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Astronomy and Space Science II : 

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 : 

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 : 

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 : 

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 : 

Examples

Light Pollution : 

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 : 

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 : 

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 Stefan’s Law Luminosity is measured in Watt.

Trick or Treat? : 

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 T4, 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 EmissionStellar Chemistry : 

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.

Spectral Classes : 

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 : 

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.

Spectral lines, Doppler effect : 

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. http://www2.enel.ucalgary.ca/People/ciubotar/public_html/Starsevol/specbin-anim.gif Note that the whole system of lines shifts accordingly.

Radial Velocity Curve for a Simple Binary System : 

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://www2.enel.ucalgary.ca/People/ciubotar/public_html/Starsevol/specbin-anim.gif http://www.roe.ac.uk/~pmw/RVorbit.htm

Galaxies and Dark Matter : 

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 : 

Redshift and Universe http://en.wikipedia.org/wiki/Hubble_law 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 = H d 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 the space.

In Depth Questions : 

In Depth Questions

Q: How bad is the light pollution in Hong Kong? : 

Q: How bad is the light pollution in Hong Kong? 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. http://partnernet.hktb.com/pnweb/jsp/comm/index.jsp

Q: What are the ways to reduce light pollution? : 

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. http://dcfever.com/photosharing/enlargephoto.php?photoID=350951 A:

Q: Can natural light affect observations? : 

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? : 

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? : 

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? : 

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? : 

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? : 

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? : 

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? : 

Q: What is simultaneous multiple wavelength observation? A: The investigation of astronomical objects in different windows of wavelengths at the same time. 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. Images provided by Prof. Bill Keel, University of Alabama

Q: How do the human eye and instruments respond to light? : 

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? : 

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? : 

Q: Why are the spectral classes arranged strangely? 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. 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.

Q: What color is the Sun? : 

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? : 

Q: How to better use our eyes for star watching? A: More: 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 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? : 

Q: For sunspopts, Lsurf/Lspot = (6000/4000)^4 = 5, less than 2 magnitude difference, why do they appear black? 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. A: Contrast with the surface in visible light.

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

Q: Why are stars grouped on the H-R diagram ? A: More: 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. 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? : 

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? : 

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 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. http://www2.enel.ucalgary.ca/People/ciubotar/public_html/Starsevol/totalvel.gif

Q: How does the radial velocity curve look when the orbit of the binary system is elliptical? : 

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? : 

Q: How to detect extrasolar planet, or exoplanets? A: 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. 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. 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? : 

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? : 

Q: Is redshift observed for remote galaxies due to Doppler effect? Classical or (special) relativistic Doppler shift. Used to measure radial velocity of stars, rotation of stars and galaxies, detect close binaries. 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. 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). A: No. More: Three causes for redshift: http://antwrp.gsfc.nasa.gov/apod/ap031102.html

Q: What is the age of the universe? : 

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? : 

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.

Q: What is outside of the universe? : 

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: what’s before the big bang? It is an ill-posed question, it is like asking what’s 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, 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? : 

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://atlasoftheuniverse.com/redshift.html for more detail. http://atlasoftheuniverse.com/expansion.gif

Q: When d > c/H, is the special relativity violated? : 

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.

Slide 47: 

A: More: 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 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: What are dark matter and dark energy?

Slide 48: 

A: Q: How is astronomy treated in the media/public? Powdered milk TV advertisement. BoA Amazing Kiss music video. It varies from place to place. Japan Hong Kong

Slide 49: 

A: alex.choy@ mensa.org.hk Q: How can I understand different designs of telescopes?

Slide 50: 

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: Are there any tips on using telescopes and observing?

Slide 51: 

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. Q: Can you suggest some equipments for schools?

Continue… : 

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? : 

Q: Can you give us some references? 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). A: Here are some of them:

Q: Are there any useful classroom teaching kits available? : 

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.

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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.

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