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Title: Astronomy%20and%20Space%20Science%20II

Astronomy and Space Science II
  • Dr. Hoi-Fung Chau
  • and
  • Dr. Alex Tat-Sang Choy
  • Jointly Organized by
  • Hong Kong Space Museum
  • HKU Physics Department
  • Co-organized by
  • CDI of EDB

Stars and the Universe
  • Stellar magnitude, luminosity
  • Light pollution
  • Blackbody radiation, Color and surface
  • Stefans law
  • Spectral classes
  • H-R diagram
  • Spectral lines, Doppler effect
  • Radial velocity
  • Red shift and universe

Parsec Revisited
  • 1 pc (parsec) distance from which 1 AU extends
    1 arcsec 3.26 ly 3.24x1016 m
  • 10 pc 32.6 ly.
  • Note a star at 10 pc has a parallax of 0.1
  • In units of AU and radian, p 1/d.

Apparent Magnitude
  • The apparent magnitude system was first proposed
    by Hipparchus. He assigned the brightness stars
    first magnitude and the dimmest visible by eye
    sixth magnitude.
  • The apparent magnitude, denoted m, now are
    determined by measuring the brightness of
    celestial objects.
  • By definition, a 1st magnitude star is 100 times
    as bright as a 6th magnitude star, and 10000
    times as bright as an 11th magnitude star.
  • An m1 star is 1001/5 2.512 times as bright as
    an m2 star.
  • In general, the ratio of brightness between two
    stars is 2.512(m2-m1) or 100(m2-m1)/5.

Name Type Apparent Absolute
Magnitude Magnitude
Sun star -26.8 4.8
Full Moon satellite -12.6
Sirius star -1.4 1.5
Pleiades (M45) open cluster 1.6 -4.1
Polaris star 2.0 -3.6
Urban Naked Eye Limit 3.0
Andromeda Galaxy (M31) galaxy 3.5 -21.4
Orion Nebula (M42) diffuse nebula 4.0 -4.5
Io satellite 5.0
M4 globular cluster 5.6 -6.7
Country Naked Eye Limit 6.0-7.0
M54 (note extragalatic) globular cluster 7.6 -10.0
Crab Nebula (M1) supernova remnant 8.4 -3.0
Ring Nebula (M57) planetary nebula 8.8 -0.3
Light Pollution
  • This is what the Earth looks like at night. Light
    escaping to the space is a wasted energy
    resources because only aliens/astronauts could
    see the light.
  • Equally unfortunately, part of the light is
    scattered back to observers on Earth, creating a
    bright background. This is called sky glow.
  • Other forms of light pollution
  • glare, the unwanted light that enters the eye
    directly, which could lead to reduction of sight.
    On the road, it could affect the safety of cars.
  • light trespass, which is unwanted light entering
    ones property, which could lead to problems such
    as sleeping deprivation.
  • Light pollution also affect migrating birds, sea
    turtles, and other parts of the ecosystems.

Absolute Magnitude
  • The apparent magnitude depends on two physical
  • the amount of light energy emitted per unit time,
    called the luminosity, of the light source
  • the distance the of the light source from the
    observer (inverse square law)
  • E.g., if a 6th magnitude star located 100 pc from
    the Earth were moved to 10 pc from us, it would
    appear 100 times brighter, and become a 1st
    magnitude star.
  • To compare the luminosity between different
    stars, the absolute magnitude, M, of a star is
    defined as the apparent magnitude of the star if
    it is located 10 pc from the observer.
  • The absolute magnitude depend only on the
  • The star used in the above example has an
    absolute magnitude of 1.

Blackbody Radiation
  • A blackbody absorbs all frequencies of EM
    radiation that falls on it, and radiates the
    energy according to Plancks law.
  • The blackbody spectrum is continuous, and is used
    to explain basic stellar spectra and color as a
    function of surface temperature.
  • The intensity and the peak frequency increases
    with temperature of the body.
  • The perceived color of stars as a function of
    surface temperature is shown on the right.

