# ASTR 109 HOMEWORK #2 (Hamilton) Solutions

1. Earth's Seasons Website.
• a) In mid-summer (Dec. 21), Christchurch gets 15.25 hours of sunlight; in mid-winter (Jun. 21) it gets only 8.75 hours.
• b) In mid-summer (Jun. 21), Anchorage gets 18.50 hours of sunlight; in mid-winter (Dec. 21) it gets only 5.5 hours.
• c) The equator gets 12 hours of sunlight per day all year round!
• d) Poleward of the Antarctic Circle a summer day can have 24 hours of sunlight (and a winter's day can have no sunlight). Equatorward of the Tropic of Capricorn it is possible for the Sun to be directly overhead.
• e) If Earth were tilted like Mercury (2 degrees) then most of the planet would have nearly 12 hours of sunlight per day over most of the year. At 43.5 degrees South, for example, we'd have 12.5 hours of sunlight in mid-summer. Seasons would be extremely mild. If Earth were tilted like Uranus (97.8 degrees), then most of the planet would have 0 or 24 hours of sunlight for much of the year. At 43.5 degrees South, we'd have the midnight Sun from October 28th through Feb. 18, and no sunlight at all from April 28 through Aug. 18. Seasons would be more extreme!
• f) The Tropic of Capricorn would coincide with the Antarctic circle if Earth were tilted by 45 degrees. For larger tilts, the Antarctic circle would be closer to the equator than the Tropic of Capricorn.
2. Changing Perspectives: A view from the Moon.
• a) Earth would be straight above you at the furthest possible distance from the horizon.
• b) The Earth would not move very much! It would oscillate back and forth a little, but would remain nearly overhead. It would never set.
• c) If the Earth appears full to you on the Moon, then the Moon would be "new" to an Earth based observer (who would be looking at the unlit side of the Moon). Your picture should show the three bodies in a straight line: Sun, then Moon, then Earth.
• d) If the Earthers see a full Moon, then you would sew a "new" or unlit Earth. Your picture should show the three bodies in a straight line with the Earth in the middle.
• e) During a total lunar eclipse, the shadow of the Earth completely covers the Moon. So from the Moon you'd see the Earth block out the Sun - a solar eclipse. As seen from the Moon, the Earth is much larger than the Sun so a solar eclipse would last around an hour rather than the normal 5 minutes on Earth.
3. Explore the Solar System.
• a) All of the planets orbit counterclockwise in the simulation, along nearly circular orbits. This is a pattern that we would like to be able to explain!
• b) Mercury (no moons), Venus (no moons), Earth (one moon), Mars (two moons). All of these moons orbit counterclockwise along nearly circular paths.
• c) The giant planets have many more moons than the terrestrial planets, and many of the most distant ones orbit clockwise. Some of these orbits are not circular.
• d) Pluto has three moons and so is more like a terrestrial planet than a giant planet in this regard.