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PH507 Astrophysics Professor Glenn White THE MULTIWAVELENGTH UNIVERSE AND EXOPLANETS School of Physical Sciences Convenor Prof. Michael Smith Taught in Term 2 Teaching Provision: 1 PH507 ECTS Credits 7.5 Kent Credits 15 at Level I 30 lectures + 4 workshops + 2 class tests Prerequisites: PH300, PH301, PH304 Aims: To provide a basic but rigorous grounding in observational, computational and theoretical aspects of astrophysics to build on the descriptive course in Part I, and to consider evidence for the existence of exoplanets in other Solar Systems. Learning Outcomes: 1. An understanding of the fundamentals of making astronomical observations across the whole electromagnetic spectrum, including discussion of photometry and spectroscopy, and the physics of the astrophysical radiation mechanisms. 2. An understanding of the motions of objects in extrasolar systems and the basic techniques required to solve the 2-body problem to measure their properties. 3. An understanding of observational characteristics of stars, and how their physical structures are derived from observation and using simple physical models. 4. To be able to discuss coherently the origin and evolution of Solar Systems and be able to evaluate claims for evidence of Solar Systems other than our own. SYLLABUS: • • • • • • Part 1: measurements Part 2: radiation Part 3: dynamics Part 4: star and planet formation Part 5: telescopes/instruments Part 6: stars and stellar structure Assessment Methods: Examination 70%, Homework 10%, 1st class test 10%, 2nd class test 10%. Recommended Texts: Carroll & Ostlie, An Introduction to Modern Astrophysics, Addison-Wesley, [QB461] Stuart Clark. Extrasolar Planets, Wiley Press C.R.Kitchin. Astrophysical Techniques, Adam Hilger Press. [Note: Changes may occur to the syllabus during the year] Prof. Michael Smith: 101 Ingram, x7654, [email protected] Office hours: 10-12am Wed Bad weather Numbers, names Locations, times of lectures Lecturers PH507 Astrophysics Professor Glenn White 2 PART 1: Measurement LECTURE 1 Distance: Distance is an easy concept to understand: it is just a length in some units such as in feet, km, light years, parsecs etc. It has been excrutiatingly difficult to measure astronomical distances until this century. Unfortunately most stars are so far away that it is impossible to directly measure the distance using the classic technique of triangulation. Trignometric parallax: based on triangulation – need three parameters to fully define any triangle e.g. two angles and one baseline. To triangulate to even the closest stars we would need to use a very large baseline. In fact we do have a long baseline, because every 6 months the earth is on opposite sides of the sun. So we can use as a baseline the major axis of the earth's orbit around the sun. BASELINE: 2 x earth-sun distance = 2 Astronomical Units (AU) (The average distance from the earth to the sun is called the Astronomical Unit.) The parallactic displacement of a star on the sky as a result of the Earth’s orbital motion permits us to determine the distance from the Sun to the star by the method of trigonometric (heliocentric) parallax. We define the trigonometric parallax of the star as the angle subtended, as seen from the star, by the Earth’s orbit of radius 1 AU. If the star is at rest with respect to the Sun, the parallax is half the maximum apparent annual angular displacement of the star as seen from the Earth. PH507 Astrophysics Professor Glenn White 3 PH507 Astrophysics Professor Glenn White 4 PH507 Astrophysics Professor Glenn White 5 1 radian is defined as: 360 57.3 degrees = 206265 arc seconds, approximately. There are 2 2 rad in a circle (360˚), so that 1 radian equals 57˚17´44.81” (206, 264.81”). 1 radian = Independent distance unit is the light year: c t ( year ) 9.47 1015 m The light year is not used much by professional astronomers, who work instead with a unit of similar size called the parsec, where 1 parsec = 1 pc = 206265 AU = 3.086 x 1016 m = 3.26 light years. The measurement and interpretation of stellar parallaxes are a branch of astrometry, and the work is exacting and time-consuming. Consider that the nearest star, Proxima/Alpha Centauri (Rigil Kent), at a distance of 1.3 pc, has a parallax of only 0.76”; all other stars have smaller parallaxes. PH507 Astrophysics Professor Glenn White 6 Formula: tan p 1AU d or d 1 AU p where p is in radians for small angles. To convert to arcseconds: 2.063 105 d AU p '' or d 1 pc . p" Technological advances (including the Hubble Space Telescope) have improved parallax accuracy to 