance and t is the time.

$x = v\cdot t$ (1)

Equation 1 can be used to determine the distance that the light travels in 1 year:  

It is necessary to find how many seconds are in 1 year (365.25 days).

$365.25 days \cdot \frac{86400s}{1 day}$  ⇒  $31557600s$

           

$x = (3x10^{8}m/s)(31557600s)$    

$x = 9.46x10^{15}m$      

Therefore, in 1 year, light travels $9.46x10^{15}$ meters.

If the distance to a star is 3.6 light-years, what is this distance in meters?  

A simple conversion between units can be used to get the distance in meters

$x_{star} = 3.6ly \cdot \frac{9.46x10^{15}m}{1ly}$ ⇒ $3.40x10^{16}m$

Hence, the distance of the star is $3.40x10^{16}$ meters.