Our Place in the Cosmos and Introduction to Astrophysics Lecture 4 Patterns in the Sky - Earth’s Motion about the Sun

Summary of Previous Lecture Night and day, and the apparent motion of the Sun and stars are due to the Earth’s rotation Latitude may be determined from the altitude of the celestial poles Changing altitude of pole with latitude provides estimate of Earth’s radius Earth’s rotation demonstrated directly by two observable effects: Foucault pendulum and Coriolis effect

Earth’s Orbit around Sun Earth orbits the Sun in same direction as its spin (counterclockwise as viewed from above North Pole) taking 1 year for a complete orbit Responsible for seasons and changing patterns of stars through the year Overhead at midnight, one is looking away from the Sun This direction changes throughout the year and so we see different stars - six months from now we will be looking in the opposite direction at midnight

Summer Autumn Winter Spring 40 deg north

The Ecliptic The Sun traces out a great circle against the background stars along a path known as the ecliptic The constellations along the ecliptic are the signs of the zodiac Nothing significant about these constellations - just random patterns of distant stars that happen to lie near the plane of the Earth’s orbit about the Sun

apparent path of SunSeptember 1 Sun in Leo

Measuring Earth’s Motion Rain falling vertically will appear to be falling at angle from a moving car By the time the raindrop has fallen from the top of the window to the bottom, the car has moved forward, and so raindrop appears to be moving backwards In the same way, light from a distant star appears to be coming from a slightly different direction due to Earth’s motion through space Over the course of a year stars appear to trace out a loop - aberration of starlight

Aberration of Starlight Cannot be detected by human eye but easily detectable with a telescope Aberration of starlight first detected in 1720s by Samuel Molyneux and James Bradley They showed that Earth moves on roughly (but not exactly) circular orbit about the Sun with average speed 29.8 km/s Since distance = speed  time, one may multiply this speed times the time for one orbit to find the circumference of the Earth’s orbit: 942 million km

Distance to the Sun For a nearly-circular orbit, radius is circumference divided by 2  : 150 million km This distance, the average distance between the Earth and Sun is known as one astronomical unit (AU) Modern measurements use radar signals bounced off Venus The AU provides the basis for the astronomical distance scale

The Seasons The seasons are not a result of the ellipticity of Earth’s orbit (it is too small) They result from the combined effects of Earth’s spin on its axis Earth’s orbit about the Sun Misalignment of the axes of these two motions

The Seasons If Earth’s rotation axis were perpendicular to the ecliptic plane, the Sun would always lie in the celestial equator, and above the horizon for exactly 12 hours per day, every day There would be no seasons In fact, rotation axis is tilted by 23.5  from perpendicular, pointing in a fixed direction as Earth orbits the Sun

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The Seasons Thus for parts of the year the North Pole is tilted towards the Sun and hence the northern hemisphere has more than 12 hours of sunshine per day (northern summer), while it is winter in the south Six months later, the North Pole is tilted away from the Sun and northern days are shorter than 12 hours (northern winter, southern summer) As well as longer days in summer, Sun is more directly overhead and hence sunlight more intense

Equinoxes Equinoxes are the times when the Sun’s apparent orbit crosses the celestial equator and the Earth’s rotation axis is perpendicular to the direction to the Sun Twice each year: Spring (or vernal) equinox around 21 March Autumn equinox around 23 September Equinox = “equal night” - day and night both last for 12 hours everywhere

Solstices At the (northern) summer solstice (“Sun standing still”), around 21 June, the Sun reaches it’s most northerly point, when North Pole points most directly towards Sun - midsummer’s day At winter solstice, around 22 December, North Pole tipped most directly away from Sun - midwinter, the shortest day of the year Northern summer solstice is southern winter, and vice versa

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Land of the Midnight Sun Above the Arctic Circle (66.5 deg north) Sun is circumpolar around midsummer - 24 hour daylight (“land of the midnight sun”) Same true below Antarctic Circle Temperatures remain cool as Sun is never very high in the sky There are equally long periods in winter when the Sun never rises

The Equator On the equator all stars, the Sun included, are above the horizon 12 hours per day Days and nights are each 12 hours long throughout the year Sun passes directly overhead on the equinoxes Sun is furthest from overhead at the summer and winter solstices The equator thus experiences eight seasons a year: two summers, two winters, two springs and two autumns, although no season is very different from another

The Tropics Between latitudes 23.5 deg south and north, twice during the year, the Sun will be directly overhead at noon This band is known as the tropics and is bounded by the tropic of Cancer to the north and the tropic of Capricorn to the south Where do these names come from? Summer solstice is located in Taurus, winter in Sagittarius

apparent path of Sun Summer Sun in Taurus Winter Sun in Sagittarius

Precession of the Equinoxes Earth’s axis wobbles slightly (like a spinning top) taking 26,000 years to complete one orbit of precession North celestial pole tracks out a large circle amongst the stars Polaris is currently close to NCP, but it has not always been! Celestial equator remains perpendicular to rotation axis, so the locations where it crosses the ecliptic - the equinoxes - also change

Precession of the Equinoxes This is known as precession of the equinoxes Tropics so-named due to Sun’s location at equinoxes in Ptolemey’s time, not today This shift of the seasons through the year from century to century played havoc with construction of reliable calendars In 1752 England and colonies dropped 11 days from calendar year to fall into line with rest of Europe. Mass rioting ensued from these 11 days being “stolen” from people’s lives

Leap years Modern calendar based on a tropical year of days, the time from one spring equinox to the next Leap years prevent extra fraction of a day causing the seasons to “drift” through the year Leap years have 366 days (extra day is 29 Feb) instead of 365 Leap year every four years gives an average of days/year, so not every 4th year is a leap year Century years apart from those divisible by 400 (eg. 2000) remain as 365 day years

Summary Our view of the stars changes during the year The ecliptic is the apparent yearly path of the Sun against the stars From simple observations of the aberration of starlight one may infer the orbit of the Earth about the Sun and the distance to the Sun The seasons are explained by the rotation of the Earth, the orbit of the Earth about the Sun and the fact that the Earth’s rotation axis is at an angle relative to the orbital axis

Seminar Quiz Q1 Draw a picture of the Earth showing the location of an observer at our latitude and his or her horizon. Mark the direction of the north and south celestial poles and the celestial equator. For how many hours per day is a star on the celestial equator visible?

Seminar Quiz Q2 A soldier fires a cannon directly at a distant target toward the east and makes a perfect hit. She then fires a shot directly at another target to the north, but the shot lands west of this target. Was the soldier in Australia or Canada? Would she have fared better on the equator?

Seminar Quiz Q3 You are half way between the Carolinas and Bermuda heading due east, and you know there is a hurricane nearby. A strong wing is blowing straight out of the south. Would you continue on to Bermuda or head back?

Seminar Quiz Q4 In which direction does the Sun rise on the morning of the spring equinox? In the summer, does the Sun rise further north or further south? And in the winter?

Seminar Quiz Q5 Suppose the Earth’s axis were tilted at an angle of 35 instead of 23.5 degrees to its orbit. At what latitudes would the Arctic and Antarctic circles and the Tropics be located? What effect would this have on our seasons?