Astronomy and Space Science I

Astronomy and Space Science I 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

Astronomy and Space Science • Astronomy Basics • Length, time, angles • Celestial sphere, star maps • Solar System • Orbital Motion of the Earth around the Sun • Geocentric models • Heliocentric models • Modern views • Q&A

Length: Power of Ten

Units of Length • 1 ls = distance light travel in 1 second = 299792485 m ≈ 3x108 m • 1 ly = distance light travels in 1 year ≈ 9.46x1015 m ≈ 1016m • 1 AU (astronomical unit) = mean distance between the Sun and Earth ≈ 1.49x1011 m • 1 pc (parsec) = distance from which 1 AU extends 1 arcsec ≈ 3.26 ly ≈ 3.24x1016 m • 1 Mpc = 106 pc ≈ 3.26x1022 m

Examples

Time Scales

Angles • Angles are measured in degree (°), arcmin ('), arcsec("); radians (rad, or no unit). • 1° = 60' = 3600" • 1 rad = 180°/π ≈ 57.3°. • Small angle approximation: angle = arc length/distance • The apparent diameter of the Sun and the Moon are about 0.5°. • Resolution limit of a 4" telescope ≈ 1". • Note: Do not confuse arcsec with inch, both use the same symbol.

Objects with Large Angular Sizes(roughly to scale) Sun, 30’. Andromeda Galaxy (M31) 180’ x 63’. Orion Nebula (M42), 85’ x 60’. M54, extragalatic globular star cluster, 12’ Moon, 30’. Pleiades, open star cluster, 180’. M4, globular star cluster, 36’

Ring nebula, planetary nebula, 1.4’ x 1’. More Examples Crab Nebula Supernova remnant, 6’x4’. Io, Jovian satellite, 1”. Polaris A’s apparent size = 0.002”. Polaris A to Polaris Ab is 0.2”; Polaris A toPolaris B is 20”; Polaris A to Dubhe ≈ 30°. Hubble Deep Field, ≈ 1.5’.

Celestial Sphere • The celestial sphere is a hypothetical sphere centered at the center of Earth. • On the celestial sphere, stars are fixed, while the Sun and the planets moves slowly. • The celestial sphere rotates, thus most stars rise and fall daily. • The celestial poles and celestial equator are projections of the poles and equator on the Earth on to the celestial sphere.

Useful Relations • Altitude of north celestial pole = latitude L • Local zenith forms an angle 90°-L with the north celestial pole • Local zenith forms an angle L with celestial equator zenith ____

Star Maps • Star maps show the sky East-side West, because it is intended for looking up. There are 88 constellations. • Brighter stars are shown with bigger dots. Many star maps also mark the location/type of deep sky objects, multiple stars, and the Milky Way.

The Solar System Source: NASA

Motion of the Sun on Celestial Sphere • Axial tilt of Earth is 23.44° ≈ 23 ½ °. • Different parts of the sky are in the glare of the Sun in different months. Vernal equinox(春分), autumnal equinox(秋分) are the points at which the Sun passes the celestial equator, while summer solstice(夏至) and winter solstice(冬至) are the northern and southern extreme points of the ecliptic (黃道).

Ecliptic Plane • the ecliptic plane is the plane in which the Earth orbits. • the ecliptic is the circle form by the ecliptic plane intercepting the celestial sphere

Planetary Motion on Celestial Sphere Planets usually moves on the celestial sphere from east to west (prograde motion) near the ecliptic; while sometimes moves from west to east (retrograde motion). Motion of Mars in 2003 and 2005. Time step=10 days. Pictures from NASA.

Geocentric Model of Planetary Motion(Apollonius, 260-190 BCE) • Explains qualitatively the prograde and retrograde motions, and brightness variation. • Motion planets around epicycle centers and epicycle centers around the Earth are uniform circular motions. • Note: the centers of epicycles for Mercury and Venus always align with the Sun, which explains their maximum elongations (29° and 48°). • Ptolemy (90-168 CE) modified this model to be quantitatively accurate compared to the observations of the time. His model was used for 1400 years until the Renaissance.