0.001” within a few years. Before 1990, fewer than 10,000 stellar parallaxes had been measured (and only 500 known well), but there are about 1012 stars in our Galaxy. Space observations made by the European Space Agency with the Hipparcos mission (1989-1993) accurately determined the parallaxes of many more stars. Though a poor orbit limited its usefulness, Hipparcos was expected to achieve a precision of about 0.002”. It actually achieved 0.001” for 118,000 stars. The method of trigonometric parallax is important because it is our only direct distance technique for stars. The ground-based trigonometric parallax of a star is determined by photographing a given star field from a number (about 20) of selected points in the Earth’s orbit. The comparison stars selected are distant background stars of nearly the same apparent brightness as the star whose parallax is being measured. Corrections are made for atmospheric refraction and dispersion and for detectable motions of the background stars; any motion of the star relative to the Sun is then extracted. What remains is the smaller annual parallactic motion; it is recognised because it cycles annually. Because a seeing resolution of 0.25” is considered exceptional (more typical it is 1”), it may seem strange that a stellar position can be determined to ±0.01” in one measurement; this accuracy is possible because we are determining the centre of the fuzzy stellar image. PH507 Astrophysics Professor Glenn White 7 In 2011 – 2013, Gaia will be set into orbit with a Soyuz rocket (and SIM Space Interferometric Mission from the US). It will be able to measure parallaxes of 10 micro-arcseconds. It consists of a rotating frame holding three telescopes. Some aims: …….Accurate distances even to the Galactic centre, 8000 parsecs away. ……..Photometry: accurate magnitudes. ……..Planet quest ……..Reference frame from distant quasars (3C273 is 800 Mpc away) In the meantime, to go further, we construct the COSMIC LADDER. If we can estimate the luminosity of a star from other properties, they can be used as STANDARD CANDLES. 2 LUMINOSITY. We can actually only measure the radiant flux of a flame and need to make a few assumptions to find the true luminosity. Luminosity depends on the distance and extinction (as well as relativistic effects). The measured flux f is in units of W/m2 , the flow of energy per unit area. The radiated power L, ignoring extinction, is given by: f d2 L 4d 2 L 4f ’ showing that a standard candle can yield the distance. The Stellar Magnitude Scale PH507 Astrophysics Professor Glenn White 8 The first stellar brightness scale - the magnitude scale - was defined by Hipparchus of Nicea and refined by Ptolemy almost 2000 years ago. In this qualitative scheme, nakedeye stars fall into six categories: the brightest are of first magnitude, and the faintest of sixth magnitude. Note that the brighter the star, the smaller the value of the magnitude. In 1856, N. R. Pogson verified William Herschel’s finding that a first-magnitude star is 100 times brighter than a sixthmagnitude star and the scale was quantified. Because an interval of five magnitudes corresponds to a factor of 100 in brightness, a one-magnitude difference corresponds to a factor of 1001/5 = 2.512. (This definition reflects the operation of human vision, which converts equal ratios of actual intensity to equal intervals of perceived intensity. In other words, the eye is a logarithmic detector). The magnitude scale has been extended to positive magnitudes larger than +6.0 to include faint stars (the 5-m telescope on Mount Palomar can reach to magnitude +23.5) and to negative magnitudes for very bright objects (the star Sirius is magnitude -1.4). The limiting magnitude of the Hubble Space Telescope is about +30. Astronomers find it convenient to work with logarithms to base 10 rather than with exponents in making the conversions from brightness ratios to magnitudes and vice PH507 Astrophysics Professor Glenn White 9 versa. Consider two stars of magnitude m and n with respective apparent brightnesses (fluxes) lm and ln. The ratio of their fluxes fn / fm corresponds to the magnitude difference m - n. Because a one-magnitude difference means a brightness ratio of 1001/5, (m - n) magnitudes refer to a ratio of (1001/5)m-n = 100(m-n)/5, or fn / fm = 100(m-n)/5 Taking the log10 of both sides (because log xa = a log x and log 10a = a log 10 = a), log (fn / fm) = [(m - n)/5] log 100 = 0.4(m - n) or m - n = 2.5 log (fn / fm) This last equation defines the apparent magnitude; note that m > n when fn > fm, that is: brighter objects have numerically smaller magnitudes. Also