53 SSM An astronomical unit (AU) is equal to the average distance from Earth to the Sun, about 92.9 X 106 mi. A parsec (pc) is the distance at which a length of 1 AU would subtend an angle of exactly 1 second of arc (Fig. 1-8). A light-year (ly) is the distance that light, trav- An angle of exactly 1 second 1 pc- eling through a vacuum with a speed of 186 000 mi/s, would cover in 1.0 year. Express the Earth-Sun distance in (a) parsecs and (b) light-years. AU 1 1 pc Figure 1-8 Problem 53.

Given that the Diameter of Earth is about 7200 miles, how many Earths would fit across the Sun? You turn toward the east, seeing the full moon rising. You find that half of your finger tip at arm's length also covers the diameter of the Moon! Given that the diameter of the Moon is about 2160 miles, approximately how far from Earth is the Moon in miles and km according to your calculations?

Show that

3) The radial acceleration, a, of a body rotating in a circle of radius r at constant speed v is given by v2 a = If v = (3.00±0.05) m/s and r= (1.5±0.1) m, a) calculate a, b) the maximum values of a, c) minimum values of a, d) the uncertainty in a.

a) Write down the metric and the inverse metric, and use the definitionrpµv = 1/2gpσ(δµgvσ + δvgµσ - δσgµv) = rpvµto reproduce the results written above for rθ ØØ and rØ θØ.