Download Astronomy and Astrophysics Homework 2: Moon Phases, Planetary Conditions, Earth's Rotation and more Assignments Astronomy in PDF only on Docsity! Introduction to Astronomy and Astrophysics Spring 2010 Homework #2 1. Assuming that the average Sun rises at 6 AM, crosses the meridian at noon, and sets at 6 PM, what are the average times for the Moon’s rising, crossing the meridian, and setting for each of the lunar phases: new, first quarter, full, and third quarter? Ignore complicating factors like inclination of the Earth’s axis, motion in and out of the ecliptic plane, time change, difference in rise times across time zones, non-spherical geometry of the Earth, atmospheric effects (refraction and diffraction), adjustments to the clock for any reason, etc. Answers should be to the nearest hour, and include AM or PM. 2. Formaldehyde (H2CO) has been discovered in interstellar space. The radius of Titan is 2600 km, the mass is 1023 kg, and the surface temperature is 94 K. (a) Calculate the mean molecular speed of formaldehyde on Titan. (b) Calculate the escape velocity from the surface of Titan. (c) Would Saturn’s satellite Titan retain formaldehyde? 3.The albedo of Venus is about 0.77 because of the cloudy atmosphere. What would the noontime temperature be? Neglect the Greenhouse Effect, but since Venus has an atmosphere one must assume that the effective radiating areas is the total surface area and the effective collecting area is the cross sectional area. Compare with the measured temperature of 750 K. 4. The synodic period of Jupiter is 398.9 days. What is Jupiter’s semi-major axis? There are 365.26 days in a sidereal year. You should not need to look up any numbers in your textbook. (Unrelated note: The Gregorian calendar attempts to approximate the tropical year, which is 365.2422 days. The tropical year is the time interval for the Earth to orbit the Sun relative to the equinoxes.) *5. According to your textbook, the period of Earth’s rotation slows by 0.002 seconds per century. The angular momentum of a spherical mass of uniform density (let’s assume this is a reasonable description of the Earth) is L = Iω = (2/5) MR2 ω, where M is the mass of the sphere, R is the radius of the sphere, and ω is the angular speed (2π/P). The orbital angular momentum of a body in a circular orbit is rmv, where r is the radius of the orbit, m is the mass of the orbiting body, and v is the speed of the orbiting body. The total angular momentum of the Earth-Moon system is (approximately) conserved. The change in orbital angular momentum of the Earth from the Earth-Moon interaction is negligible, as is the change in the Moon’s spin angular momentum. (Hint: you might want to calculate dL/dt for the spinning mass and dL/dt for the orbiting mass, and for the latter you are going to need to write L as a function of “r,” without any other variables in there that are time dependent.) (a) What is the rate of change of spin angular momentum of the Earth (dL/dt)? (b) Calculate the rate at which the Moon is moving towards or away from the Earth, and specify which it is. Express your answer in units that make the number somewhere between 0.01 and 100.
