Chapter 27, Problem 55A

The nearest star beyond the sun is Alpha Centauri, which is $4.2\times {10}^{16}$ meters away. If we were to receive a radio message from this star today, show that it would have been sent 4.4 years ago.

To determine

To show that the radio signal would be sent 4.4 years ago to Alpha Centauri star, to receive the radio message today on to the Earth.

Answer to Problem 55A

The radio message would be sent 4.4 years ago.

Explanation of Solution

Given data:

Distance (d ) = 4.2 ×10¹⁶m.

We know that,

Speed of light(c )=3×10⁸m/s.

Formula used:

  $t=\frac{d}{c}$ s.

Calculation:

We know that the time required, $t=\frac{d}{c}$ s.

Substitute the values of distance(d ) and velocity of light(c ) in the above formula,

  $=\frac{4.2\times {10}^{16}m}{3\times {10}^{8}m/s}$ s.

= 140000000 s.

Converting the seconds in to the years,

  $=\frac{140000000s}{365\times 24\times 60\times 60}years$ .

= 4.439 years = 4.4 years.

Conclusion:

It’s shown that the radio message would be sent to Alpha Centauri 4.4 years ago.