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Home , Axial tilt, Celestial pole, Declination, Right ascension

PHYS 3380 - Finding the Celestial Poles

You can always find north using the North . can be found using the big dipper. Draw a line through the two “pointer” at the end of the big dipper and follow it upwards from the dipper about four outstretched hand’s width. The big dipper is circumpolar in the US so is always above the horizon. The south can be found using the Southern Cross. There is no “South Star” PHYS 3380 - Astronomy The Big and Little Dippers PHYS 3380 - Astronomy

Motion of the Night Sky Animation PHYS 3380 - Astronomy

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The a between the horizon and Polaris is the of the observer. If Dallas is at 33º latitude, where is Polaris in the sky? Where is it at the ? PHYS 3380 - Astronomy Angular Size

Distances in the sky measured by :

Minute of arc = 1/60th of a

Second of arc = 1/3600th of a degree

Angular diameter - angular distance from one side of an object to the other PHYS 3380 - Astronomy Revolution

Earth travels around the () once per in the same direction it rotates. Its is not quite a perfect circle - it is elliptical. The location in the orbit of the minimum and maximum distances from the Sun are called perihelion and aphelion. The plane of the orbit is called the . PHYS 3380 - Astronomy ’s

Axial Tilt of the

Sun 7.25 (to the Ecliptic) ~0.01 177.4 Earth 23.439281 1.5424 25.19 Ecliptic ~4 Plane 3.13 26.73 97.77 28.32 119.61

The Earth’s axis is currently tilted about 23.5º to the ecliptic. It varies over time between 22º and 25º due the the gravitational forces from Jupiter and the other planets. PHYS 3380 - Astronomy

The axis remains at the same tilt angle - pointed at Polaris - throughout the orbit because of conservation of angular momentum. The ecliptic plane is the plane of the Earth’s orbit. Looking from the Earth, it is the apparent path of the Sun (and planets) in the sky. PHYS 3380 - Astronomy

The Relationship of the and the Ecliptic Plane PHYS 3380 - Astronomy The

The Sun appears to move steadily eastward along the ecliptic, through the of the zodiac. As Earth orbits the Sun, we see the Sun against the background of different zodiac constellations at different times of year. For example, on August 21 the Sun appears to be in the . Defines astral calendar. PHYS 3380 - Astronomy

Sun’s Path Through the Zodiac PHYS 3380 - Astronomy

Celestial The apparent Sphere Sphere of the sky Celestial The points Poles about which the appears to rotate Celestial Projection of Equator the Earth’s equator on the celestial sphere Ecliptic Apparent annual path of the sun on the celestial sphere PHYS 3380 - Astronomy Coordinate Systems Geographic Celestial

Latitude - lines of latitude parallel to - lines of declination parallel to Earth’s equator - labeled north or south celestial equator - labeled positive or relative to equator - from 90º N to 90º S negative relative to celestial equator - from - 90º to +90º - lines of longitude extend from to South Pole - by international - lines of right ascension treaty, longitude 0 (the prime ) run from north celestial pole to south runs through Greenwich, England celestial pole - by convention 0 runs through spring - measured in hours, minutes and seconds east of spring equinox - one hour is 15º PHYS 3380 - Astronomy PHYS 3380 - Astronomy Local Skies Lines of constant declination cross the sky at different altitudes, depending on your location on Earth. declination line = your latitude - goes through your the altitude of the N or S celestial pole = your latitude PHYS 3380 - Astronomy Local Skies PHYS 3380 - Astronomy Determining latitude

Find celestial pole - latitude equal to angular altitude - in Polaris is within 1º of celestial pole

For more precision - use star with known declination - determine angular altitude as it crosses your meridian - imaginary half circle drawn from your horizon due south, through zenith (point directly overhead) to horizon due north - or when star is at its highest altitude in the sky. Ancients used cross- staff or Jacob’s ladder to determine angular altitude. Modern device called a . Sextant PHYS 3380 - Astronomy