Stefans Law
  • First obtained from experiment, the Stefans law
    states that the intensity, defined as the total
    energy radiated per unit time per unit area of an
    object, is given by
  • I sT4
  • Therefore, for spherical stars with radius R, its
    luminosity is given by
  • L 4pR2sT4
  • The Stefan-Boltzmann constant is given by
  • Luminosity is measured in Watt.

Trick or Treat?
In astronomy, many constants in equations are
difficult or tedious to obtain, but the equations
can be sometimes scaled to help application.
E.g.1. Stefans law applied to a spherical
star L 4pR2sT4 and LSun 4pRSun2sTSun4
implies L/LSun
(R/RSun)2 (T/TSun)4. Or in unit of
solar parameters, L
R2 T4, or R L1/2 / T2. E.g.2.
Keplers law (R1/R2)3 / (T1/T2)2 (M1/M2), for
central force system. Taking the
Earths orbital data, i.e. AU and Year, as units,
we have R13 / T12 M1,
where M1 is in unit of solar mass.
See later example of the supermassive
black hole at the center of our galaxy.
Spectral Absorption and EmissionStellar Chemistry
  • The blackbody spectrum is continuous.
  • Stellar atmosphere or gas cloud in between the
    star and the observer produces absorption lines
    by absorbing selected frequencies of light.
  • Gas cloud near bright stars can be excited by
    star light or UV radiation thus producing
    emission lines of selected frequencies of light.
  • The lines frequencies are properties of the
    chemical composition of the gas cloud. Helium was
    discovered from solar observations.
  • Emission lines could be observed in flame test

Spectral Classes
  • Stars are classified into spectral classes
    according to their absorption spectra. Different
    spectra implies different chemical composition.
  • Absorption spectra is dependent on the surface
    temperature of the star.
  • They are listed from high to low temperatures as
  • The colors are from blue to white to reddish
  • E.g., the sun is a G type star, Rigel is of B
    type, Betelgeuse is of M type.

The popular mnemonic is Oh, Be A Fine Girl/Guy,
Kiss Me.
Hertzsprung-Russel (H-R) Diagram
  • The H-R diagram is a log-log or semi-log plot of
    stellar luminosity (or absolute magnitude)
    against the surface temperature (spectral class).
  • Conventionally, higher temperature is on the
  • Stars are not evenly distributed on the diagram,
    but form groups, indicating different stories
    behind each group.
  • Most stars are on the diagonal called the main
  • Stars at the upper right corner have low energy
    output per area (T4) but high luminosity,
    therefore are very large, called giants.
  • Conversely stars at the lower right are very
    small, called dwarfs.

Using R L1/2 / T4, or we can easily compute
the relative sizes of stars on the H-R diagram.
Spectral lines, Doppler effect
  • Doppler effect ??/? vr /c,
  • where vr is the radial velocity.
  • Note that even after the shift, the patterns of
    lines can still be recognized, see figure on the
  • For example, in binary systems, the spectral line
    of the two stars can be seen as shifting in the
    opposite direction.
  • However, in this course, we only consider the
    case where the mass of B is negligible.
  • Note also that the spectrum of A and B can be

Note that the whole system of lines shifts
Radial Velocity Curve for a Simple Binary System
  • For a small celestial body in circular orbit
    around a massive body as seen along the orbital
    plane, the radial velocity curve is a cosine
  • The functional form is vr v cos? r? cos? ,
    where r is the orbital radius, ? is the angular
    frequency obtained from the curve.
  • Thus r and period T can be found easily. The mass
    of the central body can thus be found from
    Keplers law.

Galaxies and Dark Matter
  • How fast an object revolves depends on how much
    matter inside its orbit. If all the matters are
    visible, the orbital velocities of stars, say,
    near the edge of our galaxy will follow the red
    line above.
  • However, we discovered that they are moving
    faster than expected, by Keplers law, there must
    be more matters than we have seen.
  • The extra matters are called dark matters because
    they cannot do not emit EM waves, they reveal
    their existence by their gravity.
  • This discovery was made by Vera Rubin and her
    co-workers in the 1970s. She discovered the
    rotation curve of by Doppler shift measurements
    of the edge-on spiral galaxies.

