Astronomy and Space Science II

1
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

2
Stars and the Universe

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

3
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
  arcsec.
• In units of AU and radian, p 1/d.

4
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.

5
Examples
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
6
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.

7
Absolute Magnitude

• The apparent magnitude depends on two physical
  quantities
• 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
  luminosity.
• The star used in the above example has an
  absolute magnitude of 1.

8
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.

9
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.

10
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.
11
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
  experiments.

12
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
  OBAFGKM.
• The colors are from blue to white to reddish
  orange.
• 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.
13
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
  left.
• 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
  sequence.
• 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.
14
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
  right.

• 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
  different.

Note that the whole system of lines shifts
accordingly.
http//www2.enel.ucalgary.ca/People/ciubotar/publi
c_html/Starsevol/specbin-anim.gif
15
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
  function.
• 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.

http//www.roe.ac.uk/pmw/RVorbit.htm
http//www2.enel.ucalgary.ca/People/ciubotar/publi
c_html/Starsevol/specbin-anim.gif
16
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.

17
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.

http//en.wikipedia.org/wiki/Hubble_law
18
In Depth Questions
19
Q How bad is the light pollution in Hong Kong?
http//partnernet.hktb.com/pnweb/jsp/comm/index.js
p
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.
20
Q What are the ways to reduce light pollution?

• Turn off unneeded light, reduce over
  illumination, and use timers or automatic
  switches.
• 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
  sky.
• 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
  environment.
• These measures also saves energy and hence money.
• About 30-60 of lighting are not necessary.

A
http//dcfever.com/photosharing/enlargephoto.php?p
hotoID350951
21
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.
22
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.
23
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.
24
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.
25
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.
26
Q Are there other ways to avoid the atmospheric
distortion?
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.
27
Q What is astronomical interferometry?
A High resolution interference measurements made
by combining signals of two or more
telescopes/antennas.
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.
28
Q What is simultaneous multiple wavelength
observation?
A The investigation of astronomical objects in
different windows of wavelengths at the same time.
Images provided by Prof. Bill Keel, University of
Alabama
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.

29
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.
30
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.
31
Q Why are the spectral classes arranged
strangely?
A
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.
32
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.
33
Q How to better use our eyes for star watching?
A

• Use the center of the vision to observe detail
  and color for bright object.
• Use averted vision to detect/observe dim objects.

More

• The color receptors, called cones, are
  distributed densely and mainly near the center of
  vision.
• 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).

34
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.

35
Q Why are stars grouped on the H-R diagram ?
A

• 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
  short!)
• 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
  lifetimes.

More

• The fate of a star is determined mainly by its
  mass.
• 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.

36
Q How to measure distance when parallax is too
small?
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
found.
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.

37
Q How are proper motion, radial and tangential
velocities related?
http//www2.enel.ucalgary.ca/People/ciubotar/publi
c_html/Starsevol/totalvel.gif

• 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.

38
Q How does the radial velocity curve look when
the orbit of the binary system is elliptical?
A
More The radial velocity curve can still be
fitted to find the orbital parameters. See
http//www.roe.ac.uk/pmw/RVorbit.htm for the
applet show here.
39
Q How to detect extrasolar planet, or
exoplanets?
A
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
microlensing.
More

• 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.

40
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
41
Q Is redshift observed for remote galaxies due
to Doppler effect?
http//antwrp.gsfc.nasa.gov/apod/ap031102.html
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).

42
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.
43
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
not.
44
Q What is outside of the universe?
A
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.
45
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.
http//atlasoftheuniverse.com/expansion.gif
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//atlasoftheuniverse.com/redshift.html
for more detail.
46
Q When d gt c/H, is the special relativity
violated?
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
light.
47
Q What are dark matter and dark energy?
A

• 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.

More

• 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
  neutrinos.
• 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.

48
Q How is astronomy treated in the media/public?
A
It varies from place to place.
Japan
Hong Kong
Powdered milk TV advertisement.
BoA Amazing Kiss music video.
49
Q How can I understand different designs of
telescopes?
A
alex.choy_at_ mensa.org.hk
50
Q Are there any tips on using telescopes and
observing?
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.
51
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.
52
Continue
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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55
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//www.physics.hku.hk/nature/
• J. M. Pasachoff, Astronomy From the Earth to the
  Universe (1998).
• E. Chaisson and S. McMillan, Astronomy Today
  (2005).
• 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).

56
Q Are there any useful classroom teaching kits
available?

• A Here are some of them.
• Free software such as www.stellarium.org can be
  used to simulate the motion of celestial bodies,
  to set exam questions and to plan your
  observation session.
• phet.colorado.edu contains many useful physics
  simulations to teach various NSS physics and
  chemistry topics.
• chemistry.beloit.edu/Stars/pages/heated.html
  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.

57

• 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
  launch.
• 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.