Astronomy 350: Lecture 1 - Positional Astronomy• Time– Basics of astronomical time is the rotation of the Earth on its axis.This is what casues objects to rise in the east, move across the skyand set in the west.– One sidereal day is a full rotation of the Earth relative to a fixeddistant reference point such as a star (ie. the time it takes the starto return to the meridian (see later) after a full rotation of the Earth.This rotation of 360◦takes 24 Sidereal hours or 15◦degrees per hour.– A Solar day is the time it takes the Sun to come back to its positionon the meridian after a full rotation of the Earth. This rotation of360◦takes 24 solar hours at a rate of 15◦degrees per hour.– Use Stellarium to find the difference between a solar day and a siderealday.– The orbital motion of the Earth around the Sun makes for a differencebetween the Solar day and the Sidereal day.– While rotating on its axis, the Earth is also revolving around the Sun.Since the Earth has moved about one degree in its orbit in one day,it needs to rotate one additional degree to bring the Sun back intotransit (see later). This takes about 4 minutes.– Thus a sidereal day is shorter than a solar day by about 4 minutes.So whilst t here are about 365.25 solar days in a year, there are abo ut366.25 sidereal days in a year.– Time and angles are equivalent.– 360◦, 60′/degree, 60 ” /minute.– 24 hours per 360 degrees, 4 minutes/degree, 4 seconds/minute.– Apparent solar time or solar t ime is the hour angle of the Sun (seelater). Apparent solar time 00:00 means noon and 12 :00 means mid-night. Noon solar time means the Sun is on your meridian. If the localapparent solar time is 9.00pm, that means that the Sun is 9 hours pastthe meridian.– But the length of the solar day varies throughout the year. The Earth’sorbit around the Sun is not a circle but an ellipse: the Earth movesfaster at closest approach to the Sun (perihelion) than when it is fur-thest away (a phelion) due to the conservation of angular momentum.Also due to the earth’s axis tilt, the earth moves along the eclipticwhich is tilted to Earth’s celestial equator. As the Earth moves aroundthe Sun, its NS axis a lways points in the same direction in space.1– Equinoxes and solstices.– At the equinoxes, the Sun is moving at an angle to the Celestial equa-tor, hence the projection of its motion onto the Celestial equator re-sults in a slower motion than its actual motion. At the solstices, whenit is furthest from the equator, it is actually moving parallel to it andcloser to the polar axis, so the projection of its mean motion on theCelestial equator is faster than its actial motion.– Apparent solar days are shorter at solstices (March 26-27 , September12-13) and longer at equinixes (June 18-19, December 20-21).– Define the mean Sun: Moves along the ecliptic at a constant speed andoccupies the same position as the real Sun at perihelion and aphelion.Mean solar time is the hour angle of the mean Sun. The length of themean solar day does not change during the year.– The length of the mean solar day is increasing though, by about 1.4milliseconds per century, due to tidal acceleration of the Moon by theearth and the tidal deceleration of the earth by the Moon.– In 1820, the mean solar day was 86,400 SI seconds. Now its 86400.002SI seconds.– Apparent solar day may be a s much as 22 seconds shorter to 29 sec-onds longer than the mean solar day. These are cyclical and dontaccumalate.– Mean solar day starts at noon (00:00) and midnight is (12 :0 0). Civiltime is defined as mean solar time minus 12 hours.– Difference between apparent solar time and mean solar time is theequation of time or analemma.– Mean Solar Time at Greenwich Meridian (0◦longitud e) is called Green-wich Mean Time (GMT) or Universal Time (UT).– Because the Earth rotates West to East, when the Sun is crossing themeridian at noon at Greenwich, it will be before noon at points westof Greenwich and after noon at points east of Greenwich. Thus LocalMean Solar Time (LMT) is such that LMT = GMT + L, where L isthe longitude of the location.– Civil time at longitude L a lso depends on the time zone and is theLMT of that zone’s standard– Sidereal Time: time kept relative to stars instead of relative to theSun: this reflects the actual rotation of the earth on its axis. LocalSidereal time (LST) is the right ascension crossing the local meridianat a given instant. Greenwich Sidereal time ( GST) is local siderealtime on the Gr eenwich meridian. LST = GST + L, where L is the2longitude and points east/west of Greenwich have positive/negativelongitude.– Precession: the Earth is not spherically symmetric, thus the gravi-tational attr action of the Sun and Moon causes the Earth’s axis tochange direction slowly, or precess just like a spinning top. This isalso a rotation and takes about 26,000 years. Thus the position ofthe vernal equinox changes and moves westwa r ds at about 5 0 arcsec-onds/year. The ”true” sidereal year is 86164.100 seconds, the ro t ationrelative to the vernal equinox ( ie. relative to 0 hours RA) is 86164.092seconds.– Thus astronomical positions given in terms of RA and dec (see later)change and must be given relative to a current epoch.– Universal time (UT0) is the same as GMT.– Changes in the distribution of the Earth’s mass, perhaps due to changesin the Earth’s at mosphere, result in small changes in the location ofthe poles. GMT corrected for this is UT1. It is the main for m ofUniversal time. UT1 is the same everywhere on Earth. There existssome others, UT 2, UT 2R, UT 1R, UT C etc.– The SI unit of 1 second is independent of astronomical observat io ns:The second is the duration of 9 192 631 770 periods of the radiationcorresponding to the transition between the two hyperfine levels of theground state of the Cesium 133 at om.– The Julian Day Number (JDN) is a count of days since Ja nuary 1, 4713BC, noon UT. This numnber is referred to as JD. Can have fractionalparts to it.– For example the Julian date for 2008 August 1 0 02:30:3 2.2 UT is JD2454688.604 54. Many astronomical observations are given times usingthe JD number.– Standard time is the mean solar time in the center o f the time zoneyou ar elocated in with the Earth being divided into 24 timezones,each roughly 15 degrees wide.– Basics∗ On Earth, position is measured with respect to fixed circles onthe Earth. The first is the equator.