Redshift and Universe
  • Vesto Slipher measured the redshift and hence
    radial velocity of galaxies.
  • Hubble measured the distances or galaxies. By
    combining with data on radial, he discovered the
    Hubbles law v H d
  • The most accepted value of the Hubble constant H
    is about 70 km/s/Mpc.
  • Hubbles law states that the further the galaxy
    from us, the faster it recede from us. This is
    explained by the expansion of the universe.
  • Note that this cosmological redshift not due to
    Doppler effect. The galaxies moves away from us
    because the universe (space-time) itself is
    expanding, not because they moves in the space.

In Depth Questions
Q How bad is the light pollution in Hong Kong?
A Very bad. More HKUs light pollution study in
2005-2006 shows that the apparent magnitude per
square arc second in HKs urban area and country
side are 16.4 and 19.7, respectively, while the
ideal number is 22. Since the contrast between
dim celestial objects and the background is
important for observing them, a brighter
background has the same effect as dimming the
celestial objects. Also, moisture in the air
significantly increases scattering and hence
light pollution. Therefore the sky in Hong Kongs
country side is only slightly better than some
less populated and drier cities.
Q What are the ways to reduce light pollution?
  • Turn off unneeded light, reduce over
    illumination, and use timers or automatic
  • Use proper outdoor light fixtures. For example,
    the lighting on the left illuminate only objects
    below, and is more efficient and create less
    light pollution than the one on the right, which
    glare drivers from afar and leaks light to the
  • Designers of decorative lights/building should
    weight the energy/environmental impact carefully
    against the effect they want to achieve.
    Nowadays, it is not good for publicity to have an
    energy inefficient lighting that damage the
  • These measures also saves energy and hence money.
  • About 30-60 of lighting are not necessary.

Q Can natural light affect observations?
A Yes. More For example, the moon is a source
of the glare and sky glow. Sky glow can also be
caused by atmospheric discharge due to solar
activity. The word light pollution is normally
used to describe artificial lights, however, it
is loosely used by some people to describe
natural light sources which affects observation.
The terms sky glow and glare are more
appropriate. Sky glow usually affects
observation the most because glare and light
trespass can be blocked to some extend.
Q How are the apparent and absolute magnitude
related mathematically?
A The ratio of brightness between two stars with
magnitude m1 and m2 is 100(m2-m1)/5. One can
easily check this formula with the
definition. Now if a star of apparent magnitude
m and distance d is moved to 10 pc from us and
its new apparent magnitude is M, then the ratio
of brightness is 100(M-m)/5
(d/10)2, Taking log and rearranging, we have M
m 5 log10(d/10). But by definition this M is
also the absolute magnitude. More In the real
world, it is necessary to specify what type of EM
radiation is being measured, for example a star
may have very different UV, visible, IR, etc.
magnitudes. Color index B-V is the difference in
magnitudes of a star by blue and visible
(green-yellow) filters. It can be used to
indicate color, replacing temperature on the
x-axis of the H-R diagram. However, for this
course, we use them as if they were the same.
Also, when M is used to relate to the luminosity
L, all frequencies are included. This is called
bolometric absolute magnitude.
Q How is absolute magnitude related to
luminosity mathematically?
A The ratio of luminosity between the Sun and a
star is LSun/L 100 (M-MSun)/5 Taking
log and rearranging, we have M MSun 2.5
log10(LSun/L). For the Sun, the absolute
magnitude is 4.8 and luminosity is 3.831026W. We
have M 71.3 - 2.5 log10(L), where L is in
W. More Using this and earlier formulae, we can
see how the physical quantities m, d, M, L, R, T
are related. Both m and T are directly
measurable, but d has to be obtained from
observations like parallax. However, once d is
found, M, L, R can be calculated easily. This is
an amazing achievement - even to date, the radius
can be measured directly, by resolving the
stellar disk, for only a tiny percentage of stars.
For non-stellar object, such as star clusters,
luminosities can be summed or integrated L S
Li for multiple sources. The absolute magnitude
can be found from the equation above.
Q Why is the magnitude system a logarithm system?
A When Astronomers tried to modernize the
Hipparchus system, they found that it feels like
the brightness increases linearly as the
magnitude decrease. Assuming the human response
to be a logarithm function, they defined the
relation between the magnitude and the brightness
as a logarithm function. However, it is later
discovered that human response is closer to a
power law, so the reasoning for the above
definition does not hold. However, the
magnitude-brightness relation is still in use as
a definition.
Q Why do we need space telescopes?
A The atmosphere is transparent only to visible
light, part of IR and radio wave, other
wavelengths are scattered or absorbed.
Electromagnetic wave that can not reach the
ground has to be observed by space telescopes.
More Hubble Space Telescope observes visible
light because atmospheric distortion, known as
astronomical seeing, limits the resolving power.
Also, ground objects radiates IR which is noise
for IR astronomy.
Q Are there other ways to avoid the atmospheric
A Yes, adaptive optics, in which deformable
mirrors are used to cancels the effect of
atmospheric distortion.
More In adaptive optics, portion of light from
the telescope is analyzed by a fast computer
which control in real time a deformable mirror to
cancel the atmospheric distortion. Usually, an
artificial star is created by a special laser in
the sky, so that the computer knows how to deform
the mirror. Adaptive optics helps large
telescopes to achieve their theoretical
resolution limit (1.22?/D) on Earth.
Q What is astronomical interferometry?
A High resolution interference measurements made
by combining signals of two or more
More Large number of telescopes can be used to
produce pictures with resolution similar to a
single large telescope, with the diameter of the
combined spread of telescopes. Interference is
measured by combining signals from different
telescope, though electronic means or optical
fibers. For example, the Very Large Array (VLA)
is a system of 27 dishes with a maximum baseline
of 36km, which could not be achieved with single
telescope. Very Long Baseline Interferometry
(VLBI) record the data with local atomic clock
timing for later interference of signals. Because
the antennas are not physically connected, the
baseline can be much longer.
Q What is simultaneous multiple wavelength
A The investigation of astronomical objects in
different windows of wavelengths at the same time.
Images provided by Prof. Bill Keel, University of
More From left to right, the above are the
optical, ultraviolet, X-ray, infrared and radio
wave images of M81. A lot more information can be
obtained from multiple windows of wavelengths
than just a single window. For example, the
ultraviolet image can be used to locate the very
hot O type and B type stars, while the X-ray
image may be used to find blackhole candidates.
Other events, such as the gamma-ray bursts has
been studies simultaneously in gamma-ray and
optical windows, which showed that gamma-ray
bursts are coming from cosmological distances,
solving a long mystery.

