Motions of the Earth and Moon

Transcription

1 Motions of the Earth and Moon Motions of the Moon The Moon revolves around Earth once in days. This is called its sidereal period of revolution because it is measured relative to the stars. The Moon rotates once in days. This is its sidereal period of rotation. Because of this, we always see the same side of the Moon from Earth. As the Moon moves eastward in its orbit, the part of the illuminated half that we see changes. The fraction of the illuminated half that is visible from Earth is called the phase, usually expressed as a percentage. N Sunlight eastward 1

2 Why do we always see the same side of the Moon? The Moon s rotation period is equal to its period of revolution. Earth Phases of the Moon A complete cycle of phases is called a lunation. Waxing gibbous First quarter Waxing crescent full New eastward The time to complete a cycle of phases is called the synodic period of the Moon. It is the Moon s period of revolution with respect to the Sun. Waning gibbous Third quarter Waning crescent The synodic period of the Moon is days. That is about 1 week from new to first quarter, one week from first quarter to full, etc.. 2

3 How is the time of day for an observer related to the location of that observer on Earth? Sunset Midnight North Pole Noon Sunlight Sunrise Lunar Phases and Time of Day Sunset Note: eastward is the direction in which Earth rotates. In the diagram, a line is drawn tangent to the observer s location, with the direction of rotation labeled E and the opposite direction labeled W. These two points identify the eastern and western horizons. E W W E Midnight North Pole Noon Sunlight E W W E Sunrise 3

4 Lunar Phases and the Seasons SS In this diagram, the Sun is at the vernal equinox, so the date is near March 20. AE VE WS What is the phase of the Moon if the date is March 20, and the Moon is at the summer solstice? An internet tutorial and practice quiz on the phases of the Moon is located at 4

5 Lunar and Solar Eclipses angular diameter linear diameter = distance The maximum distance between Earth and the Sun is about 152,000,000 km, and the diameter of the Sun s photosphere (the region of the Sun that is normally visible) is 1,390,000 km. Calculate the angular diameter of the Sun at this distance. d = km D= km Calculate θ. θ= d 5 D 3 θ= arcsec θ= θ= θ = 0.524º 6 8 When the Moon is closest to Earth, its angular diameter is 0.549º. If it then comes between us and the Sun, it blocks (eclipses) the photosphere. This phenomenon is called a total solar eclipse. The Sun s angular diameter can be as large as 0.542º and the Moon s as small as 0.491º. When the Moon comes between Earth and the Sun under these conditions, a ring of the photosphere is visible. This is called an annular eclipse. 5

6 The Structure of a Shadow Sun The green sphere in the diagram represents either Earth or the Moon. No sunlight reaches the region labeled U. This is the darkest part (called the umbra) of the shadow of the green sphere; it is the region in which the Sun is totally eclipsed. P labels the penumbra of the shadow, where the Sun is partially eclipsed. From region A, an observer would see an annular eclipse. penumbra A cross section of the shadow at the dotted line would look like the figure below. umbra Earth-Sun-Moon Configurations for Lunar and Solar Eclipses For a lunar eclipse to occur, the Moon must pass through Earth s shadow. This can only happen at a full Moon. For a solar eclipse to occur, the Moon s shadow must fall on Earth. This can only happen when the Moon is new. Why isn t there a lunar eclipse at every full Moon and a solar eclipse at every new Moon? Full Moon New Moon Sun Earth The Moon s orbit does not lie in the ecliptic. There is an angle of about 5º between the plane of Earth s orbit and the plane of the Moon s orbit. Because of this, the shadows usually miss as shown at the right. Ecliptic 6

