Transcript Document 7138025

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 temperature
Stefan’s 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 arcsec.
• 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 m=1 star is 1001/5 ≈ 2.512 times as bright
as an m=2 star.
• In general, the ratio of brightness between
two stars is 2.512(m2-m1) or 100(m2-m1)/5.
Examples
Name
Type
Sun
star
Full Moon
satellite
Sirius
star
Pleiades (M45)
open cluster
Polaris
star
“Urban” Naked Eye Limit
Andromeda Galaxy (M31)
galaxy
Orion Nebula (M42)
diffuse nebula
Io
satellite
M4
globular cluster
Country Naked Eye Limit
M54 (note: extragalatic)
globular cluster
Crab Nebula (M1)
supernova remnant
Ring Nebula (M57)
planetary nebula
Apparent
Absolute
Magnitude Magnitude
-26.8
4.8
-12.6
-1.4
1.5
1.6
-4.1
2.0
-3.6
~3.0
3.5
-21.4
4.0
-4.5
5.0
5.6
-6.7
~6.0-7.0
7.6
-10.0
8.4
-3.0
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 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.
Blackbody Radiation
• A blackbody absorbs all frequencies of EM radiation that falls on it, and
radiates the energy according to Planck’s 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.
Stefan’s Law
• First obtained from experiment, the Stefan’s law states that the intensity,
defined as the total energy radiated per unit time per unit area of an object,
is given by:
I = σT4
• Therefore, for spherical stars with radius R, its luminosity is given by
L = 4πR2σT4
• 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. Stefan’s law applied to a spherical star:
L = 4πR2σT4 and LSun = 4πRSun2σTSun4
implies
L/LSun = (R/RSun)2 (T/TSun)4.
Or in unit of solar parameters,
L = R2 T 4 ,
or
R = L1/2 / T2.
E.g.2. Kepler’s law: (R1/R2)3 / (T1/T2)2 = (M1/M2), for central force system.
Taking the Earth’s 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 Emission
Stellar 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.
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.”
Hertzsprung-Russel (H-R) Diagram
• The H-R diagram is a log-log or semilog 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.
Spectral lines, Doppler effect
• Doppler effect: Δλ/λ = 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/public_html/Starsevol/specbin-anim.gif
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 cosθ =
rω cosθ , where r is the orbital radius,
ω 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 Kepler’s law.
http://www.roe.ac.uk/~pmw/RVorbit.htm
http://www2.enel.ucalgary.ca/People/ciubotar/public_html/Starsevol/specbin-anim.gif
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 Kepler’s
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 1970’s. 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 Hubble’s law:
v=Hd
• The most accepted value of the Hubble
constant H is about 70 km/s/Mpc.
• Hubble’s 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
http://en.wikipedia.org/wiki/Hubble_law
the space.
In Depth Questions
Q: How bad is the light pollution in Hong Kong?
http://partnernet.hktb.com/pnweb/jsp/comm/index.jsp
A: Very bad.
More: HKU’s light pollution study in 2005-2006 shows that the apparent
magnitude per square arc second in HK’s 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 Kong’s country side is only slightly better
than some less populated and drier cities.
Q: What are the ways to reduce light pollution?
A:
•
•
•
•
•
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.
http://dcfever.com/photosharing/enlargephoto.php?photoID=350951
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 3.83×1026W. 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 = Σ 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 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 (1.22λ/D) on Earth.
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.
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 gammaray 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 Stefan’s law from Plank’s law?
A: Yes, it is just an integration away.
More: Planck’s 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 ν and ν+dν. So
L ~∫ I(v)dv.
The T4 dependence can be obtained without actually doing an integration, by
making the substitution x=hv/kT.
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.
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 brain’s
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 Sun’s 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?
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).
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 doesn’t mean
the star is perceived as green in human eye.
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.
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.
Q: How are proper motion, radial and tangential
velocities related?
http://www2.enel.ucalgary.ca/People/ciubotar/public_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 dθ/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?
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.
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.
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 Kepler’s 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
Kepler’s law.
Sky&Telescope, April 03, p.49
Q: Is redshift observed for remote galaxies due to Doppler
effect?
A: No.
http://antwrp.gsfc.nasa.gov/apod/ap031102.html
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 Earth’s 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 λobserve = λemit 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 1990’s, 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 not.
A:
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: what’s before the big bang?
It is an ill-posed question, it is like asking what’s north of north-pole. At the northpole, if you walk in one direction, you are heading south, if you walk instead in the
opposite direction, you’re 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.
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.
Q: When d > c/H, is the special relativity violated?
A: No, when d > c/H, v = Hd > 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.
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”.
Q: How is astronomy treated in the media/public?
A: It varies from place to place.
Japan
BoA Amazing Kiss music video.
Hong Kong
Powdered milk TV advertisement.
Q: How can I understand different designs of telescopes?
A:
alex.choy@
mensa.org.hk
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.
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.
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.
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).
蔡國昌 和 葉賜權 , 恆星 (2000).
葉賜權 , 星‧移‧物‧換 (2003).
香港太空館小學天文敎材套 (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 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 Hawking’s Universe (in particular, DVD 1: Seeing
is Believing, Chap 5) is a good video to teach from
spectrum all the way up to the Hubble’s law.
• Continue:
• The “Doppler Ball” is a good teaching aid to demonstrate
Doppler effect. You can make one using less than HK$50.
• 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.