Heliocentric Model of Planetary Motion(Copernicus, 1473-1543 CE) • In the heliocentric model, the Earth and other planets orbit the Sun. • The prograde and retrograde motions are apparent effects due to relative motions of the Earth and the planets.

Advantages of the Heliocentric Model • The heliocentric model of Copernicus is not intrinsically more accurate. • Calculation is easier with the Copernicus model. • Copernicus was able to determine the orbitalradii (relative to Earth orbit) of all six planets, while in Ptolemy model the lengths are incorrect. • Heliocentric models predict stellarparallax, while geocentric models predict otherwise.

Further Developments • A schematic heliocentric model is shown on the right. The heliocentric model would later be a great help to Kepler (1571-1630 CE) in finding his laws of planetary motions empirically. • Later Newton (1643-1727 CE) gave the model a firm physical basis using law of gravity and motion would • Stellar parallax, hence distance, was first measured in 1838 (Bessel). • In Copernicus’s theory, the Sun is at the center of the universe, while the Earth is merely a planet. • We now know that Sun is just one of the stars in one of the galaxies (Milky Way Galaxy) in one of the group of galaxies (Local Group) in one of the superclusters (Virgo/Local Supercluster) in the universe.

Modern View of the Solar System • Sun • Terrestrial planets • Asteroids • Gas Giants (outer planets) • Trans-Neptunian Objects (TNO) • Kuiper Belt • Scattered Disc • Oort Cloud (hypothetical) • Comets • Note: Dots represent objects. Someone looking at the solar system at this scale shouldn’t see asteroids and the Oort cloud with naked eyes. Much of the Solar System is empty space.

Beyond the Solar System (Hierarchy of Objects)[pictures from atlasoftheuniverse.com] Solar Neighborhood Orion Arm Note: nebulae are usually in spiral arms. Milky Way Galaxy (2-4x109 stars) Note: globular clusters (105-106 stars) orbit the galactic core as satellites.

Beyond the Milky Way [pictures from atlasoftheuniverse.com] Neighboring Superclusters (100 superclusters shown) Local Group (30+ galaxies) Visible Universe (107 superclusters) * visible ≠ whole but not visible has no physical relevance. Virgo Supercluster (100 groups/clusters of galaxies)

In Depth Questions

Q: What is a constellation? A: The IAU divides the celestial sphere into 88 constellations (regions) with precise boundaries (yellow dashed lines in the figure). More: Each star belongs to exactlyone constellation. The term “constellation” is also less formally used to describe a group of star visibly related to each other in a pattern, such as those connected by green lines in the figure. However, in such a scheme, some stars such as Sirrah in Andromeda, may be considered as both the head of Andromeda or part of the Square of Pegasus. Also, stars not connected by patterns still need to be assigned a constellation.

Q: How does the coordinate systems on the Celestial sphere look like? A: As shown on the graph: the longitude and latitudes of the Celestial sphere are called RA (right ascension) and DEC (declination). DEC runs from +90° to -90°. RA runs from 0 to 24 hours. Each hour has 60 minutes, and each minute has 60 seconds, just like the clock. The RA of zenith of a fixed location increases by roughly 1 hour for every hour in time. (Note: Do not confuse the minute with arc minute which is 1/60°, both measure angles.) Refer to the previous figure, the light blue lines are RA and DEC lines.

Q: Where exactly is the center of the celestial sphere? A: The center of the celestial sphere is the observer. In other words, each observer has a celestial sphere. More: The celestial sphere is a device used to represent the direction of celestial objects for observation. For example, someone in Beijing would see the Moon’s position a little differently from someone in Hong Kong, due to parallax of the observing locations. Therefore, it only make sense to have a different celestial sphere (and the objects on them) for each for observer. Another example is the satellite or space station, which, due to there close distance from Earth, depends greatly on the location of the observer. Also, if one were to observe from Mars, it would not make sense if the celestial sphere is centered on Earth! Note however that in most situations, we are observing on the Earth and most objects are far away so it is convenient to set the center of the Earth as the center of the celestial sphere.