note that when the brightnesses are those observed at the Earth, physically they are fluxes. Apparent magnitude is the astronomically peculiar way of talking about fluxes. Here are a few worked examples: (a) The apparent magnitude of the variable star RR Lyrae ranges from 7.1 to 7.8 - a magnitude amplitude of 0.7. To find the relative increase in brightness from mini-mum to maximum, we use log (fmax / fmin) = 0.4 x 0.7 = 0.28 so that PH507 Astrophysics Professor Glenn White 10 fmax / fmin = 100.28 = 1.91 This star is almost twice as bright at maximum light than at minimum. (b) A binary system consists of two stars a and b, with a brightness ratio of 2; however, we see them unresolved as a point of magnitude +5.0. We would like to find the magnitude of each star. The magnitude difference is mb - ma = 2.5 log (fa / fb) = 2.5 log 2 = 0.75 Since we are dealing with brightness ratios, it is not right to put ma + mb = +5.0. The sum of the luminosities (fa + fb) corresponds to a fifth-magnitude star. Compare this to a 100-fold brighter star, of magnitude 0.0 and luminosity l0: PH507 Astrophysics Professor Glenn White 11 ma+ b - m0 = 2.5 log [l0 / (fa + fb)] or 5.0 - 0.0 = 2.5 log 100 = 5. But fa = 2 fb, so that fb = (fa + fb)/3. Therefore (mb - m0) = 2.5 log (f0 / fb) = 2.5 log 300 = 2.5 x 2.477 = 6.19. The magnitude of the fainter star is 6.19, and from our earlier result on the magnitude difference, that of the brighter star is 5.44. What units are used in astronomical photometry? The well-known magnitude scale of course, which has been calibrated us stars which (hopefully) do not vary in brightness. But how does the astronomical magnitude scale relate to other photomet assume V magnitudes, unless otherwise noted, which are at least approx convertible to lumes, candelas, and lux'es. 1 mv=0 star outside Earth's atmosphere = 2.54 10-6 lux = 2.54 1010 phot Luminance: ( 1 nit =1 candela per square metre) 1 mv=0 star per sq degree outside Earth's atmosphere = 0.84E-2 nit = 8.4 10-7 stilb 1 mv=0 star per sq degree inside clear unit airmass nit = 6.9 10-7 stilb = 0.69E-2 PH507 Astrophysics Professor Glenn White 12 (1 clear unit airmass transmits 82% in the visual, i.e. it dims 0.2 magnitudes) One star, Mv=0 outside Earth's atmosphere = 2.451029 cd Apparent magnitude is thus an irradiance or illuminance, i.e. incident flux per unit area, from all directions. Of course a star is a point light source, and the incident light is only from one direction. Apparent magnitude per square degree is a radiance, luminance, intensity, or "specific intensity". This is sometimes also called "surface brightness". Still another unit for intensity is magnitudes per square arcsec, which is the magnitude at which each square arcsec of an extended light source shines. Only visual magnitudes can be converted to photometric units. U, B, R or I magnitudes are not easily convertible to luxes, lumens and friends, because of the different wavelengths intervals used. The conversion factors would be strongly dependent on e.g. the temperature of the blackbody radiation or, more generally, the spectral distribution of the radiation. The conversion factors between V magnitudes and photometric units are only slightly dependent on the spectral distribution of the radiation. What units are used in radiometry/infrared astronomy? Here we're not interested in the photometric response of some detector with a well-known passband (e.g. the human eye, or some astronomical photometer). Instead we want to know the strength of the radiation in absolute units: watts etc. Thus we have: PH507 Astrophysics Professor Glenn White 13 Radiance, intensity or specific intensity: W m-2 ster-1 [Å-1] SI unit -2 -1 -1 -1 erg cm s ster [Å ] CGS unit photons cm-2 s-1 ster-1 [Å-1] Photon flux, CGS units Irradiance/emittance, or flux: W m-2 [Å-1] SI unit -1 erg cm-2 s-1 [Å ] CGS unit -1 photons cm-2 s-1 ster-1 [Å ] Photon flux, CGS units Note the [A-1] within brackets. Fluxes and intensities can be total (summed over all wavelengths) or monochromatic ("per Angstrom Å" or "per nanometer"). In Radio/Infrared Astronomy, the unit Jansky is often used as a measure of irradiance at a specific wavelength, and is the radio astronomer's equivalence to stellar magnitudes. The Jansky is defined as: 1 Jansky = 10-26 W m-2 Hz-1 Absolute magnitude represents a total flux, expressed in e.g. candela, or lumens. Absolute Magnitude and Distance Modulus So far we have dealt with stars as we see them, that is, their fluxes or apparent magnitudes, but we want to know the luminosity of a star. A very luminous star will appear dim if it is far enough away, and