Q How do the human eye and instruments respond
to light?
A The response of normal and dark adapted eye
are shown below. Astronomers often use filters
for camera or other instruments. The U
(ultraviolet), B (blue), V (visual), R (red)
filters are some of the common filters. Other
filters such as line filters are also used. For
example, many Hubble images are taken with line
filters to enhance the physical features often
three line filtered images are then applied as
RGB channels to obtain a false color image.
More The magnitudes of the same star measured by
using different filters are different. For
example, the color index, defined as MU-MB, is
sometimes use as the x-axis in the H-R diagram.
Q Can I understand Stefans law from Planks law?
A Yes, it is just an integration away. More
Plancks law states
Here, I(v)dv is the amount of energy per unit
surface per unit time per unit solid angle
emitted in the frequency range between ? and
?d?. So
L ? I(v)dv. The T4 dependence can be obtained
without actually doing an integration, by making
the substitution xhv/kT.
Q Why are the spectral classes arranged
Historically, spectral type were given letters A
to Q according to the strength of hydrogen lines.
The basic work was done by the women of Harvard
College Observatory, primarily Annie Jump Cannon
and Antonia Maury. It was discovered much later
that the hydrogen line strength was connected to
stellar surface temperature.
More Each class has a subclass with a number
from 0 9. E.g. O1 is hotter than O5. The sun
is a G2 star, Rigel is a B9, Betelgeuse is an M2.
Sometimes a Roman numeral is attached at the
back to indicate the type, e.g. the Sun is a G2V,
V for main sequence stars. New spectral types
have been added for newly discovered types of
stars. E.g. class WR for the superluminous
Wolf-Rayet stars.
Q What color is the Sun?
A We should absolutely not look at the Sun
directly. Color vision is due to a result of the
response of the three types of cone receptors and
the brains interpretation of the response.
Intense light from the Sun at noon would
saturate, and even damage, the all three types of
cone receptors, giving an white appearance.
More An related question is what color would
the Sun, a G2 star, appear from a distance of,
say, a few light years away? The Suns surface
temperature is 5780K, but the blackbody spectrum
is only a good approximation. The spectrum peaks
near 470nm, which is green. However, since the
Sun emits light from red to blue in similar
intensity, the color as seen by most people would
be white, may be with a tint of light peach.
Q How to better use our eyes for star watching?
  • Use the center of the vision to observe detail
    and color for bright object.
  • Use averted vision to detect/observe dim objects.