Vega crosses your meridian in the southern sky at 78º 44’. You know it crosses your meridian at 38º 44’ north of the celestial equator. So the celestial equator must cross your meridian at an altitude of 40º so your latitude is 50º. The formula for latitude is

north/south of zenith. Sun can also be used if you know the date and the Sun’s declination on that date. Make sure you understand that north/south refers to the direction of the star from zenith at your viewing location. PHYS 3380 - Astronomy Annual Motion of the Sun

The R.A. of the Sun… increases about 2 hours per month

The Declination of the Sun… varies between –23.5º and +23.5º PHYS 3380 - Astronomy Determining longitude

Need to compare current positions of objects in your sky with positions at known longitude - Greenwich (0º Longitude). For instance - use to determine local is 3:00 PM. If time at Greenwich is 1:00 PM, you are two hours east of Greenwich and your longitude is 15º X 2 = 30º East Longitude.

Accurate determination of longitude required invention of clock that could remain accurate on a rocking ship. By early 1700s, considered so important, British government offered large monetary prize for the solution - claimed by John Harrison in 1761 after 31 of work. Clock lost only 5 seconds during a 9-week voyage.

Harrison fought government for several years, finally begin awarded part of the prize in 1773 when he was 80 years old, after appealing to King George III. PHYS 3380 - Astronomy

Seasons occur because even though the Earth's axis remains pointed toward Polaris throughout the year, the orientation of the axis relative to the Sun changes as the Earth orbits the Sun. Around the time of the summer , the Northern Hemisphere has summer because it is tipped toward the Sun, and the has winter because it is tipped away from the Sun. The situation is reversed around the time of the winter solstice when the Northern Hemisphere has winter and the Southern Hemisphere has summer. At the , both hemispheres receive equal amounts of light. PHYS 3380 - Astronomy

Why Does Flux Vary Animation PHYS 3380 - Astronomy Antarctica June 21 December 21 PHYS 3380 - Astronomy

In the summer hemisphere, the sun follows a longer and higher path. The sunlight is more intense - more direct and more concentrated. In the winter hemisphere, the sun follows a shorter and lower path. The sunlight is less direct and less intense.

Why are the warmest days one to two months after ? PHYS 3380 - Astronomy

Sun’s Altitude vs Latitude and Animation PHYS 3380 - Astronomy

The next few slides are from a paper I wrote about the seasonal, hemispherical, and solar cycle variation in the ionosphere due to variations in and output. You are not expected to remember this – I just wanted to show you some applied science associated with what you have learned about seasonal effects. I will teach you more about the sun, solar output, and the solar cycle when we talk about the sun. PHYS 3380 - Astronomy The Earth’s ionosphere is produced by solar extreme ultraviolet radiation. The amount of radiation that reaches the ionosphere and produces ionization is dependent on the solar zenith angle (the angle between the zenith and the center of the Sun's disc) which in turn varies with season. Solar output itself varies with solar cycle, and solar .

The top panel shows the daily average of the ionospheric density measured by the Defense Meteorological Satellite Program spacecraft at ~830 km. Red is in the northern hemisphere and black is in the southern hemisphere. The bottom panel shows the solar zenith angle. It shows the clear seasonal variation (and the solar cycle variation). [Anderson and Hawkins, 2015] PHYS 3380 - Astronomy

The ionospheric density (blue in the top panel) is highly correlated with the 11-year solar cycle. Solar output is measured by E10.7 (in green). The composition is also very highly correlated PHYS 3380 - Astronomy

There is also high degree of variation due to the 27-day solar rotation. Different portions of the sun produce more or less output.

Cross correlation coefficients between ionospheric density and solar output (E10.7) show a 26-day variation over several months. The x-axis shows an applied time delay between the measurements. The one less day is because the Earth is orbiting the Sun as the Sun rotates. PHYS 3380 - Astronomy

Empirical Orthogonal Function (EOF) analysis, closely related to Principal Components Analysis, can pull out the various dependencies of data variation.

