Astronomy: Understanding Time and Calendars
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Questions and Answers

Which astronomical phenomenon is the basis for defining a month?

  • The apparent movement of stars across the sky.
  • The Earth's orbital period around the Sun.
  • The Moon's orbital period around the Earth. (correct)
  • The Earth's rotation around its axis.
  • Why do astronomical time systems pose problems when creating calendars?

  • Astronomical phenomena are independent of each other and their periods are not commensurate. (correct)
  • Astronomical phenomena are too fast and difficult to measure accurately.
  • Astronomical phenomena are aesthetically unpleasing.
  • Astronomical phenomena are constantly speeding up.
  • What dictates the local time in astronomical time systems?

  • The declination of the Sun.
  • The altitude of the observer.
  • The hour angle of a specific object. (correct)
  • The right ascension of the Moon.
  • What is the modern definition of one second (1 s)?

    <p>The time equal to $9,192,631,770$ periods of radiation corresponding to the transition between two levels of the hyperfine structure of the ground state of the caesium 133Cs atom. (B)</p> Signup and view all the answers

    According to the Special Theory of Relativity, how does motion affect the passage of time?

    <p>Clocks moving relative to an observer appear to run slower. (C)</p> Signup and view all the answers

    How does a stronger gravitational field affect the passage of time, according to the General Theory of Relativity?

    <p>Time runs slower for an observer in a stronger gravitational field. (C)</p> Signup and view all the answers

    What is sidereal time defined as?

    <p>The hour angle of the (mean) vernal equinox. (D)</p> Signup and view all the answers

    Why is the first point of Aries not an object that can be observed?

    <p>It is a mathematical point of the celestial sphere. (A)</p> Signup and view all the answers

    What adjustment must be made when crossing the International Date Line from east to west?

    <p>The date is advanced by one day. (A)</p> Signup and view all the answers

    Which type of calendar is based on the phases of the moon?

    <p>Lunar calendar (A)</p> Signup and view all the answers

    What does $T^*$ represent in the context of sidereal time measurement?

    <p>The sidereal time, which equals the object's right ascension at upper culmination. (D)</p> Signup and view all the answers

    When do Central European Time (CET) and Eastern European Time (EET) occur, respectively?

    <p>CET = UT + 1h, EET = UT + 2h (D)</p> Signup and view all the answers

    What is the approximate length of a synodic month?

    <p>29.530589 days (B)</p> Signup and view all the answers

    If the right ascension of a star at its upper culmination is 10 hours, what is the sidereal time ($T^*$)?

    <p>10 hours (D)</p> Signup and view all the answers

    What is the mean solar day?

    <p>$86400.0009 s$ (B)</p> Signup and view all the answers

    What causes the sidereal day to be shorter than the Earth's rotation period?

    <p>The precessional motion of the vernal equinox. (A)</p> Signup and view all the answers

    What is the approximate difference ($\Delta$) between the Earth's rotation period and a sidereal day?

    <p>0.0084 seconds (B)</p> Signup and view all the answers

    What is the tropical year currently?

    <p>$365.242190 d$ (B)</p> Signup and view all the answers

    What is the formula that relates local times and longitudes?

    <p>$t - λ = const$ (A)</p> Signup and view all the answers

    Why is true solar time defined as $T_{☉} = t_{☉} + 12h$ , instead of $T_{☉} = t_{☉}$?

    <p>To align the date change with midnight. (A)</p> Signup and view all the answers

    What is the reference point Universal Time (UT)?

    <p>Mean solar time at Greenwich meridian (C)</p> Signup and view all the answers

    Which instrument accurately displays true solar time, assuming proper alignment?

    <p>Sundial (A)</p> Signup and view all the answers

    What celestial event defines a true solar day?

    <p>Two successive lower culminations of the Sun. (A)</p> Signup and view all the answers

    If the hour angle ($t_{☉}$) of the Sun is 6 hours, what is the true solar time ($T_{☉}$)?

    <p>18 hours (B)</p> Signup and view all the answers

    What are the units for specific intensity ($I_\nu$) in the context of radiation fields?

