(II) A light-year is the distance light travels in one year (at speed there in 1.00 light-year? (b) An astronomical unit (AU) is the average distance from the Sun to Earth, 1.50 X 10° km. How many AU are there in 1.00 light-year? (c) What is the speed of light in AU/h? 2.998 × 10° m/s). (a) How many meters are 1. :(2.998 x 1o m)co0) c 60) C24) C365) 9.454x1015 m 265 X 24 x 62 X 6 0 (9.454 150X do

(III) The smallest meaningful measure of length is called the Planck length, and is defined in terms of three fundamental constants in nature: the speed of light c the gravitational constant G = 6.67 × 10-11 m³/kg•s², and Planck's constant h = 6.63 × 10-34 kg·m²/s. The Planck length {p is given by the following combination of these three constants: 3.00 × 10° m/s, Gh lp Show that the dimensions of lp are length [L], and find the order of magnitude of lp. [Recent theories (Chapters 32 and 33) suggest that the smallest particles (quarks, leptons) are “strings" with lengths on the order of the Planck length, 10-35 m. These theories also suggest that the “Big Bang," with which the universe is believed to have begun, started from an initial size on the order of the Planck length.]

(II) A light-year is the distance light travels in one year (at speed = 998 * 108 m/s). (a) How many meters are there in 1.00 light-year? (b) An astronomical unit (AU) is the average distance from the Sun to Earth, 1.50 * 108 km. How many AU are there in 1.00 light-year?