This shows the EOFs (or eigenvectors of the covariance matrix) for the first two principal components (which capture over 95% of the variation) plotted vs geographic latitude. The second EOF (red) is near zero at the equator and maximum at high (where the SZA annual variation is the greatest). The first EOF (blue) shows little variation in latitude indicating that the solar EUV effects are relatively independent of latitude. [Anderson and Hawkins, 2015] PHYS 3380 - Astronomy

Why are the more extreme in the Northern hemisphere? PHYS 3380 - Astronomy

1. Most of Earth’s land mass in in the Northern Hemisphere. Water takes longer to heat or cool than soil or rock (water has a higher heat capacity). The water temperature remains relatively constant, thereby moderating the . 2. Earth is slightly farther from the sun during northern summer solsitce - moves slower in its orbit so summer/winter is 2 - 3 days longer/shorter. This effect is more important then the slightly more intense sunlight due to Earth being closer/farther away. PHYS 3380 - Astronomy Five Major Circles of Latitude

1. The Circle (66.5 degrees N) 2. Tropic of (23.5 degrees N) 3. The Equator 4. The Tropic Capricorn (23.5 degrees S) 5. The (66.5 degrees S) What is special about these latitude circles? PHYS 3380 - Astronomy Five Major Circles of Latitude

The Arctic and Antarctic Circles - One day a year the sun shines all day and one day a year it doesn’t shine at all. (Capricorn) - The sun is never directly overhead at higher latitudes. PHYS 3380 - Astronomy

(a) A spinning top slowly wobbles, or precesses, more slowly than it spins. (b) The Earth's axis also precesses. Each precession cycle takes about 26,000 years. Note that the axis tilt remains about the same throughout the cycle, but changing orientation of the axis means that Polaris is only a temporary North Star. PHYS 3380 - Astronomy

Precession Movie PHYS 3380 - Astronomy

Gravitational Attraction

The Sun’s gravity (and the Moon’s to a lesser degree) tugs on the Earth trying to straighten out its rotational axis. However, like any rotating object, the Earth tends to keep spinning around the same axis. The result is that gravity succeeds only in making the axis precess. PHYS 3380 - Astronomy Climate Changes

41,000 yrs 26,000 yrs 100,000 yrs

Changes in Earth’s orbit and orientation cause cyclic changes in climate - ice ages. Mildest period about 5,000 years ago - headed for another . PHYS 3380 - Astronomy Milankovitch Theory

Variations in Earth's orbit, the resulting changes in solar energy flux at high latitude, and the observed glacial cycles. Milankovitch Theory - precession of equinoxes, variations in tilt of Earth's axis (obliquity) and changes in eccentricity of the Earth's orbit responsible for observed 100 kyr cycle in ice ages by varying amount of sunlight received by the Earth particularly noticeable in high northern latitude summer. PHYS 3380 - Astronomy Aspects of an Inferior .

Various configuration of an inferior planet are defined as shown here. Any planet whose orbit is smaller than Earth’s orbit is called a “inferior” planet. Mercury and Venus are the only inferior planets. PHYS 3380 - Astronomy Mercury

As viewed from Earth, Mercury can be seen only near times of greatest eastern or western elongation. • At greatest western elongation (when the planet is farthest west of the sun in the sky), Mercury rises about 1 1/2 hours before sunrise. • At greatest eastern elongation (when the planet is farthest east of the sun in the sky), Mercury sets about 1 1/2 hours after sunset. PHYS 3380 - Astronomy Venus

Venus is at maximum elongation at 47° - at maximum brilliancy at 39º - combination of amount of sunlit Venus visible and distance from Earth - brightness of reflected light PHYS 3380 - Astronomy

Venus and Mercury can sometimes be seen in the west at sunset - “evening stars” or in the east at sunrise - morning “stars”.