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Feb 20, 2024

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1 Lab #2: Lunar Phenomena Introduction The Moon is the only natural satellite of the Earth, and is the only other body in the solar system where humans have walked on. The Moon orbits an average distance of 384,000 km from Earth, has a radius of about 1,738 km (~¼ of R Earth ), and a mass of 7.3× 10 22 kg, ~1/80 th the mass of Earth. The most widely accepted explanation for the Moon’s formation is that it accreted from the debris thrown off from a collision of the primordial Earth with a Mars- sized planetesimal. This theory is supported by the composition and age of the moon, as found from the samples brought back by the Apollo astronauts. The Lab’s Objective The purpose of this lab exercise is to familiarize you with how the earth-sun-moon geometry gives rise to 1) the phases of the moon as seen from earth, and 2) solar and lunar eclipses. Both, a distant view of an observer looking down on earth, as well as a perspective of an observer looking at the sky, are necessary to understand the nomenclature. To help you identify the earth-sun-moon geometry, use the Lunar Phase Simulator from the University of Nebraska-Lincoln at ( http://astro.unl.edu/naap/lps/animations/lps.html ). The objective is to not only able to identify the phases of the moon but also to understand the geometry giving rise to them from various perspectives, and to be able to correlate those perspectives. Synchronous Orbit Until spacecraft were sent to orbit and image the whole Moon, humans on Earth had only seen the n ear side. Since the Moon rotates once about it’s own axis for every time it orbits around the Earth, we can only see one side of the Moon while standing on the surface of the Earth. The moon is said to be face-locked because the gravitational interaction with Earth has “nearly” synchronized the orbit with it's rotational period. This phenomenon is shown graphically in the Figure to the right. If we imagine that there is one large mountain on the hemisphere facing the Earth (denoted by the triangle), then this mountain is always visible to us no matter where the Moon is in its orbit around the Earth. The “nearly” above stems from the fact that the Moon’s orbit is slightly elliptical, not perfectly circular. This causes a slight wobble on the face shown to the Earth during a lunar cycle.

2 Lunar Phases The changing appearance of the moon is the most commonly observed astronomical phenomenon. The moon's cycle of phases has importance in almost all cultures, and even some periods of time — the week and month — likely have their origin in lunar cycles. The sequence of images above (1-8, correspond to orbit locations in the Figure below) show the phases of the moon in their relative order. During the first half of the cycle (new to full) the moon is illuminated on the right hand side, and during the second half of the cycle (full back to new) it is illuminated on the left hand side. Note that the edge of the shadow moves from right to left (assuming our observer is based in the northern hemisphere). These phases — new (1), first quarter (3), full (5), and last (or third; 7) quarter — occur at a precise moment in the moon's orbit around the Earth and are called primary phases . Between these we define intermediate phases that get their names based on how much appears lit and how its appearance is changing. When the percent illumination is increasing we say that the moon is waxing , and when it’s decreasing we say that the moon is waning . When the moon is more than 50% illuminated it is gibbous , and when it’s <50% illuminated it is a crescent . Time of Day One of the most familiar reminders of the passage of time is the continuous cycle of day and night. As you know, the sun's apparent motion in the sky is caused by the Earth's rotation once every 24 hours. For observers on the side of earth closest to the sun it’s noontime. On the other side of the earth the time is midnight — people here are in the darkness of the Earth’s shadow. So for a given observer, the local time depends on his or her location and the current orientation of the earth. The stick figure in the diagram above represents a North American observer. The view is from directly above the North Pole. Note that sunrise and sunset in the diagram are always at 6:00 am and 6:00 pm. This simplification glosses over the seasonal changes caused by the Earth's tilt. 1 2 3 4 5 6 7 8

3 Lunar and Solar Eclipses An “eclipse” refers to events involving three celestial bodies; in this case it is the Sun, the moon, and the Earth. A lunar eclipse occurs when the Earth passes between the Moon and the Sun, and the Earth's shadow obscures the moon or a portion of it. During a Solar eclipse, it’s the moon passing between the Sun and the Earth, and the moon’s shadow obscuring part of the Earth. An eclipse can be total, partial, or annular. For example, a total solar eclipse happens when the moon blocks out the Sun entirely, a partial eclipse is when it blocks out a portion of the Sun, and an annular eclipse is when the moon is at its furthest point in orbit and does not cover the Sun completely. So, during an annular eclipse, we can see a thin ring of light emerging from the outside rim of the moon — like a ring of fire. Tides Twice daily, the tides are primarily the result of the moon’s differential gravitational pull on material from Earth’s crust and ocean. However, the actual tides are a combination of the pulls from the moon, and a smaller effect from the pull of the sun. The Earth stretches into a prolate spheroid towards the moon. Spring tides (see Figure below, part A) occur when the moon and the sun pull in the same line of action — these are the most pronounced tides, with the largest water displacement. Neap tides (B) happen when the sun cancels out some of the moon’s effect— not as spectacular as the spring tides. A) B)

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