    <p>W m$^{-2}$ rad$^{-2}$ Hz$^{-1}$ (B)</p> Signup and view all the answers

    What physical quantity does flux ($F_\nu$) measure in the context of radiation?

    <p>The net energy flow across an area per unit time in a spectral range (C)</p> Signup and view all the answers

    The Stefan-Boltzmann law relates which two physical quantities?

    <p>Flux emitted by a black body and its temperature (B)</p> Signup and view all the answers

    What is the effective temperature ($T_{eff, \odot}$) of the Sun?

    <p>5780 K (C)</p> Signup and view all the answers

    Which of the following is true regarding stars and black body radiation?

    <p>Stars do not radiate as black bodies. (C)</p> Signup and view all the answers

    What is implied when the specific intensity ($I_\nu$) does not depend on $\phi$ and $\theta$?

    <p>The radiation is isotropic. (C)</p> Signup and view all the answers

    Which of the following scientists was a recipient of the Nobel Prize in Physics in 2006 for work related to black body radiation and cosmic microwave background?

    <p>John C. Mather (B)</p> Signup and view all the answers

    What does the effective temperature represent?

    <p>A local quantity representing the temperature a black body would need to have in order to emit the same total amount of radiation (B)</p> Signup and view all the answers

    What time scale was adopted in 1991 as a new standard?

    <p>Terrestrial Time (TT) (C)</p> Signup and view all the answers

    What does the equation $TT = TAI + 32.184 s$ signify?

    <p>It indicates the standard offset for Terrestrial Time from International Atomic Time. (C)</p> Signup and view all the answers

    What time standard is essentially based on Earth's rotation?

    <p>Universal Time (UT) (A)</p> Signup and view all the answers

    What factor does UT1 account for that UTC does not?

    <p>Polar motion of the Earth (D)</p> Signup and view all the answers

    How is ΔT defined?

    <p>As the difference between Terrestrial Time and UT1. (A)</p> Signup and view all the answers

    What is the significance of the last leap second introduced on December 31, 2016?

    <p>It was the last adjustment to account for Earth's rotational variations. (A)</p> Signup and view all the answers

    What is a black body in the context of physics?

    <p>An idealized body that absorbs all incident electromagnetic radiation. (A)</p> Signup and view all the answers

    What is black-body radiation?

    <p>Radiation emitted by a black body in thermal equilibrium with its environment. (C)</p> Signup and view all the answers

    What fundamental method is used to derive the effective temperature (Teff)?

    <p>By measuring the angular diameter and total flux (D)</p> Signup and view all the answers

    What does the angular diameter θ depend on according to the conservation of energy?

    <p>It depends on the stellar radius and distance (A)</p> Signup and view all the answers

    Which of the following is a technique for measuring angular diameters?

    <p>Lunar occultations (D)</p> Signup and view all the answers

    What can be inferred from the successful measurement of angular diameters via diffraction?

    <p>It indicates that measurements are accurate even at great distances (A)</p> Signup and view all the answers

    What was a significant factor in the lunar occultation event observed in 1991?

    <p>Photomultiplier and time step (A)</p> Signup and view all the answers

    Which scientific concept links angular diameter with stellar observation techniques?

    <p>Diffraction at an opaque barrier (C)</p> Signup and view all the answers

    In the context of stellar observation, what does the total flux measured at Earth represent?

    <p>The brightness of a star as perceived from Earth (D)</p> Signup and view all the answers

    What does the formula $\theta = \frac{2R}{D}$ illustrate in stellar observations?

    <p>The angular diameter based on stellar radius and distance (A)</p> Signup and view all the answers

    Flashcards

    Astronomical Time System

    A system for measuring time based on astronomical phenomena.

    Second (unit of time)

    Defined as 9,192,631,770 radiation periods of caesium 133.

    Local Time

    Time defined by the hour angle of a specific astronomical object.

    Time Dilation

    Time is perceived to pass slower for objects in motion.

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    Gravitational Redshift

    Time runs slower in stronger gravitational fields.