a low-luminosity star may look bright if it is close enough. Our Sun is a case in point: if it were at the distance of the closest star (Alpha Centauri), the Sun would appear slightly fainter to us than Alpha Centauri does. Hence, distance links fluxes and luminosities. PH507 Astrophysics Professor Glenn White 14 The luminosity of a star relates to its absolute magnitude, which is the magnitude that would be observed if the star were placed at a distance of 10 pc from the Sun. (Note that absolute magnitude is the way of talking about luminosity peculiar to astronomy). By convention, absolute magnitude is capitalised (M) and apparent magnitude is written lowercase (m). The inverse-square law of radiative flux links the flux f of a star at a distance d to the luminosity F it would have it if were at a distance D = 10 pc: F / f = (d / D)2 = (d / 10) 2. If M corresponds to L and m corresponds to luminosity l, then m - M = 2.5 log (F / f ) = 2.5 log (d/10)2 = 5 log (d / 10) PH507 Astrophysics Professor Glenn White 15 Expanding this expression, we have useful alternative forms: since m1 m2 2.5 log d1 5 log d1 5 log d2 , d2 defining the absolute magnitude m2 = M at d2 = 10 pc, so m1 = m and d2 = d, m - M = 5 log d - 5 M = m + 5 - 5 log d In terms of the parallax, M = m + 5 + 5 log p” Here d is in parsecs and p” is the parallax angle in arc seconds. The quantity m - M is called the distance modulus, for it is directly related to the star’s distance. In many applications, we refer only to the distance moduli of different objects rather than converting back to distances in parsecs or lightyears. PH507 Astrophysics Professor Glenn White 16 Magnitudes at Different Wavelengths The kind of magnitude that we measure depends on how the light is filtered anywhere along the path of the detector and on the response function of the detector itself. So that problem comes down to how to define standard magnitude systems. PH507 Astrophysics Professor Glenn White 17 Magnitude Systems Detectors of electromagnetic radiation (such as the photographic plate, the photoelectric photometer, and the human eye) are sensitive only over given wavelength bands. So a given measurement samples but part of the radiation arriving from a star. Four images of the Sun, made using (a) visible light, (b) ultraviolet light, (c) X rays, and (d) radio waves. By studying the similarities and differences among these views of the same object, important clues to its structure and composition can be found. Because the flux of starlight varies with wavelength, the magnitude of a star depends upon the wavelength at which PH507 Astrophysics Professor Glenn White 18 we observe. Originally, photographic plates were sensitive only to blue light, and the term photographic magnitude (mpg) still refers to magnitudes centred around 420 nm (in the blue region of the spectrum). Similarly, because the human eye is most sensitive to green and yellow, visual magnitude (mv) or the photographic equivalent photo visual magnitude (mpv) pertains to the wave-length region around 540 nm. Today we can measure magnitudes in the infrared, as well as in the ultraviolet, by using filters in conjunction with the wide spectral sensitivity of photoelectric photometers. So systems of many different magnitudes (colour combinations) are possible. In general, a photometric system requires a detector, filters, and a calibration (in energy units). The properties of the filters are typified by their effective wavelength, 0, and bandpass, ∆ which is defined as the full width at half maximum in the transmission profile. The three main filter types are wide (∆≈ 100 nm), intermediate (∆≈ 10 nm), and narrow (∆≈1 nm). There is a trade-off for the bandwidth choice: a smaller ∆ provides more spectral information but admits less flux into the detector, resulting in longer integration times. For a given range of the spectrum, the design of the filters makes the greatest difference in photometric magnitude systems. A commonly used wide-band magnitude system is the UBV system: a combination of ultraviolet (U), blue (B), and visual (V) magnitudes, developed by H. L. Johnson. These three bands are centred at 365, 440, and 550 nm; each wavelength band is roughly 100 nm wide. In this system, apparent magnitudes are denoted by B or V and the corresponding absolute magnitudes are sub-scripted: MB or MV. PH507 Astrophysics Professor Glenn White 19 To be useful in measuring fluxes, the photometric system must be calibrated in energy units for each of its bandpasses. This calibration turns out to be the hardest part of the job. In general, it relies first on a set of