astronomy - william & mary physics departmentphysics.wm.edu/~hancock/171/notes/ch3.pdf ·...
TRANSCRIPT
Astronomy Today: Eclipses and the Motion of the Moon
> Phases of the Moon> Why we only see one side of the
Moon> Solar and Lunar eclipses> Why lunar eclipses are not all total> Solar eclipses are only visible in
some locations> How ancient Greek astronomers
deduce the size of the Earth, Moon and Sun
A. Dayle Hancock
Office hours: MTWR 10-11am
Page 1http:// physics.wm.edu/~hancock/171/
First homework on WebAssign is due Thursday at 11:00pm
Orbital Motion of the Moon
The Moon travels (orbits) the earth in 29.5 days. The Moon is bright not because of light that emitted from its surface but because of sunlight that is reflected from its surface.
The orbital position of the Moon determines how much of the Moon we see (… not the shadow of the Earth) Half of the Moon is illuminated by the Sun at all times but we can sometimes not see any of the Sun illuminated area (a 'new Moon') and sometimes we can see all of the Sun illuminated area ('full Moon').
Phases of the Moon
First Quarter:• Earth-Moon-Sun at 90°
• Moon appears half illuminated from earth
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Phases of the Moon
Waxing Gibbous• Sun-Earth-Moon Angle > 90°
• Illuminated region is increasing (waxing)
• More than half of moon is illuminated (gibbous)
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Phases of the Moon
Full:• Moon-Earth-Sun on a straight line
• earth is between Sun and Moon
• Moon appears fully illuminated
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Phases of the Moon
Waning Gibbous:• Moon-Earth-Sun angle is > 90°
• Illuminated region is decreasing (waning)
• More than half of moon is illuminated (gibbous)
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Phases of the Moon
Third Quarter:• Earth-Moon-Sun at 90°
• Moon appears half illuminated from earth
• Other half of moon is illuminated compared to 1st quarter
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Phases of the Moon
Waning Crescent:• Moon-Earth-Sun angle is
< 90°• Illuminated region is decreasing (waning)
• Less than half of moon is illuminated (crescent)
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Phases of the Moon
New:• Moon-Earth-Sun on a straight line
• Moon between Sun and Earth
• Moon appears dark
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Phases of the Moon
Waxing Crescent:• Moon-Earth-Sun angle is < 90°
• Illuminated region is increasing (waxing)
• Less than half of moon is illuminated (crescent)
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Phases of the Moon
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First Quarter:• Earth-Moon-Sun at 90°
• Moon appears half illuminated from earth
The Moon always Show the Same Face
The Moon always has the same hemisphere (face) towards the earth. The Moon does rotate. It rotates exactly once for each orbit in a synchronous rotation.Note that there is nodark side of the Moon since every area of the Moon is in sunlight during some point of the orbit.
This synchronous rotation is caused by 'tidally locking' due to the Earth's gravity
Sidereal and Synodic Month
The sidereal month is how long it takes the Moon to compete on complete orbit around the earth with respect to the background stars.
Since the Earth moves in its orbit, the synodic month is the time between new moons.The synodic month is longer than a sidereal month.
Eclipses
• An eclipse occurs when the Sun, Earth, and Moon are directly in line with each other
• A solar eclipse occurs when the Moon passes between the Sun and Earth, with the Moon casting its shadow on the Earth causing a midday sky to become dark as night for a few minutes. This occurs when there is a new moon.
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Eclipses
A lunar eclipse occurs when the Moon passes through the shadow of the Earth. There must be a full moon for this to occur so the Earth is between the Sun and Moon.
Eclipses
Question: Since the Moon orbits in 29.5 days, why is there not a solar eclipse once a month followed by a lunar eclipse two weeks later?
Eclipses
Question: Since the Moon orbits in 29.5 days, why is there not a solar eclipse once a month followed by a lunar eclipse two weeks later?
Answer: The plane of the Moon's orbit is tilted by 5o
Eclipses
The plane of the Moon's orbit is inclined by 5o with respect to the ecliptic plane (plane of the Earth's orbit). Where the planes intersect is call the line of nodes. Eclipses can only occur with the line of nodes points at the sun.
Full or partial Eclipse?
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• Penumbral and Umbra caused by a non-point source of light.
• Penumbral eclipse (partial)• Umbra (the full shadow)
> Moon & Earth both have umbra & penumbra
Full or partial Eclipse?
Dark region in the middle is the umbra. The partial dark area is the penumbra
If the Moon is at its perigee (point nearest the Earth) then the eclipse has a larger width. If the Moon is at its apogee (furthest from the earth) then only part of the Sun is blocked out in an annular eclipse.
Full or partial Eclipse?
Solar Eclipses 1997-2020
Classical (Greek) Astronomy
• Through use of models and observations, they were the first to use a careful and systematic manner to explain the workings of the heavens
• Limited to naked-eye observations, their idea of using logic and mathematics as tools for investigating nature is still with us today
• Their methodology is in many ways as important as the discoveries themselves
Shape of the Earth
• Ancient Greeks knew the Earth was round
• Pythagoras taught of a spherical earth (500 BC)
• Aristotle (500 BC)> Shape of earth’s shadow in
eclipse> New Stars become visible as
you travel south> Distant ships disappear
bottom first
Size of the Earth
• Eratosthenes (200 BC) devised a clever way of measuring it using shadows and a bit of geometry> His method
assumes the sun is far away
Size of the Earth
Since 7o is about 1/50 of a circle (7o/360o) and Eratosthenes know it was about 5000 stades from Syene to Alexandria then 50 x 5000 gives the Earth's circumference as 250,000 stades. If the length of a stade is 1/6 km (modern guess) the the earth is about 42,000 km (actual is 40,000 km)
Aristarchus (250 BC) on the Earth and Moon
• He estimated the relative size of the Earth and the moon > Used Earth’s shadow on the moon in
a lunar eclipse (Earth is about 3 times larger)
Aristarchus on Solar System Distances
By measuring the angle between the Sun and Moon to be 87o during a quarter moon and using geometry, Aristarchus conclude the sun is about 20 times the distance to the Moon since sin(90o – 87o) = .05