Lectures on Astronomy, Astrophysics, and Cosmology Luis A. Anchordoqui Department of Physics and Astronomy, Lehman College, City University of New York, NY 10468, USA Department of Physics, Graduate Center, City University of New York, 365 Fifth Avenue, NY 10016, USA Department of Astrophysics, American Museum of Natural History, Central Park West 79 St., NY 10024, USA (Dated: Spring 2016) I. STARS AND GALAXIES minute = 1:8 107 km, and one light year × 1 ly = 9:46 1015 m 1013 km: (1) A look at the night sky provides a strong impression of × ≈ a changeless universe. We know that clouds drift across For specifying distances to the Sun and the Moon, we the Moon, the sky rotates around the polar star, and on usually use meters or kilometers, but we could specify longer times, the Moon itself grows and shrinks and the them in terms of light. The Earth-Moon distance is Moon and planets move against the background of stars. 384,000 km, which is 1.28 ls. The Earth-Sun distance Of course we know that these are merely local phenomena is 150; 000; 000 km; this is equal to 8.3 lm. Far out in the caused by motions within our solar system. Far beyond solar system, Pluto is about 6 109 km from the Sun, or 4 × the planets, the stars appear motionless. Herein we are 6 10− ly. The nearest star to us, Proxima Centauri, is going to see that this impression of changelessness is il- about× 4.2 ly away. Therefore, the nearest star is 10,000 lusory. times farther from us that the outer reach of the solar According to the ancient cosmological belief, the stars, system. except for a few that appeared to move (the planets), On clear moonless nights, thousands of stars with vary- where fixed on a sphere beyond the last planet; see Fig. 1. ing degrees of brightness can be seen, as well as the long The universe was self contained and we, here on Earth, cloudy strip known as the Milky Way. Galileo first ob- were at its center. Our view of the universe dramatically served with his telescope that the Milky Way is comprised changed after Galileo's first telescopic observations: we of countless numbers of individual stars. A half century no longer place ourselves at the center and we view the later Wright suggested that the Milky Way was a flat disc universe as vastly larger [1, 2]. The distances involved of stars extending to great distances in a plane, which we are so large that we specify them in terms of the time it call the Galaxy [3]. takes the light to travel a given distance. For example, Our Galaxy has a diameter of 100,000 ly and a thick- one light second = 3 108m = 300; 000 km, one light ness of roughly 2,000 ly. It has a bulging central \nu- × cleus" and spiral arms. Our Sun, which seems to be just another star, is located half way from the Galactic center to the edge, some 26; 000 ly from the center. The Sun orbits the Galactic center approximately once every 250 million years or so, so its speed is 2π 26; 000 1013 km v = × = 200 km=s : (2) 2:5 108 yr 3:156 107 s=yr × × The total mass of all the stars in the Galaxy can be esti- mated using the orbital data of the Sun about the center of the Galaxy. To do so, assume that most of the mass is concentrated near the center of the Galaxy and that the Sun and the solar system (of total mass m) move in a circular orbit around the center of the Galaxy (of total mass M). Then, apply Newton's 2nd law, F = ma, with a = v2=r being the centripetal acceleration and the force F given by the universal law of gravitation GMm v2 = m ; (3) r2 r 11 2 2 where G = 6:674 10− N m kg− [4]. All in all, × r v2 FIG. 1: Celestial spheres of ancient cosmology. M = 2 1041 kg : (4) G ≈ × 2 Assuming all the stars in the Galaxy are similar to our days. Humans would be much happier if there were an Sun (M 2 1030 kg), we conclude that there are integral number of days in a year. Derive Newton's form roughly 1011≈ stars× in the Galaxy. of Kepler's third law and figure out three ways to make In addition to stars both within and outside the Milky the length of earth's year exactly 354.000 (solar) days. Way, we can see with a telescope many faint cloudy (This would also make the months be more coordinated patches in the sky which were once all referred to as \neb- with the phases of the moon. We could have 6 months of ulae" (Latin for clouds). A few of these, such as those 29 days and 6 months of 30 days. Since the orbital period in the constellations of Andromeda and Orion, can actu- of the moon is about 29.5 days, and 12 months times ally be discerned with the naked eye on a clear night. 29.5 days/month = 354 days, I think this would make a In the XVII and XVIII centuries, astronomers found great calendar!) Check your answers experimentally by that these objects were getting in the way of the search actually changing the mass of the Sun and Earth, and for comets. In 1781, in order to provide a convenient the orbital radius of the Earth. list of objects not to look at while hunting for comets, Messier published a celebrated catalogue [5]. Nowadays astronomers still refer to the 103 objects in this catalog II. DISTANCE MEASUREMENTS by their Messier numbers, e.g., the Andromeda Nebula is M31. We have been talking about the vast distance of the Even in Messier's time it was clear that these ex- objects in the universe. We now turn to discuss different tended objects are not all the same. Some are star methods to estimate these distances. clusters, groups of stars which are so numerous that they appeared to be a cloud. Others are glowing clouds of gas or dust and it is for these that we now mainly A. Stellar Parallax reserve the word nebula. Most fascinating are those that belong to a third category: they often have fairly One basic method to measure distances to nearby stars regular elliptical shapes and seem to be a great distance employs simple geometry and stellar parallax. Parallax beyond the Galaxy. Kant seems to have been the first is the apparent displacement of an object because of a to suggest that these latter might be circular discs, but change in the observer's point of view. One way to see appear elliptical because we see them at an angle, and how this effect works is to hold your hand out in front are faint because they are so distant [6]. At first it of you and look at it with your left eye closed, then your was not universally accepted that these objects were right eye closed. Your hand will appear to move against extragalactic (i.e. outside our Galaxy). The very large the background. By stellar parallax we mean the ap- telescopes constructed in the XX century revealed parent motion of a star against the background of more that individual stars could be resolved within these distant stars, due to Earth's motion around the Sun; see extragalactic objects and that many contain spiral Fig. 2. The sighting angle of a star relative to the plane arms. Hubble did much of this observational work in of Earth's orbit (usually indicated by θ) can be deter- the 1920's using the 2.5 m telescope on Mt. Wilson mined at two different times of the year separated by six near Los Angeles, California. Hubble demostrated that months. Since we know the distance d from the Earth these objects were indeed extragalactic because of their to the Sun, we can determine the distance D to the star. great distances [7]. The distance to our nearest spiral For example, if the angle θ of a given star is measured galaxy, Andromeda, is over 2 million ly, a distance to be 89:99994◦; the parallax angle is p φ = 0:00006◦: 20 times greater than the diameter of our Galaxy. It From trigonometry, tan φ = d=D, and since≡ the distance seemed logical that these nebulae must be galaxies to the Sun is d = 1:5 108 km the distance to the star is × similar to ours. Today it is thought that there are 8 10 d d 1:5 10 km roughly 4 10 galaxies in the observable universe { D = = × = 1:5 1014 km ; (5) × tan φ ≈ φ 1 10 6 × that is, as many galaxies as there are stars in the Galaxy. × − or about 15 ly. EXERCISE 1.1 Why do we have seasons? Briefly Distances to stars are often specified in terms of explain the two main reasons. Use diagrams. You must parallax angles given in seconds of arc: 1 second (1") is talk about energy, and say more than \tilt of axis." 1/60 of a minute (1') of arc, which is 1/60 of a degree, so 1" = 1/3600 of a degree. The distance is then specified EXERCISE 1.2 Suppose you are building a scale in parsecs (meaning parallax angle in seconds of arc), model of the nearby stars in our Galaxy. The Sun, which where the parsec is defined as 1/φ with φ in seconds.