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Salah Nasri " Basic Astronomy & Astrophysics: WithQ’s andA’s" January 2, 2019 In these notes, I discuss a selected number of topics in Astronomy and Astrophysics in the form of questions. For a non-physics major student or layman, very short answers to these questions are provided, whereas for people with special interest in physics and astrophysics more details are given. I also included many appendices with comprehensive discussion relevant to the questions discussed in these notes. 1 1 The Questions (Q1): How did the ancients knew that Earth was round ? (Q2): How did the ancients measured the size of the Earth? (Q3): What is the simplest clear experimental evidence that the Earth spins around its axis? (Q4): How fast does the Earth spin at the equator? (Q5): How fast does the Earth move around the Sun? (Q6): what is the universal law of gravitation ? (Q7): What is the mass of the Earth ? (Q8): what is the acceleration of gravity at the surface of an astro- nomical object of mass M and radius R? (Q9): What is the escape velocity from the Earth? (Q10): What is the minimum speed to launch a satellite from Earth ? (Q11): What is the age of the Earth? (Q12): What is the critical temperature, Tcritical, of the atmosphere of a planet (of mass M), above which a particular atmospheric component (of mass m) will be lost into space ? (Q13): What is the ozone and where is it in the atmosphere ? (Q14): What is the electromagnetic spectrum ? (Q15): What type of electromagnetic radiation can reach the Earth’s surface ? (Q16): What is a parallax angle, a parsec, and a light year ? (Q17): What is the apparent and absolute magnitude of a stellar ob- ject ? (Q18): What is the distance between the Earth and Moon ? (Q19): What is the mass of the Moon ? 2 (Q20): How was the distance between the Earth and the Sun accu- rately measured before the 20th century ? (Q21): How was the mass of the Sun first measured ? (Q22): What is average solar power density reaching the Earth’s at- mosphere ? (Q23): What is the luminosity of the Sun? (Q24): How to estimate the surface temperature of a star ? (Q25): What is the size of the Sun? (Q26): What are the temperature and pressure at the Sun’s center ? (Q27): What are the layers of the Sun’s atmosphere ? (Q28): What is the direct method for measuring the mass of a stars ? (Q29): What is dynamical time scale of a star ? (Q30): What is Kelvin-Helmholtz time scale of a star? (Q31): What is nuclear time scale of a star? (Q32): How does the Sun shine ? (Q33): What is the chemical composition of the Sun? (Q34): How does the Luminosity (L∗) of a main-sequence star de- pends on its mass (M∗) and radius (R∗)? (Q35): What is the life-time of a star as function of its mass ? (Q36): What is the lower mass a star can have? (Q37): What is the maximum mass a star can have ? (Q38): What is a white dwarf ? (Q39): How big is a white dwarf ? (Q40): What is the Chandrasekhar limit? (Q41): What is a supernovae ? 3 (Q42): What is a neutron star ? (Q43): What is a black hole ? (Q44): What is a quasar ? (Q45): When did the most recent extinction event on Earth occur ? (Q46): What is the size of the Milky Way galaxy ? (Q47): How long does it take a spacecraft to reach the planet Mars ? (Q48): How did astronomers know that the Milky Way is not the only galaxy in the Universe ? (Q49): What is the age of our universe ? (Q50): How did we know that our Universe is not static? (Q51): How did the light elements, hydrogen and helium, form during the evolution of is the universe ? (Q52): How did the heavy elements form in the Universe? (Q53): which type of telescope is most used by astronomers ? (Q54): what is Hubble Space telescope ? (Q55): what is Olber’s paradox ? (Q56): what are the Greenhouse gases ? 4 The idea of spherical Earth was first proposed by Pythagoras, however it was based on aesthetic ground. It a A1): was Aristotle who argued, based on observational facts, ( that the shape of the Earth is spherical. aAncient Greek philosopher and scientist who lived between circa 384 B.C and 322 B.C, and is considered one of the greatest thinkers in history. More Details The observational facts are: • Stars that are visible in the Northern hemisphere are not for an observer in the Southern hemisphere. Similar argu- ment holds the other way around. For instance, an observer lo- cated in the Southern hemisphere can not see the star "Polaris", but once in the Northern hemisphere it becomes