Q: I heard that the definition of the ecliptic plane has been changed, is it? A: Yes, but for all purpose in this course, the change has no real effect. More: • A very first definition is the ecliptic plane is the plane in which the Earth orbits. • A few amendments have been made since then. • In 2006, the IAU adopted a new definition: • the ecliptic pole is explicitly defined by the mean orbitalangular momentum vector of the Earth-Moon barycenter in an inertial reference frame. • This change is to better agree with dynamical theories, however, the actual change in value is extremely small. • As a result the Earth’s orbital plane is very slightly different from the ecliptic plane.

Q: What’s the relation between solar motion and the calendar? A: The Sun’s position relative to Vernal Equinox is important for determining the seasons and the calendar. A major function of the calendar was for agriculture. • Solar motion on the ecliptic is notuniform (due to the Earth’s elliptical orbit), hence seasonal lengths are different. • The mean tropical year, i.e. the mean duration for the Sun to pass though the same point on the ecliptic twice, is 365.242 190 419 days (epoch 2000). • A good approximation is 365 + 97/400 = 365.2425 days. This leads to 97 leap years in every 400 years (Gregorian calendar). The rule for assigning leap year is: leap years are all years divisible by 4, except for those divisible by 100 but not 400. E.g. 1900, 1999 are not leap years; 1996, 2000, 2004 are leap years. • A less accurate approximation is 365 + ¼ = 365.25 days. This leads to a leap year in every 4 years (Julian calendar). But in the order of hundreds of years, the calendar will become less accurate. This approximation, however, is convenient for many estimations. More:

Q: How was the Sun/Earth orbit modeled by Greek astronomers? • A: Seasonal lengths are sensitive to the Sun’s motion, therefore the non-uniform motion of the Sun was discovered early. In Hipparchus model, the Earth is shifted off-center of the deferent. This point is called the eccentric. Effectively, this model approximates the Kepler ellipse and area laws. • More: • Using the length of seasons (i.e., time taken for the Sun to pass between equinoxes and solstices), Hipparchus found parameters to his model, which agreed well with observations until Tycho/Kepler’s time. • Note that the length of seasons changes over time, due to precession of the equinoxes. However, eccentricity does not change.

Q: What is the cause for precession of the equinoxes? A: Precession is caused by the torque applied by the Sun, the Moon, and the planets. The torque is the result of the gravitational pull on Earth’s equatorial bulge. More: The lower left picture explains the effect due to the Sun. The lower right picture shows the 26000 year periodprecession of the north celestial pole. Pictures from Wikipedia.

Q: What is a day anyway? A: A (solar) day is the duration for the Sun to pass the meridian twice. More: • The celestial sphere rotates about 360.9856° daily, i.e. it takes about 23 hr 56min for stars to go around in a circle. In other words, stars rises 4 minutes earlier each day. (360/365.25 ≈ .9856, 24x60/365.25 ≈ 3.94). • As a result, the Sun passes the meridian (highest) at the approximately same time each day. For Greenwich, it is 12:00pm; for HK, it is 12:24pm.

Q: Can you give some example of planetary events? A: Some events are: • Conjunctions (合): • Two objects closest from Earth’s point of view • Stationary (留): • When the ecliptic longitude (sometimes RA) do not change • Greatest elongation (大距): • Approximately the best time forobserving inferior planets • Transit (凌日) of inferior planets across the Sun: • Mercury: …, 11/1999, 5/2003, 8/11/2006 (during sunrise in HK), 5/2016, … • Venus: …, 12/1882, 6/2004, 6/6/2012 (visible in HK), 12/2117, … • Eclipse (蝕) of Sun or Moon. • Similar events in the Jupiter system.

Continue… • Opposition (衝): • Best time for observing superior planets • For Mars, opposition occurs approximately every 2.14 year. Due to higher orbital eccentricity (0.093) and smaller semi-major axis (1.52 AU), the Earth-Mars distance varies between 0.66 and 0.38 AU (1.52×(1 ± 0.093)–1), giving large size and brightness variation at opposition. Great opposition of Mars (near perihelion) (火星大衝) occurs every 15-16 years. The one in 2003 was the closest in 60,000 years, which the media made a big deal of. However, as shown on the graph, the other great oppositions such as the 1988 one are not much further away. Note: since great opposition occurs near perihelion, when Mars is the hottest, planet-wide dust storms could occur, so observe early. Picture: C.F. Chapin, http://www.astromax.com/planets/images/mars2003.gif

Q: What is Aristotle’smodel of the universe? A: See figure. • Aristotle’s (384-322 BCE) model placed the superior planets in right order using their speed on the celestial sphere. • It explains simple phenomena such as dailyrise and set of celestial objects, but not the details in longer time scales. • In this model, the Earth is at the center the universe, surround by water, air, fire, etc. • As more were known about the planetary motion through observation, ancient astronomy would transform slowly to a qualitative science, then a quantitative science.

