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Introduction to Astronomy and Astrophysics Introduction to Astronomy and Astrophysics o Lectures Planets 1. Astronomy – and Observational Science 2. The Sun 3. Planets of the Solar System 4. Extra-solar Planets 5. Observing the Universe 6. Properties of Stars 7. Life and Death of Stars 8. Galaxies and Large Scale Structure of the Universe 9. Cosmology – Origin and Evolution of the Universe Cluster of Stars Stars and Planets Galaxies (Whirlpool Galaxy) Cosmic Microwave Background Introduction to Astronomy and Astrophysics Introduction to Astronomy and Astrophysics o Recommended text: Introduction to Astronomy and Cosmology (Morison; Wiley) o Lecturer: o Prof. Peter Gallagher o Head of Solar Physics and Space Weather Research Group o Director of Astrophysics Degree o Email: [email protected] o Assessment: o Examination – written paper: 70% o Online tutorials (3): Cluster of Galaxies 30% Lecture 1: Astronomy – An Observational Science o Overview: Early Models of the Solar System o Ptolomy’s (AD 100-170) Geocentric Model o Early astronomy – motion of the planets o Ptolomy, Copernicus, Galileo o Laws of Planetary Motion and Gravity o Kepler, Newton o Earth at centre o Planets move in circular ‘epicycles’, whose centres move around Earth in circular ‘deferents’ o Note: Mercury nearer to Earth than Venus Retrograde motion o The Solar System Today o Chapter 1 of Introduction to Astronomy and Cosmology o Explained ‘retrograde’ motion of planets like Mars and Jupiter Early Models of the Solar System o Retrograde motion of Mars Early Models of the Solar System o Copernicus’s (1473-1543) Helcentric Model o Centre of Universe is near Sun o Distance from Earth to Sun is imperceptible compared with distance to stars. o Rotation of Earth accounts for the apparent daily rotation of the stars. o Apparent annual cycle of movements of Sun is caused by the Earth revolving round it. o Apparent retrograde motion of planets caused by motion of Earth from which one observes. o Explains retrograde motion – Earth overtakes Mars on “inside track” Retrograde motion Early Models of the Solar System Orbits of the planets o Ptolemaic model: o Venus between Earth and Sun o Could only show crescent phases o Little variation in angular size o Copernican model: o Venus orbits Sun o Phases and almost full phase o Large chance in angular size o Laws governing planetary motion formulated by Johannes Kepler (1571-1630) based on Tycho Brahe’s observations o Kepler’s Laws: 1. Planets have elliptical orbits with the Sun at one focus Galileo’s drawings of Venus’ phases o Galileo (1564-1642) proved Sun not Earth at centre of solar system by observing Venus with telescope => Copernicus correct! Modern images Kepler s 1st Law: Law of Orbits 2. As a planet orbits, a line connecting the planet to the Sun sweeps out equal areas in equal times 3. The square of the orbital period is proportional to the cube of the semi-major axis of the orbit Kepler s 2nd Law: Law of areas o Planets move in elliptical orbits with the Sun at one focus. o The radius vector (line joining planet to Sun) sweeps out equal areas in equal times: dA = const dt => Planet movies faster at perihelion. Semi-minor axis € Semi-major axis Aphelion Perihelion Kepler s 2nd Law: Law of areas Kepler s 3rd Law: Law of Periods o The square of a planet’s period (T) is proportional to the cube of the semimajor axis of the orbit (a): o Consequence of conservation of energy: Kinetic Energy + Potential Energy = const r ⎯⎯ → max GM s m p PE = − ⎯⎯ → max r 2 KE = 1 / 2m p v p ⎯⎯ → min GM s m p = const r mp r Ms v p ⎯⎯ → min where k is a constant. r ⎯⎯ → min GM s m p PE = − ⎯⎯ → min r 2 KE = 1 / 2m p v p ⎯⎯ → max o Note: If a is in Astronomical Units (AU), then k = 1 and T is in years o 1 AU = Earth-Sun semi-major axis = 149 million km Semi-major Axis (AU) 1 / 2m p v 2p − T 2 = k a3 T 2 = k a3 v p ⎯⎯ → max Period (T) in Years In Class Problem Consequences of Kepler’s Laws o Calculate the semi-major axis of Mars in AU and km given that the period of its orbit is 1.88 years. Gave superb map of the Solar System o BUT, could not give a scale. No idea of distances. o Answer: o Know: o T2 =k a3=> a= o Cassini in 1672 using observations of Mars from Paris and French Guiana measured Earth-Mars distance. Using Kepler’s 3rd Law, he then calculated Earth-Sun distance (140 million km). T2/3 1 AU o Therefore, for Mars a = (1.88)2/3 = 1.523 AU o As 1 AU = 149 million km => Mars’ semi-major axis = 227.9 million km 1.523 AU Consequences of Kepler’s Laws o Led Newton (1642-1726) to the Law of Gravity. o Used Newton’s Laws of Motion (F = ma) and Kepler’s 3rd Law to derive Law of Gravitation. The Solar System Today Oort Cloud Edgeworth-Kuiper Belt Asteroid Belt Lecture 1 Practical Task o Find Venus, Mars and Jupiter just before sunrise in East. What can you see after sunrise? Moon on Oct 8 Moon on Oct 9 Moon on Oct 10 o Find out more at www.jb.man.ac.uk/astronomy/nightsky/