Celestial Calculations by Lawrence J. L.;

Author:Lawrence, J. L.; [Неизв.]
Language: eng
Format: epub
Tags: Computational astronomy; Celestial mechanics; Equatorial coordinates; Ecliptic coordinates; Horizon coordinates; Kepler's equation; Equation of the center; Orbital elements; True anomaly; Mean anomaly; Eccentric anomaly; Keplerian elements; State vectors; Julian day number; Phases of the Moon; Equinoxes; Solstices; Eclipses; Angular diameter; Elongation; Phase angle; Planet; Dwarf planet; Two-Line Elements; Orbital propagator; Ephemeris
Publisher: MIT Press

7.9  Exercises

For these sample problems, solve the equation of the center when it is necessary to calculate the Sun’s position.

1. An observer is at 95° W longitude, 30° N latitude. The date is August 9, 2000, and the observer is in the Central Standard Time zone on daylight saving time. If the LCT is 12h, what are the Moon’s ecliptic, equatorial, and horizon coordinates?

(Ans: βm = 3.044500°, λm = 257.219940°, αm = 17.094802h, δm = −19.794427°, hm = −50°44′, Am = 84°56′.)

2. For the observer in the last problem, at what time will the Moon rise and set?

(Ans: LCTr = 15h47m, LCTs = 2h35m the next day.)

3. Another observer is located at 30° W longitude, 20° S latitude within the Eastern Standard Time zone. For the date May 15, 2010, assume that the observer is on daylight saving time. If the LCT is 14h30m, what are the ecliptic, equatorial, and horizon coordinates for the Moon?

(Ans: βm = 2.417166°, λm = 76.416359°, αm = 4.998364h, δ = 25.150750°, hm = 26°32′, Am = 313°24′.)

4. At what time will the Moon rise and set for the previous observer?

(Ans: LCTr = 6h21m, LCTs = 16h25m.)

5. At 12h UT on August 9, 2005, for an observer at 0° latitude, 0° longitude, how far away was the Moon? What was its angular diameter?

(Ans: Distm = 363, 361 km or 225,782 miles, θm = 0°33′.)

6. At 14h30m UT on May 6, 2005, for an observer at 0° latitude, 0° longitude, how far away was the Moon? What was its angular diameter?

(Ans: Distm = 363, 402 km or 225,807 miles, θm = 0°33′.)

7. On August 9, 2005, at 12h UT, what was the Moon’s age? What was the phase of the Moon? What percentage of the visible portion of the Moon was illuminated?

(Ans: A = 42°, Adays = 3.5 days, F = 0.13, K% = 13%, which is closest to a Waxing Crescent Moon.)

8. On May 6, 2005, at 14h30m UT, what was the Moon’s age? What was the phase of the Moon? What percentage of the visible portion of the Moon was illuminated?

(Ans: A = 331°, Adays = 27.1 days, F = 0.06, K% = 6%, which is closest to a Waning Crescent Moon.)

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