7 Line of Nodes Under ideal lunar eclipse conditions, the length of Earth s umbra is 1.4 million km and the distance from Earth to the Moon is 363 thousand km. The diameter of Earth s umbra at that distance is 9500 km, and the diameter of its penumbra is 16,000 km. Since the diameter of the Moon is only 3476 km, it is possible for the entire Moon to pass through Earth s umbra. The Moon is then seen totally eclipsed by anyone on Earth who can see the Moon. Three kinds of lunar eclipse are possible: total, partial, and penumbral. eastward Penumbral: Moon passes through the penumbra. Total: all of the Moon passes through the umbra. Partial: only part of the Moon passes through the umbra 7

8 Lunar Eclipse During the penumbral phase of a total lunar eclipse or during a penumbral eclipse, the full Moon is slightly fainter than usual. During the total phase, it is not completely dark because some sunlight is refracted (i.e., bent))toward the Moon by earth s atmosphere. As it passes through Earth s atmosphere, the sunlight is also scattered. More blue light is scattered than red, so the Moon looks orange during totality as shown in these photographs. Under ideal lunar eclipse conditions, the diameter of the Moon s umbra is about 270 km, and the diameter of its penumbra is about 6000 km. Since Earth s radius is about 6380 km, the only people who can see a total solar eclipse are those who happen to be along the narrow path followed by the umbra; this path is called the path of totality. Earth Umbra of Moon s shadow For an observer at Earth s equator, the umbra moves at about 1730 km/h due to the combination of the orbital motion of the Moon and the rotation of Earth. The time for the umbra to pass over such an observer is therefore no more than about 7.5 minutes. Total eclipses at higher latitudes are even shorter. On the other hand, it can take as much as 1 hour and 45 minutes for the Moon to traverse Earth s umbra. There are three kinds of solar eclipse: total (photosphere completely blocked by the Moon, partial (photosphere partially blocked by the Moon), and annular (Moon blocks the central part of the photosphere, but leaves a thin ring of photosphere visible. 8

9 This is a satellite view of the passage of the Moon s shadow over the surface of Earth during a total solar eclipse. While the umbra passes over a region, the people in that region see a total solar eclipse. Solar Eclipse from Satellite Because Earth rotates and the Moon moves in its orbit, the shadow moves at more than 1000 mph. Since the diameter of the umbra is no more than about 168 miles, a total solar eclipse can last no more than 7.5 minutes. Total Solar Eclipse as Seen from the Ground Notice that just, before the beginning and just before the end of totality,there is a bright flash near the edge of the Sun. This phenomenon is called the diamond ring effect. It is the result of sunlight passing through a valley on the Moon while the rest of the Sun is eclipsed. The white halo seen during totality is the part of the Sun s atmosphere called the corona. 9

10 Chromosphere and Prominences When the photosphere is eclipsed, the outer regions of the Sun s atmosphere can be seen. The pink region, which has an average depth of several thousand km, is called the chromosphere. The corona is the tenuous, but very hot, region that shows up as a white irregular halo around the Sun during totality. The clouds of hot gas that rise above the chomosphere into the corona are called prominences. Predicting Eclipses The Moon's orbit is tilted 5 o 8' 43" to the plane of the ecliptic. It crosses the ecliptic twice a month. These crossing points are called the nodes of its orbit. Conditions for an eclipse to occur: 1. The Moon must be full (lunar eclipse) or new (solar eclipse). 2. The Sun must be near a node of the Moon s orbit. Eclipse season: a time interval during which the Sun is close enough to a node for an eclipse to occur about 32 days for solar eclipses, 22 days for lunar eclipses. Line of nodes: a line that passes through the two nodes of the Moon s orbit. Eclipse year: the amount of time for the Sun to return to a node = days The eclipse seasons begin 19 days earlier each year. 10

11 1 1 saros cycle = 18 years 11 days = days = 223 lunar synodic periods = = If the line of nodes points toward the Sun on a given date, and the Moon is new, a solar eclipse will occur days later, an eclipse of the same type will occur but it will be seen = 120 o farther west. Annular eclipse on 8/21/2017. When will the same eclipse occur again? When will it occur again and be visible from the same location? Total Solar Eclipses Visible from the USA 11