  • The color receptors, called cones, are
    distributed densely and mainly near the center of
  • The more sensitive rods can only detect light
    intensity, and are distributed mainly outside the
    center of vision. From bright to dark places, it
    takes 7-10 minutes for saturated rods to become
    dark adapted and even longer for detecting dim
    star light, therefore shining light on someone
    watching stars is rude.
  • In dark, read with a red light to protect dark
    adaptation, because rods are not very sensitive
    to red light.
  • Dim stars and galaxies appear colorless because
    their light are too weak to excite cones. On the
    other hand, extremely bright objects appear white
    when the cones are saturated. Therefore the
    perceived color depends on the intensity as well.
  • Color is not an objective quantity when the
    source is not monochromatic, different
    people/instruments can report different
    perceived/report colors.
  • The topic of vision and color is a good example
    of multiple discipline study, it is related not
    only to physics and astronomy, chemistry
    (photosensitive pigments), biology, psychology
    (color perception, illusion), technology
    (displays, CCD, printing, lighting) and art
    (painting, photography, films).

Q For sunspopts, Lsurf/Lspot (6000/4000)4
5, less than 2 magnitude difference, why do they
appear black?
A Contrast with the surface in visible light.
  • Note that all wavelengths contribute to
    luminosity. However, only visible lights
    contribute to the visual brightness.
  • The spectral peak of the sunspot is at infrared,
    the amount of visible light has a more
    significant difference. The sunspot alone would
    still be bright, they appear dark due to the
    contrast the brighter surface.
  • One should always be careful when spectral
    response in the question. For example a spectrum
    that peaks at green doesnt mean the star is
    perceived as green in human eye.

Q Why are stars grouped on the H-R diagram ?
  • The H-R diagram is a statistical view of
    collections of stars, such as a galaxy or star
    clusters at an instant of time. (Our lifetime is
  • A crowded region on the H-R diagram means there
    are more stars in such a state. It may also mean
    stars spend more time in that state during their

  • The fate of a star is determined mainly by its
  • A star starts its life on the cool side of the
    diagram and evolves as it gets hotter. When
    temperature is high enough for fusion of
    hydrogen, it became a main sequence star and
    stays that way for most of its lifetime.
  • After most hydrogen is brunt, heavier stars start
    to burn heavier elements and enter a period of
    expansion (cooling, giants) and contraction
    (heating) until they finally explode as a
    supernova or die as a white dwarf.
  • A star less than about 0.4 solar mass quietly and
    steadily burns the hydrogen to helium until it
    becomes a white dwarf.

Q How to measure distance when parallax is too
A Parallax for remote stars clusters and
galaxies are too small to be measured accurately.
Uses standard candles, which are objects with
known luminosity. From L, M and hence d can be
More The most famous standard candles are
  • Cepheid variables are a class of variable stars
    which have a tight correlation between their
    period of variability and absolute luminosity.
    The Cepheids about 103 to 104 as bright as the
    Sun, therefore are suitable for measuring
    distance of clusters and galaxies. Hubble
    measured the Cepheids in galaxies, leading to the
    famous Hubble law.
  • Type Ia Supernovae are the explosions resulted
    from white dwarf accreting matter from a nearby
    companion giant. When total mass of the dwarf and
    the accreted mass is close to about 1.4 solar
    mass, fusion of carbon and oxygen, given out
    enough energy to break the star, and a luminosity
    of about 5 billion suns. Since the mass is always
    about 1.4 solar mass at the explosion, the
    luminosity is about the same for all type 1a
    supernovae. Because of their brightness, they are
    useful for measuring distance of remote galaxies.

