Lecture 3 Angular Sizes, Moon Phases, and Ptolemy

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Lecture 3 Angular Sizes, Moon Phases, and Ptolemy September 12, 2018 2 Measuring Angles • Apparent distances in the sky are determined by measuring the angle between two objects. • There are 360 degrees in a circle. • Each degree is split into 60 arcminutes 3

Angular Size

As distance increases, angular size decreases

q 4 Linear Size from Angular Size

qr D = 180 rq = 57.3 5 The Sun and the Moon have roughly the same angular size. However, the Sun is 400 times more distant than the Moon. What is the linear size of the Sun compared to that of the Moon? A. 400 times greater B. 400 times smaller C. 200 times greater D. 200 times smaller 6 The Sun and the Moon have roughly the same angular size. However, the Sun is 400 times more distant than the Moon. What is the linear size of the Sun compared to that of the Moon? qr A. 400 times greater Sun Sun DrSun180 Sun B. 400 times smaller == qr DrMoonMoon Moon Moon C. 200 times greater 180 D. 200 times smaller 400r ==Moon 400 rMoon 7 Phases of the Moon

• The Moon orbits the Earth ~ every month. • The Moon appears to have different phases because we see more or less of the lighted side of the Moon depending on where it is with respect to the Sun. • Sidereal period: time to complete one revolution with respect to the stars (27.3 days) • Synodic period: time to return to same phase as seen from Earth (29.5 days) 8 Sidereal and Synodic Month 9 First Quarter Phases of the Moon

Waxing Waxing Gibbous Crescent

Full Moon New Moon

Flash Applet Waning Waning Gibbous Crescent Animation Last Quarter 10 Phases - Photos 11 Changes in the Full Moon

Laurent Laveder of Quimper, Bretagne, France photographed 12 full Moons of 2005-2006 and stitched the pictures together to make this movie. The Moon swells and shrinks, it rocks back and forth and up and down. This is a result of the Moon's motion around its tilted, elliptical orbit. Each full Moon occurs at a different point in that orbit, and so we see it from a slightly different distance and angle. The rocking motions are called libration; because of them we can see 59% of the Moon's surface rather than the 50% you might have learned in school. Spaceweather.com 5/15/06 When does the third quarter moon rise?

A. About 6 AM B. About noon C. About 6 PM D. About midnight When does the third quarter moon rise? first quarter A. About 6 AM B. About noon

C. About 6 PM W E D. About midnight

third quarter 14 Shape of the Earth – Aristotle ( 384-322 BC) • Earth’s shadow was curved during a lunar eclipse. • Ships appeared to sink below the horizon. • View of stars differs from different locations. 15 The Geocentric Universe • Ancient people (Aristotle) “knew” from observations that – The stars appear fixed on the sky relative to each other. – Planets, moon and Sun change position with respect to the stars. – Mercury and Venus are only seen near Sun.

• These observations led them to theorize that the spherical Earth is at the center of a great celestial sphere containing all heavenly objects. 16 Basic Geocentric View • Order of planets somewhat arbitrary. • Mercury and Venus always orbit at a velocity that keeps them near the Sun.

Celestial Sphere Saturn Mars

E Mercury Jupiter Moon

Venus Sun 17 Retrograde Motion • Direct Motion: Planets usually move from west-to-east in the sky with respect to the stars over long periods of time. • Retrograde Motion: Planets sometimes change direction and go east-to-west with respect to the stars

East West 18 Ptolemy (140 AD) • Planets move on “epicycles” • Epicycles moved on deferent that was centered not on the Earth, but on an equant point.

• All motions were on epicycle circles (“perfect shape”) 19 Ptolemy (140 AD) • Size and rates of motion on epicycles was calculated using tabulated data

• Predicted positions of planets very accurately. • Accepted theory for ~15 centuries! 20 Epicycles

Animation (Figure 3.11 p.61) In Ptolemy’s model, when is a planet closest to Earth? A. When the planet crosses the deferent. B. During its retrograde westward motion. C. When it is closest to the equant point. D. There is no specific time in its orbit when the planet is closest to Earth.