This document discusses various units used to measure astronomical distances and time. It describes key units like the astronomical unit (distance from Earth to Sun), light year, parsec, and solar mass. Parallax is introduced as a key method to measure distances to stars based on their apparent shift against background objects when observed from opposite sides of Earth's orbit. Standard candles like Cepheid variables are also discussed as important tools for determining extragalactic distances. A variety of timekeeping systems are outlined, including universal time, sidereal time, and their local variations important for astronomical observations and calculations.

1. Astronomical ScalesAstronomical Scales

2. Astronomical DistancesAstronomical Distances

3. Importance of Distance
Measurement
Importance of Distance
Measurement
Distances are necessary for estimating:
• Total energy emitted by an object
(Luminosity)
• Masses of objects from their orbital motions
• True motions through space of stars
• Physical sizes of objects

4. Astronomical UnitAstronomical Unit
• It is the average from Earth to the Sun, about
93 million miles (150 million km), and is used
to measure relatively short distances, such as
those between the Sun and its planets or
between the stars in a binary system.
• This distance varies as Earth orbits the Sun,
from a maximum (aphelion) to a minimum
(perihelion) and back again once a year.

5. Light YearLight Year
• The distance light travels in one year, which is
about 5.88 trillion miles or almost 800 times
the diameter of the solar system.
• The nearest star is 4.2 light-years away.
• The nearest spiral galaxy lies about 2.5 million
light-years from Earth.

6. ParsecParsec
• A parsec is a unit of distance equal to 3.26
light-years. The name means “PARallax-
SECond,” and it refers to a way to measure
the distances to other stars.
• The distance of the stars us measured using
the basic mathematical geometry systems.

7. Astronomical distancesAstronomical distances
• The distances are measured after every six
month. This is the time when the earth is on
opposite sides of the sun.
• Measured by the methods of Parallax.

8. ParallaxParallax
• Effect of seeing a pen with both the eues one
by one.
• This effect is called parallax.
• If a star has a parallax of one second — in other
words, if it appears to shift back and forth
across the sky by exactly one second of arc
(1/3600 degree) — then its distance is one
parsec.

9. ParallaxParallax
Assuming the angle ‘p’ is small, the
distance to the object measured in
parsecs (in terms of speed of light) is
equal to the reciprocal of the parallax
angle measured in arcseconds.
D(parsec) = /1 p(arcsec)

10. ParallaxParallax
Parallax decreases with Distance
• As the distance to a star increases, the its
parallax decreases.

11. Examples: parallaxExamples: parallax
• The star alpha Centauri has a parallax of
p=0.742-arcsec. Calculate its distance. (1.35
pc)
• A star is measured to have a parallax of
p=0.02-arcsec

12. Standard CandleStandard Candle
• A standard candle is an astronomical object that has a
known absolute magnitude.
• Measuring the apparent magnitude of the object
distance can be measured using the formula:
m-M = 5 log d – 5
where m is the apparent magnitude of the object, M is
the absolute magnitude of the object, and d is the
distance to the object in parsecs.
Cepheid Variable stars and RR Lyrae stars are used as
standard candles.

13. Chart of measuring distanceChart of measuring distance
The cosmic distance ladder

14. Astronomical distancesAstronomical distances

15. Methods to find distancesMethods to find distances
Main sequence fitting method
•Absolute magnitude for a group of stars is plotted against the spectral
classification of the star, in a Hertzsprung–Russell diagram
•Evolutionary patterns are found that relate to the mass, age and
composition of the star. By measuring these properties from a star's
spectrum, the position of a main sequence star on the H–R diagram
can be determined, and thereby the star's absolute magnitude
estimated.
•A comparison of this value with the apparent magnitude allows the
approximate distance to be determined, after correcting
for interstellar extinction of the luminosity because of gas and dust.

16. Extragalactic distance scaleExtragalactic distance scale
• The extragalactic distance scale is a series of
techniques used today by astronomers to
determine the distance of cosmological bodies
beyond our own galaxy, which are not easily
obtained with traditional methods.
1.Wilson–Bappu effect: spectroscopic parallax
2.Classical Cepheids (variable stars)
3.Hertzsprung-Russell-diagram
4.Red Shift

17. Red ShiftRed Shift
• v = H × d
v = speed of light
with which
galaxies recede
H = Hubble
constant
D = distance of the
gaalxy

18. Astronomical massAstronomical mass
• Solar mass is used to measure
astronomical objects.
• Represented by M .☉
• 1 solar mass (M☉)
= 1.98892×1030
kg
• M☉ 333000 times the mass of
the Earth or 1,048 times the
mass of Jupiter.
SOLAR
MASS

19. Astronomical massAstronomical mass

20. Astronomical LuminositiesAstronomical Luminosities
Astronomical Luminosities are given by Solar Luminosity

21. Astronomical timeAstronomical time
• Atomic Times
– TAI - International Atomic Time
– UTC - Coordinated Universal Time (Mean Solar Time)
• Earth Rotation Times
– UT - Universal Time (Greenwich Mean Time)
– GMST - Greenwich Mean Sidereal Time
– GAST - Greenwich Apparent Sidereal Time
– LMST - Local Mean Sidereal Time
– LST - Local Sidereal Time

22. Universal TimeUniversal Time
• UT is the GMT.
• UT is observed rotation of the earth with
respect to the mean sun corrected for the
observer's longitude with respect to the
Greenwich Meridian.
• one more day in a sidereal year than in a solar
year.

23. GMST - Greenwich Mean Sidereal
Time
GMST - Greenwich Mean Sidereal
Time
• Sidereal time is the measure of the earth's rotation
with respect to distant celestial objects.

24. Local Mean Sideral TimeLocal Mean Sideral Time
• Local Mean Sidereal time is GMST plus the
observer's longitude measured positive to the
east of Greenwich.
• observatory's sidereal clock.
• LMST = GMST + (observer's east longitude)

25. Local Sideral TimeLocal Sideral Time
• The definition of Local Sidereal Time is "the
local hour angle of a catalog equinox."
• Hour Angle = LST - Right Ascension

26. ECLIPTIC AND EQUATORECLIPTIC AND EQUATOR