standard stars that define the magnitudes, for a particular filter set and detector; that is, these stars define the standard magnitudes for the photometric system to the precision with which they can be measured. Infrared Windows The UBV system has been extended into the red and infrared (in part because of the development of new detectors, such as CCDs, sensitive to this region of the spectrum). The extensions are not as well standardised as that for the Johnson UBV system, but they tend to include R and I in the far red and J, H, K, L, and M in the infrared. As well as measuring the properties of individual stars at different wavelengths, observing at loner wavelengths, particularly in the infrared, allows us to probe through PH507 Astrophysics Professor Glenn White 20 clouds of small solid dust particles, as seen below A visible-light (left) vs. 2MASS infrared-light (right) view of the central regions of the Milky Way galaxy graphically illustrating the ability of infrared light to penetrate the obscuring dust. The field-of-view is 10x10 degrees Infrared passbands which allow transmission (low absorption): J Band: 1.3 microns H Band: 1.6 microns K band: 2.2 microns L band 3.4 microns M band 5 microns N band 10.2 microns Q band 21 microns Bolometric magnitudes can be converted to total radiant energy flux: One star of Mbol = 0 radiates 2.97 1028 Watts. System is defined by Vega at 7.76 parsecs from the Sun with an apparent magnitude defined as zero. With Lbol = 50.1 Lsolar and Mbol = 0.58. Sun: mbol = -26.8 Full moon: -12.6 PH507 Astrophysics Professor Glenn White 21 Venus: -4.4 Sirius: -1.55 Brightest quasar: 12.8 For Vega: mb = mv = 0. mk = +0.02 Sun: Mb = 5.48, Mv = 4.83, Mk = 3.28 Colour Index: B-V, J-H, H-K are differences magnitude….flux ratios. But cooler, redder objects possess higher values. in Extinction Interstellar Medium modifies the radiation. Dust particles with size of order of the wavelength of the radiation. Blue radiation is strongly scattered compared to red: blue reflection nebulae and reddened stars. Colour Excess: measures the reddening. E(B-V) = B-V - (B-V)o Modified distance modulus: m() = M() + 5 log d – 5 + A() where A () is the extinction due to both scattering and absorption, strongly wavelength dependent. The optical depth is given by I exp( ) . Io Therefore A() = 1.086 The optical depth is PH507 Astrophysics Professor Glenn White 22 where N is the total column density of dust (m-2) between the star and the observer and is the scattering/absorption cross-section (m2). ISM Law related extinction to reddening: Av / E(B-V) = 3.2 + - 0.2 Spectroscopic Parallax Hertzsprung-Russell deduced the main-sequence stars for nearby objects, relating their luminosity to their colour. Groups of distant stars should also\line along the same main-sequence strip. However they appear very dim,\of course due to their distance. On comparison of fluxes, we determine the distance. This works out to about 100,000 pc, beyond which main-sequence stars are too \dim. Cepheids as Standard Candles: The Period-Luminosity Relationship Cepheids show an important connection between period and luminosity: the pulsation period of a Cepheid variable is directly related to its median luminosity. This relationship was first discovered from a study of the variables in the Magellanic Clouds, two small nearby companion galaxies to our Galaxy that are visible in the night sky of the southern hemisphere. To a good approximation, you can consider all stars in each Magellanic Cloud to be at the same distance. Henrietta Leavitt, working at Harvard in 1912, found that the brighter the median apparent magnitude (and so the luminosity, since the stars are the same distance), the longer the period of the Cepheid variable. A linear relationship was found. PH507 Astrophysics Professor Glenn White 23 Harlow Shapley recognised the importance of this periodluminosity (P-L) relation-ship and attempted to find the zero point, for then a knowledge of the period of Cepheid would immediately indicate its luminosity (absolute magnitude). This calibration was difficult to perform because of the relative scarcity of Cepheids and their large distances. None are sufficiently near to allow a trigonometric parallax to be determined, so Shapley had to depend upon the relatively inaccurate method of statistical parallaxes. His zero point was then used to find the distances to many other galaxies. These distances are revised as new and accurate data become available. Right now, some 20 stars whose distances are known reasonably well (because they are in open clusters) serve as the calibrators for