Q How are proper motion, radial and tangential
velocities related?
  • The proper motion of a celestial object is the
    change of angle per unit time due to its real
    motion. It is given by d?/dt vtang/d, where d
    is the distance to observer.
  • The tangential velocity can be found if proper
    motion and d are measurable.
  • The radial velocity is measured by spectroscopy.
  • vtot2 vtang2 vr2.

Q How does the radial velocity curve look when
the orbit of the binary system is elliptical?
More The radial velocity curve can still be
fitted to find the orbital parameters. See
http// for the
applet show here.
Q How to detect extrasolar planet, or
Due to the high difference in brightness between
a planet and its host star, direct observation of
exoplanet is very difficult. Only one exoplanet
has been imaged directly (in IR). About 200
exoplanets now known are found indirectly by
Doppler spectroscopy, astrometry, transit, pulsar
timing, circumstellar disks, or gravitational
  • Radial velocity measurement though Doppler
    spectroscopy has been the most successful method.
    Small change in radial velocity of the main star
    can be used to calculate the orbit and the mass
    of the planet.
  • Astrometry refer to the small wobble in position
    due to the gravitational pull of the planet.
  • Note
  • Most exoplanet found have high masses because
    they are easier to discover. However, smaller
    planets may be quite common as well.
  • Most known exoplanets orbits F, G, K stars
    roughly similar to the Sun. O-type stars may
    evaporate dust clouds before they can form
    planets. M-type dwarfs may have lower mass
    planets which are harder to detect.

Q Is there really a supermassive black hole at
the center of the Milky Way?
A Very likely.
More From measure of stars around Sagittarius A
for several years, the orbit of the stars and
hence the mass inside the orbit. As an estimate,
consider the star SO-20, neglecting the
inclination, R 1500 AU, T 30 yr, from
Keplers law the mass inside the orbit is
15003/302 4 million solar masses. The
published result using SO-2 is 3.7 1.5 million
solar masses, confined in a region of 120 AU.
Only a black hole allows the presence of so much
mass in such a small region. Note 1. Visible
light from the Milky Way center is obscured by
dust clouds, but IR can penetrate though the dust
clouds. 2. Sagittarius A is a bright radio
source. 3. Although the center is a supermassive
black hole, the orbits star stars sufficiently
far away still obey Keplers law.
SkyTelescope, April 03, p.49
Q Is redshift observed for remote galaxies due
to Doppler effect?
A No.
More Three causes for redshift
  1. Classical or (special) relativistic Doppler
    shift. Used to measure radial velocity
    of stars, rotation of stars and galaxies, detect
    close binaries.
  2. Gravitational redshift (general relativity). As a
    photon climbs the gravitational field, the
    measured wavelength is reduced. The effect is
    most prominent near massive objects such as
    neutron stars or black holes, and tiny (but
    measurable) near Earths surface.
  3. Cosmological redshift (expansion of space). Since
    the cosmic scale factor a increase as a function
    of time, the observed wavelength of a photon
    emitted by a remote galaxy at time t is given by
    ?observe ?emit anow / a(t).

