Astronomy: Understanding Time and Calendars

Astrophysics I: Lecture 2

• Lecture Focus: Time in astronomy, blackbody radiation, and effective temperatures.
• Astronomical Time Systems:
  • Originate from observable astronomical phenomena.
  • Common units:
    • Day: Earth's rotation around its axis.
    • Month: Moon's orbit around Earth.
    • Year: Earth's orbit around the Sun.
  • These periods are not independent/commensurate, causing calendar challenges.
  • Local times: defined by hour angle of a specific object, closely related to Earth's rotation. Locations sharing the same astronomical meridian have the same local time and longitude.

Definition of a Second

• The modern SI unit is 1 second (1 s).
• Defined as 9,192,631,770 periods of radiation corresponding to the transition between two levels in the hyperfine structure of the ground state of a caesium-133 atom at rest (0 K).
• Earlier definitions linked the second to Earth's rotation, as 1/86400 of an average solar day or 1/31,556,925.9747 part of the tropical year 1900.

Special and General Relativity: Effect on Time

• Special Relativity: Time is not absolute; moving clocks run slower relative to a stationary observer (time dilation).
• General Relativity: Time runs slower in stronger gravitational fields.

Sidereal Time

• Defined as hour angle of the mean vernal equinox.
• Vernal equinox is a mathematical point, not an observable object.
• Measuring time using an observable object is possible using its hour angle, and upper culmination.
• Sidereal day: time interval between two successive culminations of the vernal equinox.
  • Divides into 24 sidereal hours and 86400 sidereal seconds.
  • Shorter than a solar day due to precessional motion of the vernal equinox by 0.0084 s.
  • Sidereal day = 23h56m04.09145
  • Rotation period=23h56m04.09985

True Solar Time

• Measured from hour angle of the Sun.
• Defined for practical reasons (date changes at midnight). True solar day is the interval between two lower culminations of the Sun. True solar days are not the same length due to Earth's orbit eccentricity and variability of Δα/Δλο.

Mean Solar Time

• Introduced to create more uniform time.
• The 'mean Sun' is a mathematical point moving along the equator at a constant rate (da/dt = constant).
• Mean solar day: time interval between two consecutive lower culminations of the mean Sun. Mean solar days are of the same length.

Equation of Time

• Explains the difference between mean solar time and true solar time.
• Two main components:
  • Period of half a year, due to the true Sun's movement along the ecliptic and the mean Sun's equatorial path (Amplitude = 9.87 min).
  • Period of one year, due to the eccentricity of the Earth's orbit around the Sun (Amplitude = 7.68 min).

Analemma

• Graphical representation of position of the sun over the year.

Local Time and Geographical Longitude

• Local time is related to geographical longitude.
• The relationship between the local times at two locations is expressed by t2 − t1 = λ2 − λ1, where t1 and t2 are the local times, and λ1 and λ2 are the longitudes, in angular measure.

Universal Time (UT)

• Mean solar time at Greenwich meridian.
• Zone times are often used, differing from UT by integer/half-integer numbers of hours (CET, EET).

International Date Line

• Arbitrarily defined line near the 180° meridian.
• Crossing the line changes the date by one day (east to west +1 day, west to east−1 day).

Calendars

• Different calendar types: lunar, solar and combined
• Basic time units: day, synodic month, tropical year.
• Gregorian calendar: mean year length = 365.2425 d

Units of Time Summary

• Provides a summary table of various time units (day, month, year).

Time Scales

• Different time scales are used, including universal time (UT), coordinated universal time (UTC), atomic time (TAI), relativistic time scales like Barycentric Dynamical Time (BDT) and Terrestrial Time (TT).

Deviation of Day Length from SI-Based Day

• Shows variation of day length from the SI standard (86400 s).
• Variations are caused by secular slowing from tidal friction, random adjustments (secular), short-term periodic adjustments (lunar-induced tides, and meteorological).

Uniform Time Scales: Ephemeris Time (ET), International Atomic Time (TAI)

• Ephemeris time: Dynamical time scale used from 1952 to 1984. The ephemeris second was defined in 1960.
• International Atomic Time (TAI): Scale implemented in 1972 and fully based on atomic clocks.

Uniform Time Scales: Barycentric Dynamic Time (BDT), Terrestrial Dynamic Time (TDT), Terrestrial Time (TT)

• Barycentric Dynamical Time (BDT): Implemented in 1976 to account for relativistic effects.
• Terrestrial Dynamical Time (TDT): Replaced ET in 1984, the proper time of an observer moving with Earth (relativistic effects of orbital speed are included, but not Earth rotation).
• Terrestrial Time (TT): Implemented in 1991, practically equivalent to TDT.

Blackbody Radiation

• Blackbody is a theoretical object that absorbs all radiation incident on it.
• Blackbody radiation accurately describes radiation emitted by an object in thermal equilibrium with its surroundings.
• Planck's function describes spectral energy density.
• Wien's law describes the peak wavelength of the radiation.

Effective Temperature

• A measure representing the temperature of a star that would emit the same flux if it were a blackbody.