Q: What does Ptolemy’s geocentric model look like? A: • The epicycle is used to explain prograde/retrograde motion • The epicycle center rotated uniformly aboutequant E, instead of the center of deferent M. • The Earth is located off-center at the eccentric. • Distances EM = MO. • This is the geocentric model that agrees quantitatively with observations of the time. From the time of Apollonius to Ptolemy, planetary theories changed gradually from qualitative to quantitative science.

Q: Ptolemy model looks quite different from Kepler’s, why did it work so well? A: Ptolemy was approximating Kepler’s law, without knowing it. More: • The reasons are: • the elliptical orbits of the planet are close to a circle • the eccentric takes the role of a focus, approximating Kepler’s first law • Ptolemy’s equant has the effect of approximating Kepler’s second law • Using Tycho’s data, Kepler refitted Ptolemy’s model, which gave a maximum error of only 8’ for Mars. • Since uncertainty for Tycho’s data is only 1’, Kepler was forced to give up the circles. Equant Eccentric/Sun Comparing the elliptical orbit of Mars (red) to a circle (blue).

Q: How to transform between geocentric and heliocentric models? • The two models are equivalent if constructed as shown. The vectors pointing from the Earth to the planet are always the same between the two models. • Copernicus used his own observation as well as Ptolemy’s data to obtain parameters to his model. • The precisions of the two models are the roughly same. Earth Sun

Q: One arcmin is about the size of a HK$1 coin in 88 m away, how did Tycho Brahe achieve this accuracy without telescopes? A: Great care for accuracy, a whole lifetime of pursuit, and a lot of support. More: • He was the first one to notice the problem relating observation accuracy and have the ability to improve on them. He improved the sight with a slit design, and also added gradual scale to improve reading. Very large instruments help measuring smaller angles, but they requires stronger materials and mechanical parts. To support Tycho’s work, the King of Denmark granted him the estate of the island Hven, on which he built world’s best observatory called Uraniborg. D=3 m Left: The sight’s aligned horizontally if the star can be seen just on the CBGF edge and ADHE edge at the same time. The vertical alignment can be found similarly. For solar alignment, sunlight is allowing to pass thru the hole in the front and fall on a circle drawn on the ABCD plate.

Q: Did Galileo really invented the telescope? A: No. But Galileo did designed and made his own telescopes, and improved on them.He was ahead of others by a few months in telescope quality, enough for him to claim most of the discoveries. • More: A typical Galilean refractor had a plano-convex objective lens with 30-40 inches focal length; plano-concave eyepiece of focal length about 2 inches focal length. It was good enough to discover Lunar features, Jupiter’s four moons, phase of Venus, as well as sunspots. • (Note: He became blind in his last years, due to observing the Sun directly through the telescope without proper filter or projection.) Galileo’s telescopes are quite unimpressive by today’s standard, with 0.5-1 inch effective objective aperture, about 15-20x power, and a very narrow (15’) field of view, not to mention significant aberrations. But they were the best at the time.

Q: Was Galileo jailed? A: He was found guilty in his trial and sentenced to jail for life. However, his treatment was closer to house arrest. He worked and published during this time. More: Some ideas Galileo held, such as the Earth moves around the Sun, the celestial bodies are not perfect, the Bible was not meant to teach science, etc., were considered heresy at the time. A less fortunate astronomer named Giordano Bruno was burned at the stake. To understand why Galileo was treated leniently, perhaps one should understand that Galileo was well known not only to those who practice science, but to influential people of the society and even to the Church. He made many discoveries such as the law of motion, measured gravity, invented a thermometer, studied the pendulum, etc. The physics taught at the time stress qualitative arguments, Galileo however believed in the importance of mathematics and experiments. He was thus called the “father of modern science”. What made him stand out from other scientist of his time, was the skill of mixing of theory and practice.Galileo was also very successful in getting supports from many people. Although there were people who refused to even look though the telescopes, Galileo succeeded in introducing the telescopes to many nobles and military officials who quickly understood the practical and military applications of the telescope.