the P-L relationship. Further work showed that there are two types of Cepheids, each with its own separate, almost parallel P-L relationship. PH507 Astrophysics Professor Glenn White 24 The classical Cepheids are the more luminous, of Population I, and found in spiral arms. Population II Cepheids, also known as W Virginis stars after their prototype, are found in globular clusters and other Population II systems. Classical Cepheids have periods ranging from one to 50 days (typically five to ten days) and range from F6 to K2 in spectral class. Population II Cepheids vary in period from two to 45 days (typically 12 to 20 days) and range from F2 to G6 in spectral class. Population I and II Cepheids are both regular, or periodic, variables; their change in luminosity with time follows a regular cycle. PH507 Astrophysics Professor Glenn White 25 Cepheids are bright and distinct. They can be used to determine distances to quite distant galaxies, to about 5 Mpc. HST stretched this to 18 Mpc (Virgo cluster). Tully-Fisher Relation In a spiral galaxy, the centripetal force of gas and stars balances the gravitational force: mV2/R = GmM/R2. If they have the same surface brightness ( L/R2 is constant) and the same mass-to-light ratio (M/L is constant), then L ~ V4. So, provided we can measure V, certain galaxies can be used as standard candles. (determine V through the 21 cm line of atomic hydrogen in the galaxy). Type 1a Supernovae. PH507 Astrophysics Professor Glenn White 26 The peak light output from these supernovae is always about Mb = -19.33 +- 0.25. Therefore we can infer the distance from the inverse square law. Being so bright , they act as standard cadles to large distances: to 1000 Mpc. Why are they standard candles? White dwarfs I binary systems. Material from\ a companion red giant is dumped on the white dwarf surface until the WD reaches a critical mass (Chandrasekhar mass) of 1.4 solar masses. Explosion occurs with fixed rise and fall of luminosity. Other methods: time delay of light rays due to gravitational lensing, cluster size influences Compton scattering of CMB radiation and bremsstrahlung emission (X-rays). Combining, yields the size estimate (Sunyaev-Zeldovich effect). Or, rotational properties of stars with starspots……. New Method? Reverse argument: knowing the Hubble constant is 72 km/s/Mpc, (WMAP result), distances can be found directly from the redshift! PH507 Astrophysics Professor Glenn White Questions How do we scale the solar system? How do we find the distance to gas clouds? PLANET REVIEW The Terrestrial Solar System 27 PH507 Astrophysics Professor Glenn White 28 In the picture above we see the positions of the asteroid belt (green) and other near-earth objects The material in the plane of the Solar System is known as the Kuiper Belt. Surrounding this is a much larger region known as the Oort Cloud, that contains material that occasionally falls in, under the influence of gravity, towards the Sun as comets. PH507 Astrophysics Professor Glenn White 29 The Sun At over 1.4 million kilometers (869,919 miles) wide, the Sun contains 99.86 percent of the mass of the entire solar system: well over a million Earths could fit inside its bulk. The total energy radiated by the Sun averages 383 billion trillion kilowatts, the equivalent of the energy generated by 100 billion tons of TNT exploding each and every second. Planetary configurations • Some of the definitions below make the assumption of coplanar circular orbits. True planetary orbits are ellipses with low eccentricity and inclinations are small so the concepts are applicable in real cases. • Copernicus correctly stated that the farther a planet lies from the Sun, the slower it moves around the Sun. When the Earth and another planet pass each other on the same side of the Sun, PH507 Astrophysics Professor Glenn White 30 the apparent retrograde loop occurs from the relative motions of the other planet and the Earth. As we view the planet from the moving Earth, our line of sight reverses its angular motion twice, and the three-dimensional aspect of the loop comes about because the orbits of the two planets are not coplanar. This passing situation is the same for inferior or superior planets. PH507 Astrophysics Professor Glenn White 31 A Retrograde loop occurs when a superior planet moves through opposition, and occurs as the earth's motion about its orbit causes it to overtake the slower moving superior planet. Thus close to opposition, the planet's motion relative to fixed background stars, follows a small loop. PH507 Astrophysics Professor Glenn White 32 PH507 Astrophysics Professor Glenn White 33