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    Sidereal Time

    Time defined by the hour angle of the mean vernal equinox.

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    Periods of Time

    Days, months, and years are independent astronomical measures.

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    Earth's Rotation

    The period it takes for Earth to spin once on its axis.

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    Sidereal Day

    The time interval between two successive culminations of the vernal equinox.

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    Length of Sidereal Day

    Sidereal day is 23h 56m 04.0914s long due to Earth's rotation.

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    Analemma

    A diagram showing the position of the sun at the same time each day throughout the year.

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    Earth's Rotation Period

    The time it takes for the Earth to complete one rotation around its axis, 23h 56m 04.0998s.

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    Universal Time (UT)

    Mean solar time at the Greenwich meridian, used as a time standard.

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    Differential Time

    The difference in time between the sidereal day and Earth's rotation period, which is 0.0084s.

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    Time Zone

    Region of the Earth that has the same standard time.

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    True Solar Time

    The time based on the position of the Sun, calculated as Tₙ = tₙ + 12h.

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    Upper Culmination

    The point at which an astronomical object is at its highest point in the sky.

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    Central European Time (CET)

    Time zone that is 1 hour ahead of Universal Time during winter.

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    True Solar Day

    The interval between two consecutive lower culminations of the Sun.

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    International Date Line

    An imaginary line where the date changes when crossed.

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    Hour Angle

    The angular measurement of time since a celestial object's upper culmination, often related to true solar time.

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    Lunar Calendar

    Calendar based on the phases of the moon, such as new or full moons.

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    Solar Year

    A calendar year based on the Earth's orbit around the sun, approximately 365.242 days.

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    Synodic Month

    The time between successive new moons, about 29.530589 days.

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    Terrestrial Dynamical Time (TDT)

    The proper time of an observer moving with the Earth, affected by relativistic time dilation from Earth's orbital speed.

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    Terrestrial Time (TT)

    The standard time scale adopted in 1991, equivalent to TDT and defined as TT = TAI + 32.184 s.

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    Coordinated Universal Time (UTC)

    The primary global time standard, regulating clocks and time based on Earth's rotation adjustments.

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    UT1

    A form of Universal Time that accounts for polar motion.

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    ΔT

    The difference between Terrestrial Time (TT) and Universal Time (UT1), represented as ΔT = TT - UT1.

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    Leap Second

    An extra second added to UTC to keep it in sync with Earth's rotation, the last was on December 31, 2016.

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    Black Body

    An idealized object that absorbs all electromagnetic radiation and emits black-body radiation when in thermal equilibrium.

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    Effective Temperature (Teff)

    The temperature of a star derived from its total flux and angular diameter.

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    Conservation of Energy

    A fundamental principle stating that energy cannot be created or destroyed.

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    Total Flux (f)

    The total amount of energy emitted by a star per unit time.

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    Distance (D)

    The space between the Earth and the observed star.

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    Angular Diameter (θ)

    The angle that an object appears to occupy in the sky.

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    Lunar Occultation

    When the Moon passes in front of a star, blocking its light.

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    Diffraction

    The bending of waves around obstacles, affecting angular measurement.

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    Code et al. (1976)

    A research reference used for deriving effective temperature methods.

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    Planck Function

    Describes the spectral distribution of electromagnetic radiation from a black body.

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    Black Body Radiation

    The electromagnetic radiation emitted by an idealized perfect absorber at thermal equilibrium.

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    Stefan-Boltzmann Law

    The total energy radiated per unit surface area is proportional to the fourth power of the temperature.

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    Effective Temperature

    A measure of a star's radiative output based on its emitted spectrum.

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    Specific Intensity

    The power per unit area per unit solid angle per unit frequency emitted by a source.

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    Flux

    Net energy flow across an area in a specified direction over time in a spectral range.

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    Nobel Prize in Physics 2006

    Awarded to John C. Mather and George F. Smoot for discoveries in the cosmic microwave background radiation.

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    Effective Temperature of the Sun

    The effective temperature of the Sun is approximately 5780 K.

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    Study Notes

    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.

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