PHYS 3380 - Astronomy Finding the Celestial Poles You can always find north using the North Star. Polaris can be found using the big dipper. Draw a line through the two “pointer” stars 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 celestial pole 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 a The angle a between the horizon and Polaris is the latitude of the observer. If Dallas is at 33º latitude, where is Polaris in the sky? Where is it at the Equator? PHYS 3380 - Astronomy Angular Size Distances in the sky measured by angular distance: Minute of arc = 1/60th of a degree 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 sun (orbits) once per year in the same direction it rotates. Its orbit 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 ecliptic. PHYS 3380 - Astronomy Earth’s Axial Tilt Axial Tilt of the Planets Sun 7.25 (to the Ecliptic) Mercury ~0.01 Venus 177.4 Earth 23.439281 Moon 1.5424 Mars 25.19 Ecliptic Ceres ~4 Plane Jupiter 3.13 Saturn 26.73 Uranus 97.77 Neptune 28.32 Pluto 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 Celestial Equator and the Ecliptic Plane PHYS 3380 - Astronomy The Zodiac The Sun appears to move steadily eastward along the ecliptic, through the constellations 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 constellation Leo. 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 celestial sphere 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 Declination - 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 Longitude - lines of longitude extend from North Pole to South Pole - by international Right ascension - lines of right ascension treaty, longitude 0 (the prime meridian) run from north celestial pole to south runs through Greenwich, England celestial pole - by convention 0 runs through spring equinox - 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 zenith 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 northern hemisphere 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. 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 Celestial Navigation Determining longitude Need to compare current positions of objects in your sky with positions at known longitude - Greenwich (0º Longitude). For instance - use sundial to determine local solar time 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 years 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 solstice, the Northern Hemisphere has summer because it is tipped toward the Sun, and the Southern Hemisphere 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 equinoxes, both hemispheres receive equal amounts of light. PHYS 3380 - Astronomy Why Does Flux Sunlight 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 summer solstice? PHYS 3380 - Astronomy Sun’s Altitude vs Latitude and Season 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 solar irradiance 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 rotation. 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 latitudes (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 seasons more extreme in the Northern hemisphere? PHYS 3380 - Astronomy 1.