Q What is the age of the universe?
A The current scientific consensus holds this to
be about 13.7 billion years, obtained from
measurement of the small variation in cosmic
microwave background (CMB).
More A rough estimate can be done by asking how
long it take for two galaxies to move away from
each other to a distance d apart, at a constant
velocity v. This time, d/v 1/H, is called the
Hubble time, and is approximately 14 billion
years. Of course, this is only an approximation
because v does not have to be a constant.
Different models predicts accelerations of either
positive, zero, or negative. Note In the
1990s, by studying the brightness of Type Ia
supernovae very far away, there is some evidence
that the sum of the dark energy density and mass
density is about equal to the critical density.
Hence, we may be living in a flat universe .Those
studies also suggest that the expansion of the
universe is accelerating. The sum of mass density
and the dark energy density determine
acceleration. The dark energy is the energy of
the vacuum, which is also called the cosmological
constant. Although we can measure it, we do not
know much about it.
Q How big is the universe, or is it infinite?
A We normally use the term universe for
observable universe. The radius of the
observable universe is 46.5 billion ly. The
observable universe centers around us. Note when
we look now at the galaxies, we are looking into
the history of different time. The further is a
galaxy, the early was the light emitted.
More From the models of the universe, if the
density of the universe is smaller than/equal
to/larger than a value called the critical
density, then it is open/flat/close. The universe
should be infinite if it is open and flat, finite
if it is closed. For a finite universe, it is
possible that light from some remote galaxies
have not reach us yet since the beginning of
time, and therefore the universe may be bigger
than what we can observe. However, what might be
outside of the observable universe is of no
importance to us before there can be no physical
consequence or evidence whether they exist or
Q What is outside of the universe?
If there exists any objects outside the
observable universe, light/information from them
has not arrived us given all the time since big
bang, so there would be no prove as to what, if
anything, is out there.
A related question whats before the big
bang? It is an ill-posed question, it is like
asking whats north of north-pole. At the
north-pole, if you walk in one direction, you are
heading south, if you walk instead in the
opposite direction, youre still heading south.
Q If the age of the universe is 13.7 billion
years, how could the farthest observable object
be 46.5 billion ly away?
A Because we are talking about the comoving
distance, which tells us the distance of the
object today.
More Although the light from the farthest
observable object only has 13.7 billion years to
travel, but the space is expanding at the same
time, therefore the object is much further away
than 13.7 billion ly now. Because the universe
is expanding, there are several physically useful
definition of distance, the most often referred
one is the comoving distance as defined above.
See http//
for more detail.
Q When d gt c/H, is the special relativity
A No, when d gt c/H, v Hd gt c. However, this is
not a violation of special relativity because the
galaxy are receding due to the expansion of
space, not due to the motion of galaxies.
More The radius of the observable universe is
about 14000Mpc, c/H 4000Mpc, beyond which
galaxies recede from us faster than the speed of
Q What are dark matter and dark energy?
  • Dark matter is matter that does not emit or
    reflect enough EM radiation to be detected, but
    it show its presence though gravity.
  • Dark energy is a hypothetical energy of the
    vacuum and has strong negative pressure. It
    accelerates the expansion of space-time.

  • We know little about the composition of dark
    matter and dark energy, but only 4 of total
    energy density can be seen directly, 22 is dark
    matter, 74 is dark energy.
  • The composition of dark matter is unknown, but it
    may include
  • baryonic dark matter matter made of protons and
    neutrons, such as brown dwarfs, black holes, dark
    gas clouds. This ordinary matter are not enough
    to explain the missing mass.
  • non-baryonic dark matter such as neutrinos, or
    hypothetical elementary particles such as weakly
    interacting massive particles (WIMP).
    Non-baryonic dark matter seems to be a major
    portion of dark matter.
  • Dark matter may also be classified as
  • hot dark matter fast moving particles like
  • cold dark matter slow moving particles/objects
    like brown dwarfs.
  • Existence of dark energy is equivalent to having
    a cosmological constant term in general
    relativity. It has the meaning of the cost of
    having space.

