924 Elementary Problems and Answers in Solar System Astronomy

Chapter 3. Sun, Earth, and Moon

~ ~ ~ CHAPTER 3 Sun, Earth, and Moon 214. It is sometimes said that Cavendish's balance experiment is a method for "weighing the Earth". What, exactly, is the physical constant that is measured in this experiment? 215. How can the mass of the Earth be determined? 216. The North-South distance (measured along the surface of the Earth) from New Orleans to Peoria is 770 miles. It is observed on a particular day that the Sun's altitude when it is on the observer's meridian (local noon) is 11 degrees greater at New Orleans than it is at Peoria. What is the radius of the Earth? 217. Describe a simple geometric method for finding the radius of the Earth. 218. The circumference of the Earth is about 40,000 km. Therefore, one minute oflatitude corresponds to a North-South distance of ____ km on the surface of the Earth. 31 32 / Sun, Earth, and Moon 219. For an observer at height H above the surface of the sea, the distance d to the horizon is given by the approximate formula where R is the radius of the Earth (= 6,371 km). What is d in kilometers when H = 30 meters? Note that all quantities must be in the same units when doing the calculation. 220. The pilot of an aircraft at 30,000 ft can see a sea-level city as distant as about (a) 420; (b) 67; (c) 106; (d) 210 miles. 221. The peak of a coastal mountain can be just seen on a clear day from a small boat 50 miles away. The approximate height of the peak above sea level is (a) 1,700; (b) 550; (c) 8,000; (d) 3,400 ft. 222. The radii of the Earth and the Sun are 6,371 and 696,000 km, respectively. About how many Earths would fit into the volume occupied by the Sun? 223. The most satisfactory determination of the age of the Earth has come from (a) study of the relative abundances of various radiogenic elements in granites; (b) measuring changes in the rate of rotation of the Earth; (c) classifying fossils in ancient limestone beds; (d) measuring changes in the precise orbit of the Moon; (e) accurate observation of the precession of the equinoxes. 224. The age of the Earth has been determined by radioactive dating to be about (a) 40 billion; (b) 4 billion; (c) 1 billion; (d) 4 million years. 225. The most widely accepted age of the Earth is about (a) 4 X 109 years; (b) 5 million years; (c) 5 X 1010 seconds; (d) 4.5 X 1010 years. Sun, Earth, and Moon / 33 226. On the basis of radioactive dating of samples of terrestrial and lunar material it has been determined that the Earth and the Moon both solidified about (a) 100 million; (b) 4.5 billion; (c) 50 billion; (d) 4.5 million years ago. 227. Consider the radioactive decay of Rb81 to Sr81 with a half-life of 5 X 1010 years. Estimate the approximate age of a sample in which the present atomic abundance ratio Rb81jSr81 = 18. Assume that there was no Sr81 in the original sample and that it is not the product of any other radioactive process. 228. The radioactive element Th232 decays to the stable element Pb208 with a half-life of 14 billion years. In a particular geological sample, the atomic abundance ratio Pb208jTh232 is found to be 0.25. Estimate the age of the sample (since solidification) assuming no other source of Pb208. 229. If the mass of the Earth were increased by a factor of four and its radius increased by the same factor, the "acceleration due to gravity" on its surface would be g. 230. The mean density of the Earth is 5.52 g cm-3. What is the significance of this fact in terms of the composition of the Earth? 231. What evidence would you cite to refute a claim that the Earth is made mostly of iron? 232. The departure of the shape of the Earth from that of a sphere is caused primarily by (a) lunar tidal forces; (b) its rotation; (c) its orbital motion; (d) solar tidal forces. 233. The mean temperature of the surface of the Earth is about 270 degrees Kelvin. What would this temperature be if the Earth were at 16 AU from the Sun? The surface temperature of...