924 Elementary Problems and Answers in Solar System Astronomy

Answers to Chapter 4. The Sky as Observed from the Rotating, Revolving Earth

ANSWERS TO CHAPTER 4 The Sky as Observed from the Rotating, Revolving Earth 411. To find • phases of the Moon; • times of sunrise and sunset; • times of moonrise and moonset; • dates of vernal equinox, summer solstice, autumnal equinox, and winter solstice; • positions of the planets; • descriptive tables of solar and lunar eclipses; • lists of stellar positions; • orbital elements of planetary orbits; • motion of planetary satellites; and many other astronomical data. 412. (d) The ecliptic. 413. (b) 21 March. 414. All of the stars within an arbitrarily adopted portion of the celestial sphere. 187 188 / The Sky as Observed from the Rotating, Revolving Earth 415. Signs of the Zodiac. 416. One for each month of the calendar year. 417. Anyone of the twelve constellations of the Zodiac. 418. 12. 419. Polaris, a UMi, is easily visible to the unaided eye and is nearly true North and at an altitude nearly equal to the observer's latitude. At the present epoch Polaris is 0.77 degree from the celestial pole and convenient tables may be used to find true North and latitude exactly from observations of Polaris. 420. (d) Pegasus. 421. October. 422. Southward passage of the Sun through the autumnal equinox (right ascension 12h, declination zero degrees). 423. (a) 21 March. 424. Right ascension 18h , declination 23.5 degrees South. 425. All stars in a given constellation are near each other (± about 15 degrees) on the celestial sphere but their distances along the line of sight are in general totally unrelated to each other. There are some special exceptions. 426. There is in general no relationship between distances to stars and their angular separations on the celestial sphere. 427.• Latitudinal variation of the acceleration due to gravity. • Wind circulation patterns around high and low pressure areas and in hurricanes and tornadoes (Coriolis force). • Oblateness of the Earth. • Motion of a Foucault pendulum. The Sky as Observed from the Rotating, Revolving Earth / 189 • Necessary corrections for launching a satellite of the Earth (see problems 120 and 121). • Corrections required in the targeting of ballistic missiles. • Diurnal variation of the Doppler shift in the radio signal from a distant spacecraft or in the optical spectrum of a star. 428. Counterclockwise. 429. The mean Sun. 430. (b) Atomic clocks. 431. The sidereal day is the lapse of time between successive meridian transits of the vernal equinox or of any designated star. 432. (a) The vernal equinox is the position on the celestial sphere of the ascending node of the ecliptic on the Earth's equator. (b) Sidereal time at a specified observing point is the local hour angle of the vernal equinox. 433. (d) Orbital motion of the Earth about the Sun. 434. (Equation of time) = (apparent solar time) - (mean solar time). 435. One radian is the angle subtended at the center of a circle of radius r by an arc of length r along the circumference of the circle. 1 radian = 360/211" = 57.30 degrees. 436. 5280 feet (1 mile). 437. (a) Ratio of the Earth-Moon distance to the diameter of the Earth. 439. One-half of the angular change in the star's apparent position during the course of a year relative to much more distant stars on the celestial sphere; or, stated otherwise, the ratio of 1 AUto the star's distance, usually measured in seconds of arc. 190 / The Sky as Observed from the Rotating, Revolving Earth 440. A planet moves with respect to the star field from night to night. Also, at a more subtle level, a planet "twinkles" less than a star and has a distinctive color. 441. A personal observation. 442. About 2,500. 443. Select the brightest stars and compare the pattern of their geometrical relationships with a star chart. 444. Because of the brightness of the sky caused by scattered sunlight in the atmosphere. 445. (a) Moonlight scattered by the Earth's atmosphere. 446. About one mile. 447. The circular intersection of the sphere with a plane passing through its center. 448. The circular intersection of the sphere with a plane that does not pass through its center. 449.• Celestial coordinates-Earth-centered, referred to the vernal equinox and Earth's equator (right ascension and declination). • Geocentric ecliptic coordinates-Earth-centered, referred to the vernal equinox and ecliptic (longitude and latitude). • Heliocentric ecliptic coordinates-Sun-centered, referred to the vernal equinox and ecliptic (longitude and latitude). • Geographic coordinates-Earth-centered, referred...