Q: Does the discovery of phase of Venus disproves the geocentric theory? A: No. Models, such as Tycho’s model, which require the Venus and Mercury to revolve around the Sun give the correct phase of Venus.

Q: What is a planet? A: Definition by theInternational Astronomical Union (IAU) in 2006: (1) A planetis a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighborhood around its orbit. • A “dwarf planet” is a celestial body that satisfies, (a) and (b) but not (c), and is not a satellite. • All other object orbiting the Sun, except satellites, are called “Small Solar System Bodies”. More: Since some recently found “minor planets” are similar in size or even bigger (Eris) than Pluto, there was a need for redefinition. The new definition is based on planetary formation theory that, given enough time, a large enough object would be able to collide with or scatter away objects and dominate its orbit. The redefinition has been criticized and remains controversial. Note also that the line between (2) and (3) is left for later meetings. For many small object, the hydrostatic equilibrium condition (b) is not easy to test.

Q: After the invention of telescope, how was position/angle measured? A: First by using wired micrometer eyepiece, then by measuring photographic plate. More: The wired can be moved to match the star’s position. In some other eyepieces, a patterned glass is placed at the focus for reading out data. Angles can be measured from a photographic plate using the focal length and the lengths measured on the plate.

Q: We’ve been focusing on the development of the West, what about the work of Chinese? A: Ancient Chinese astronomers developed sophisticated tools to observe the positions of celestial objects. Unfortunate their work did not affect the western astronomy development much. More: As an example, the drawing on the right shows an invention in the Song Dynasty. The main instruments (red, blue, and yellow) are driven by water-powered gear systems to simulate Earth’s rotation and tell time automatically. Source: HK Science Museum, 星‧移‧物‧換

Q1: Was Copernicus the first to think the Earth moves around the Sun? Q2: Did Copernicus model have epicycles? A: Q1: No. Q2: Yes. More: • Ancient Greek and Indian astronomers had proposed heliocentric views. However, Copernicus model was the first to have the good length, time, and angle parameters. It was the reasonably close to modern model of the Solar System. • In Copernicus model, the epicycles are used to account for elliptical orbits; where as Ptolemy’s epicycles are used to account for Earth’s motion. • Since the full Copernicus model is rather complex, the simplified heliocentric model is usually presented to students. This toy model does not have epicycles, but in practice, it has almost no predictive value.

Q: What are the true advantages of the heliocentric model? A: Easier to compute, correct orbital radii, predicts stellar parallax. More: • For those who computed using hand and tables, his simplification was much appreciated. Therefore, it was accepted first as a computational method rather than a physical model of the cosmos, even for those who are not willing to take a view different from the Church. • Attempts to measure the distance to the planets were not successful at the time. In the geocentric models, the radii of deferent and epicycle of a planet are not obtained from observations (angle and time), only their ratios. Since the radii of planetary epicycles are the same as Earth’s orbital radius in the heliocentric model, Copernicus was able to determine the orbitalradii (relative to Earth orbit) of all six planets. • Heliocentric models predict stellarparallax, which is exactly why Tycho did not accept the heliocentric model. He could not observe parallax for stars, which are much further then he thought, and have a much smaller parallax (<1”) than he could measure.

Q: What is the role of human/Earth in cosmology? A: It has been decreasing since history. • Earth is the center of the universe • Earth is slightly off the center of planetary orbits. (Ptolemy) • The Sun is the center of the universe • The Sun is one of the stars in the Milky Way Galaxy • The Milky Way Galaxy is just one of the galaxies • The universe has no center • We are not even made of the dominant form of matter (see nonbaryonic dark matter) • The universe is made up of more energy (in the sense of E/c2) than matter (see dark energy). More: Here are some paradigm shifts:

Q: How can I understand different designs of telescopes? A:

Q: Can you suggest some equipments for schools? A: 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 imagingwork, 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: 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.) 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.

Astronomy and Space Science I