Q How is astronomy treated in the media/public?
It varies from place to place.
Hong Kong
Powdered milk TV advertisement.
BoA Amazing Kiss music video.
Q How can I understand different designs of
Q Are there any tips on using telescopes and
A Some important points are 1. Set up telescope
on grass field for less air convection, this is
important for high resolution views for planets.
Check for water sprinklers. Concrete pavements
absorbs heat during the day and release heat
through convection the few hours after
sunset. 2. In HK moisture can be a big problem,
dew shield is must. In outdoors, the equipment
can fall below the dew point easily, if problem
is strong, dew heater is needed. After a lens is
dew up, wiping it would not help. Without a dew
heater, dew up lens implies packing time. 3.
Dust on lens require no cleaning, if dust becomes
a serious problem, they can be blow off with
compressed air or brush off using camera lens
cleaning kits. Dew on lens should not be wiped
off, the scope should be left in warm in door for
the dew to evaporate off, and then store in dry
place, with desiccant. 4. Small particle can
scratches the lens permanently during lens
cleaning (with lens liquid), therefore, it is
advised that cleaning should be avoid. If you
clean your lens more than once a year, it is most
likely too much. 5. Keep warm, bring some food
and drink. Observing chairs are great.
Q Can you suggest some equipments for schools?
A It is said that the best telescope is the one
you use most. Different schools have different
needs due to their programs, location, budget,
number of students, etc. It is important to know
if the equipments are for visual or imaging work,
or for inspiration. The following are just some
possible equipment choices, popular in the
amateur astronomy community, and are benefited by
cost saving due to mass productions
Small high quality refractors with small
equatorial or alt-az mounts, GOTO or not best
image quality, very versatile, most expensive. A
compromise is to have a small one for portable
and frequent uses. Good for planet/solar/lunar
visual observations, wide field imaging. (Front
Solar filter required for solar observations thru
the telescope. Filter manufacturers recommend
against using front solar filters on
non-refractors for safety reasons.) Medium size
catadioptrics with GOTO mounts reasonable price,
reasonable image quality, but a bit low in
contrast and have narrower field, very powerful
when combined with a GOTO and tracking system.
Good for high power imaging or general purpose
visual observations. Large reflectors with
dobsonian mounts cheap for the size, good image
quality, but no tracking. Their large sizes allow
observation of dimmer objects.
Eyepieces a set of high, medium, and low power
eyepiece for each scope is the minimum. Quality
is important for high power eyepieces, while good
wide field low power eyepieces are also quite
expensive. There are many good and low cost
medium power eyepiece. Some company sells a set
of eyepieces which could be a low cost way to
start with. Neutral density moon filter.
Binoculars are low cost, very useful, and can
be given to students no using the telescopes.
Note DO NOT distribute binoculars for solar/day
time sections! Solar projection screen. FRONT
solar filter. Cooled CCD cameras with high
quality optical and tracking systems can take the
best DSO (deep sky objects) pictures, but are
very expensive. Some cheap CCD/CMOS based webcams
are very good for taking videos of planets for
stacking, as well as class demonstration. Digital
cameras with proper adaptors can take good
stack-and-track images for planets and bright
DSO. In recent years, binoviewers have become
very cost effective. Experience has show that
their views are very effective for attracting the
attention of the untrained eyes. Recommended if
budget allows.
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Q Can you give us some references?
A Here are some of them
  • NASA. The NASA site contain many useful
    information and images.
  • Wikipedia. Note The Wikipedia is probably the
    quickest way to find information. However,
    because it can be edited by anyone, one should
    not trust the information without checking
    independent sources or risk getting wrong or
    misleading (intentional or not) information.
  • HKU Physics Department, Nature of the Universe
    web site http//
  • J. M. Pasachoff, Astronomy From the Earth to the
    Universe (1998).
  • E. Chaisson and S. McMillan, Astronomy Today
  • M. A. Hoskin, Cambridge Illustrated History of
    Astronomy (2000).
  • ??? ? ??? , ?? (2000).
  • ??? , ??????? (2003).
  • ???????????? (2000).
  • Stephen Hawking's Universe, PBS Home Video.
    (1997) .
  • Cosmos Carl Sagan , Cosmos Studio. (1980).
  • October Sky, Universal Studios. (1999).

Q Are there any useful classroom teaching kits
  • A Here are some of them.
  • Free software such as can be
    used to simulate the motion of celestial bodies,
    to set exam questions and to plan your
    observation session.
  • contains many useful physics
    simulations to teach various NSS physics and
    chemistry topics.
    contains some interesting videos on blackbody.
  • Steven Hawkings Universe (in particular, DVD 1
    Seeing is Believing, Chap 5) is a good video to
    teach from spectrum all the way up to the
    Hubbles law.

  • Continue
  • The Doppler Ball is a good teaching aid to
    demonstrate Doppler effect. You can make one
    using less than HK50.
  • Planets (BBC) (such as Disc 1 Different Worlds,
    Chap 4) contains a few historical films of rocket
  • One may discuss the science involved in a few
    movies, such as Apollo 13 and 2001 A Space
    Odyssey, in class.
  • October Sky is a good movie to inspire student to
    study science and engineering. Consider showing
    it after class.
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