The distance to the north star, polaris, is approximately 6.44 3 1018 m.
(a) if polaris were to burn out today, how many years from now would we see it disappear?
(b) what time interval is required for sunlight to reach the earth?
(c) what time interval is required for a microwave signal to travel from the earth to the moon and back?
(the average earth�moon distance is 3.84 108 m.) s

a) 2,042.1 years. b) 500 sec. c) 2.56 sec.

Explanation:

Visible light, is just an electromagnetic wave approximately within 400-700 nm) , so , in vacuum, propagates at a constant speed of 3. 10⁸ m/s.

So, in order to get the time needed for the light coming from any point of the universe can reach us, we just need to apply the velocity definition equation, as follows:

v = Δx / Δt, and solve for Δt, taking into account units.

a) if d = 6.44. 3.10¹⁸ m, and v = 3.10⁸ m/s, we find t as follows:

t = 6.44.3. 10¹⁸ / 3. 10⁸ s = 6.44 . 10¹⁰ sec.

Converting seconds to years:

6.44. 10¹⁰ sec . (1min/60 sec).(1h/60 min). (1d/24h)(1y/365d) = 2,042.1 years.

b) As the average distance earth-sun is 1.5.10⁸ m, we find t as follows:

t = 1.5 10¹¹ m / 3.10⁸ m/s = 500 sec = 8.33 min

c) As the average distance Earth-Moon is 3.84. 10⁸ m, we find t to be as follows:

t = 2. (3.84. 10⁸ m / 3. 10⁸ m/s) = 2.56 sec.