PHYS Astronomy Homework Set #2 8/31/16 Due 9/12/16 Chapter 3 Review Questions 1, 2, 9 Problems 1, 7, 9, 11 Using the small angle formula, calculate the angular size of Venus as viewed from Earth at inferior conjunction.

PHYS Astronomy Images taken at UTD of Mercury transit of November, 2006

PHYS Astronomy Venus orbit tilted 3.4º to the ecliptic Transits of Venus only occur in pairs about 8 years apart every ~120 years. Transits occurred in 2004 and 2012 (June) Edmund Halley one of few to observe first transit in 1677 after invention of telescope - called upon future astronomers to observe subsequent transits. On his first voyage, Captain Cook traveled to Tahiti to observe transit of 1769 in an attempt to estimate the distance from the Earth to the Sun using triangulation and the parallax effect. Measurements not very accurate: - intense sunlight filtering through Venus' atmosphere fuzzed the edge of the disk and decreased the precision with which Cook could time the transit - his measurements disagreed with those of ship's astronomer Charles Green, who observed the transit beside Cook, by as much as 42 seconds. Venus Transits

PHYS Astronomy Solar Parallax

PHYS Astronomy - Cook and Green also observed the "black drop effect." When Venus is near the limb of the sun - the critical moment for transit timing - the black of space beyond the Sun's limb seems to reach in and touch the planet - made it hard to say just when the transit began or ended. - a problem for observers elsewhere - observations of Venus' 1769 transit from 76 points around the globe not precise enough to set the scale of the solar system. Astronomers didn't manage that until the 19th century when they used photography to record the next pair of transits.

PHYS Astronomy Venus Transit of the Sun

PHYS Astronomy Various configurations of superior planet are defined as shown here. Any planet whose orbit is larger than Earth’s orbit is called a “superior” planet. Aspects of a Superior Planet.

PHYS Astronomy

Moon’s appearance and rise and set times change with the cycle of the lunar phases The sun illuminates one side (half) of the moon - appearance varies with side of moon facing the Earth - the angle between the sun-Earth line and the Earth-moon line. Lunar Phases

PHYS Astronomy Phases of the Moon Animation

PHYS Astronomy Lunar Phase Terminology Phases of the Moon’s 29.5 day cycle new crescent first quarter gibbous full gibbous last quarter crescent waxing waning

PHYS Astronomy Lunar Phases

PHYS Astronomy New Moon  First Quarter  Full Moon

PHYS Astronomy Full Moon  Third Quarter  New Moon

PHYS Astronomy Moon Rise and Set Animation

PHYS Astronomy What’s wrong with this moon (at night)?

PHYS Astronomy Earthshine The dark portion of the lunar face is not totally dark - you can see the outline of the full face of the Moon even when the Moon is not full - in particular the crescent phase. Because the crescent phase is nearly a new moon as seen from Earth, the Earth is nearly full as viewed from the moon. The light of Earth illuminates the night moonscape - just as the full moon illuminates the Earth landscape. Because Earth is much larger than the Moon, the full earth is much bigger and brighter in the lunar sky than the full moon is in Earth's sky. This faint light illuminating the “dark” portion of the Moon's face is often called the ashen light or earthshine.

PHYS Astronomy Eclipses The Earth & Moon cast shadows. When either passes through the other’s shadow, we have an eclipse Solar eclipse - when Earth passes through Moon’s shadow - occurs at new Moon Lunar eclipse - When Moon passes through Earth’s shadow - occurs at full Moon

PHYS Astronomy The shadow cast by an object in sunlight. Two distinct regions - sunlight is fully blocked in the umbra and partially blocked in the penumbra. Umbral shadow totally dark, penumbral shadow only slightly darker than no shadow. Shadows

PHYS Astronomy Types of Lunar Eclipses Total Moon in Earth’s umbra - maximum duration in total eclipse region minutes Partial Moon partly in Earth’s umbra Penumbra Moon in Earth’s penumbra - virtually undetectable

PHYS Astronomy Lunar Eclipses: Present There are typically 2 partial or total lunar eclipses per year.

PHYS Astronomy As viewed from Earth, Earth's shadow can be imagined as two concentric circles. - type of lunar eclipse is defined by the path taken by the Moon as it passes through Earth's shadow.

PHYS Astronomy Generally two lunar eclipses per year, separated by 6 synodic months (177 days) - one on ascending node and one on descending node Descending node Ascending node

PHYS Astronomy

Lunar Eclipses Animation

PHYS Astronomy Evolution of Total Lunar Eclipse Animation

PHYS Astronomy Total Lunar Eclipse A total lunar eclipse can last up to 1 hour and 40 min. During a total eclipse, the moon has a faint, red glow, reflecting sun light scattered in Earth’s atmosphere.

PHYS Astronomy α D d The Small-Angle Formula - a mathematical approximation - relates the linear size (D) of an object to its angular size (α) and its distance from the observer (d) - is a valid approximation if α is small.

PHYS Astronomy Solar Eclipses We are fortunate - the sun appears approximately as large in the sky (same angular diameter ~ ) as the moon.  When the moon passes in front of the sun, the moon can cover the sun completely, causing a total solar eclipse.

PHYS Astronomy Types of Solar Eclipses Total If the eclipse occurs when the Moon is close to the Earth - umbra covers small area of Earth’s surface (no more than 270 km in diameter) - anyone in this area sees a total eclipse. Partial Anybody in penumbral shadow (about 7000 km in diameter) will see a partial eclipse. Annular If the eclipse occurs when the Moon is far from the Earth - the umbra does not reach the Earth, only the penumbra. Anyone in this area directly behind the umbra sees an annular eclipse

PHYS Astronomy Evolution of a Partial Solar Eclipse Animation

PHYS Astronomy Evolution of a Total Solar Eclipse Movie

PHYS Astronomy Earth and Moon’s Orbits Are Slightly Elliptical Sun Earth Moon (Eccentricities greatly exaggerated!) Perihelion = position closest to the sun Aphelion = position furthest away from the sun Perigee = position closest to Earth Apogee = position furthest away from Earth

PHYS Astronomy Annular Solar Eclipses The angular sizes of the moon and the sun vary, depending on their distance from Earth. When Earth is near perihelion, and the moon is near apogee, we see an annular solar eclipse. Perigee Apogee Perihelion Aphelion

PHYS Astronomy Almost total, annular eclipse of May 30, 1984