visible. Figure 1: More stars are visible to an observer moving toward the north and looking to the sky toward the North. Similarly,more stars will be visible to her/him when moving toward the south and looking to the sky in the direction toward the south. • The Earth’s shadow on the moon surface during the dif- ferent phases of the lunar eclipse always evolves from 5 arched to circular, and this is regardless where you are on the Earth1. Moreover, when the moon was in different positions dur- ing an eclipse, the sunlight struck the earth from different angles, and yet the shape of the Earth’s shadow, as it moves across the moon, always looked part of a circle. This means that Earth has a shape that casts a circular shadow in every possible angle. This could only be caused by a spherical shape. • When standing on the shore, and watching a ship moving away, the bottom of ship2 in sea starts to disappear first over the horizon, and then, gradually, the mast. Around 240 B.C, Eratosthenes of Cyrenea determined the circumference of the Earth by measuring the differ- ence in the angles between the incident light and the (A2): vertical at two different locations, and using simple ge- ometry. aModern day Libya. More Details Eratosthenes [276−194 BC], noticed that at noon during the summer solstice3, the light shone straight down into the bottom of a very deep well4 in the Egyptian city of Syene5, which means that vertical sticks cast no shadow. At the same time in Alexandria, where he lived, it casts a shadow. By measuring the length of the shadow casted by a tower in Alexandria, he determined the angle between the vertical tower and the Sun’s ray6 to be equal to 7:2 degrees. He also knew that the distance between Alexandria and Syene is 5000 Stadia, which was 1 If the Earth had a shape of a disk, then the moon would have to be directly overhead to get a round shadow, which means the sun would be directly below the earth. If that was the case, the entire surface of the Earth would be dark during a lunar eclipse. 2Also called the Hull. 3This is when the Sun reaches its highest position in the sky, which occurs between June 20 and June 22 in the Northern Hemisphere, and between December 20 and December 22 in the Southern Hemisphere. 4 The water was illuminated but not the walls of the well. 5Now known as Aswane. 6Knowing the height of the tower and the length of the shadow one can deduce the angle between the vertical tower and the Sun’s ray. 6 the unit of lengths used at that time7. Figure 2: Measuring the size of the Earth. So, Eratosthenes reasoned that if 7◦ decomposes the circumference, C, of the Earth to an arc of length 5000 stadia, then 360◦ C = × 5000 Stadia = 250; 000 Stadia 2 [40; 000 − 45; 000 km] 7◦ Thus, the radius of the Earth is 40; 000 km R⊕ = 2 [6370 − 7325 km] 2π 7Unfortunately, there is not an exact conversion of 1 stadia to our unit metric system. However, many historians put it in a range between 0:16 km and 0:18 km. 7 which is close to the true value. This is really remarkable considering the very simple method that he used for this measurement8. In 1851, the French physicist Leon Foucault, hang up a very long pendulum from a ceiling at the Pantheon (A3): in Paris and let it swing, and showed that its path "ap- peared " to be slowly shifting, which was a clear evidence that the Earth rotates around its axis. More Details • To understand how does Foucault’s pendulum demonstrates the rotation of the Earth around its axis, we need to discuss the so called Coriolis force, which was named in honor of the French mathematician Gustave Coriolis9 who proposed the existence of pseudo-force (i.e. an apparent force) that a body experiences when it is moving in a rotating frame. To be more specific, let us consider a body that is located at a point (r; θ; φ) in spherical coordinates. Its velocity as seen in a reference frame, R, attached at the Earth’s surface (see Fig.3) is ^ ^ υjR = υrr^ + υθθ + υφφ (1) Here r^; θ^, and φ^ form an orthonormal basis in the spherical coor- dinate system. Then, the Coriolis force is given by Fcoriolis = −2m! × υjR (2) where ! = !z^ is the angular velocity vector of the Earth. Using the vector identities z^ × r^ = sin θφ^; z^ × θ^ = cos θφ^; z^ × φ^ = − sin θr^ − cos θθ^ (3) 8One might wonder what if Eratosthenes assumed that Earth is flat. In this case, for the tower to cast a shadow the Sun has to be be very close to the Earth Surface.
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