lecture7.ppt ©R.S. Nerem 20041ASEN 5050SPACEFLIGHT DYNAMICSTime SystemsDr. Steve NeremUniversity of Colorado - Boulderlecture7.ppt ©R.S. Nerem 20042Time systems• Time is important:– Signal travel time of electromagnetic waves• Altimetry, GPS, SLR, VLBI• For positioning– Orbit determination– One nanosecond (10–9 second) is 30 cm of distance– Relative motion of celestial bodieslecture7.ppt ©R.S. Nerem 20043Astronomical clocks• We commonly define time in terms of astronomicaland geodetic periods:– Rotation of the Earth (day)– Revolution of the Earth around the sun (year)– Orbit of the moon around the Earth (month)– Number of bodies in the solar system visible to the nakedeye or 1/4 of a lunar cycle (week)• These astronomical clocks are not consistent– The current length of a year is 365.242190 days– 1900: 365.242196 days– 2100: 365.242184 daylecture7.ppt ©R.S. Nerem 20044Mechanical clocks• When mechanical clocks were less accurate than variations inastronomical clocks, astronomical clocks were used to correctmechanical clocks.– The pendulum clock was invented in the 17th century• In 1928 with the invention of the quartz clock.– Apparent that the uncertainty in the astronomical day was 10–7 due toirregularities in Earth rotation• Atomic clocks– The idea of using hyperfine quantum states of atoms for a clock wasfirst proposed by U.S. physicist Isador Rabi in 1945.lecture7.ppt ©R.S. Nerem 20045Atomic clocks• Certain atoms in a the magnetic field can exhibit one of twohyperfine states– The spin of the outermost electron of an atom either points in the samedirection as the magnetic field of the nucleus, or it points opposite.– The laws of quantum physics forbid other orientations.• Generally, an atom remains in its hyperfine state. But whenprodded by electromagnetic radiation at a specific frequency,it will switch to the other state, undergoing the so-called“hyperfine transition”.• Essentially, an electronic clock selects atoms in one hyperfinestate and exposes them to radiation which causes them toswitch to the other state. The frequency of the radiationcausing the transition becomes the regular beat that the clockcounts to register time.• Hydrogen-masers, cesium, and rubidium standards are usuallyused– Each GPS satellite has 2 Cs and 2 Ru clockslecture7.ppt ©R.S. Nerem 20046International Atomic Time (TAI)• Atomic Time, with the unit of duration the SystemeInternational (SI) second defined in 1967 as the duration of9,192,631,770 cycles of radiation corresponding to thetransition between two hyperfine levels of the ground state ofcesium-133 The second defined in 1967 to correspond totraditional measurement.• A uniform time-scale of high accuracy is provided by theInternational Atomic Time (Temps Atomique International,TAI). The origin of TAI was chosen to start on 1 January1958 0h. It is estimated by a large set (> 200) of atomicclocks.– Mostly cesium atomic clocks and a few hydrogen masers at 60laboratories worldwide.• Time centers compare clocks, using GPS observations as timelinks. A weighted mean of local time center results in the TAI.lecture7.ppt ©R.S. Nerem 20047Fundamentals of TimeSolar Time – determined from the rotation of the Earth WRTthe Sun (position of the Sun WRT the Greenwich meridian).Sidereal Time – period of rotation of the Earth WRT the stars(or the hour angle of the Vernal Equinox) – GreenwichSidereal Time:Nonuniform due tochanges in Earth’sRotation! "GST="GST 0+#$% &UT1lecture7.ppt ©R.S. Nerem 20048Sidereal time• Sidereal time is directly related to therotation of the Earth.• Local Apparent (or true) Sidereal Time(LAST) refers to the observer’s localmeridian. It is equal to the hour angle ofthe true vernal equinox.• The vernal equinox is the intersection ofthe ecliptic and the equator, where the sunpasses from the southern to the northernhemisphere.– The vernal equinox is affected by precessionand nutation and experiences long and short-period variations.lecture7.ppt ©R.S. Nerem 20049Solar time and Universal Time• Solar time is used in everyday life• It is related to the apparent diurnal motion of the sun about theEarth.• This motion is not uniform, assumes a constant velocity in themotion about the Sun.• Mean solar time is equal to the hour angle of the mean sunplus 12 hours. If referred to the Greenwich mean astronomicalmeridian, it is termed Universal Time (UT). Its fundamentalunit is the mean solar day, the interval between two transits ofthe sun through the meridian.• Conversion of UT to GMST is defined by convention, basedon the orbital motion of the Earth (about 360°/365 days):1 mean sidereal day = 1 mean solar day – 3 m 55.90 s =86164.10 s.lecture7.ppt ©R.S. Nerem 200410Fundamentals of TimeUniversal Time (UT) – Greenwich hour angle of a fictitious Sununiformly orbiting in the equatorial plane, augmented by 12hours (eliminates ecliptic motion of the Sun). UT0 isdetermined from motions of the stars, thus function of siderealtime. UT1 is UT0 corrected for polar motion. Closelyapproximates mean diurnal motion of the Sun (Solar Time).Dynamic Time (Ephemeris Time) – derived from planetarymotions in the solar system (deduce time from position ofplanets and equations of motion). Independent variable in theequations of motion.– Barycentric Dynamic Time (BDT) is based on planetary motions WRTthe solar system barycenter.– Terrestrial Dynamic Time (TDT) derived from satellite motions aroundthe Earth.lecture7.ppt ©R.S. Nerem 200411UTC• A practical time scale, as needed in navigation for instance,has to provide a uniform unit of time and maintain a closerelationship with UT1.• This led to the introduction of the Coordinated UniversalTime (UTC).• Its time interval corresponds to atomic time TAI and its epochdiffers by not more than 0.9 sec from UT1. In order to keepthe differenceleap seconds are introduced to UTC when necessary.– A specification of a UTC clock should always differ from TAI by aninteger number of seconds.• GPS provides easy access to UTC with an accuracy within100 nanoseconds.– GPS navigation data provides the integer offset for TAI.! DUT1 = UT1" UTC < 0.9seclecture7.ppt ©R.S. Nerem