Question

a radio signal is detected from a previously unknown star. the star is found to be $6.0\times10^{16}$ m away. how long did it take the light to reach earth?
○ 3.1 years
○ $5.0\times10^{7}$ years
○ $2.0\times10^{8}$ years
○ 6.3 years

Explanation:

Step1: Recall the speed of light formula

The speed of light \(c = 3\times10^{8}\text{ m/s}\). The formula for time \(t=\frac{d}{c}\), where \(d\) is distance and \(c\) is speed.

Step2: Calculate time in seconds

Given \(d = 6.0\times 10^{16}\text{ m}\) and \(c = 3\times10^{8}\text{ m/s}\), then \(t=\frac{6.0\times 10^{16}}{3\times10^{8}}= 2\times10^{8}\text{ s}\).

Step3: Convert seconds to years

We know that \(1\) year has \(365\times24\times3600 = 3.1536\times10^{7}\text{ s}\). So \(t=\frac{2\times 10^{8}}{3.1536\times10^{7}}\approx6.3\) years.

Answer:

6.3 years