18. Distances in space are often quoted in units of light years, the distance light travels in one year. (a) How many meters is a light year? (b) How many meters is it to Andromeda, the nearest large galaxy, given that it is 2.00*106 light years away? (c) The most distant galaxy yet discovered is 12.0*109 light years away. How far is this in meters?

a) d = 9,454 10¹⁵ m, b) 18.9 10²¹ m c) 113 10²⁴ m

Explanation:

The light years unit is used because the distances are so large that it is not very manageable.

The speed the light is the space is

c = 2,998 10⁸ m / s

a) As the speed is constant we can use the equations of uniform motion

t = 1 year (365 days / 1 year) (24 h / 1 day) (3600 s / 1h) = 3.1536 10⁷ s

c = d / t

d = c / t

d = 2,998 10⁸ 3,136 10⁷

d = 9,454 10¹⁵ m

b) let's transform is distance to meters

d = 2.00 10⁶ light year (9,454 10¹⁵ m / 1 ly)

d = 18.9 10²¹ m

c)

d2 = 12.0 10⁹ ly (9,454 10¹⁵ / 1 ly)

d2 = 113 10²⁴ m