Standard units of mass, length and 7me. Kilograms (kg) Meters (m) Seconds (s)

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Edgar Hutchinson
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1 Standard units of mass, length and 7me Kilograms (kg) Meters (m) Seconds (s) Astronomical masses and distances are o?en very large, e.g. the mass of the Sun is: 2,000,000,000,000,000,000,000,000,000,000 kg 1

2 Frequently use the mass of the Sun as a convenient unit of mass: Sun itself has mass 1 M Sun Most massive stars are about 100 M Sun Milky Way center black hole 4.5 million M Sun For distance use light year the distance light travels in one year, or parsec : 1 parsec (pc) = 3.26 light years ecall three squared is writen 3 2 = 9, three cubed is 3 3 = 27 etc Write large or small numbers as powers of 10: 10 = =10x10=10 2 1,000=10 3 1,000,000=10 6 2,000,000=2x10 6 number of zeroes following the first digit 2

3 ecall three squared is writen 3 2 = 9, three cubed is 3 3 = 27 etc Write large or small numbers as powers of 10: 0.1=1/10= = = =2x10-3 number of zeroes preceding the first non- zero digit 1 M Sun = 2 x kg 1 parsec = 3 x m 3

4 Nicolaus Copernicus ( ) planets orbit the Sun, not the Earth Johannes Kepler ( ) planetary orbits are not circles, but ellipses, described by simple laws Galileo Galilei ( ) discovered the moons of Jupiter orbital mo7on is universal Forces cause accelera.on F = ma Gravity is a force: same force on Earth extends to the Moon explains the Moon s orbit about the Earth gravity also explains planetary orbits Gravita7onal forces: propor7onal to mass: 2 x m = 2 x force decrease with distance squared: 2 x d = ¼ force 4

5 1/17/13 M d F= m GMm d2 G is Newton s gravita7onal constant: measures how strong gravity is Newton s theory of gravity is unbelievably successful Explains the mo7ons of the planets almost perfectly, used to model spacecra? trajectories, collisions between galaxies 5

force (its iner7a ) Features of Newtonian gravity Mass is used to refer to two (in principle) dis7nct

6 Features of Newtonian gravity Mass is used to refer to two (in principle) dis7nct concepts The strength of the gravita7onal forces a body creates How resistant it is to being accelerated by a given force (its iner7a ) Features of Newtonian gravity Mass is used to refer to two (in principle) dis7nct concepts A gold bar and a lead bar that have an iner7al mass of 1 kg produce the same gravita7onal forces too 6

1/17/13 Speed of light Ole oemer (1676) es7mates the speed of light by 7ming transits of Jupiter s moons Light has to travel extra distance, transit appears late Speed of light Modern value: ~182,000

7 1/17/13 Speed of light Ole oemer (1676) es7mates the speed of light by 7ming transits of Jupiter s moons Light has to travel extra distance, transit appears late Speed of light Modern value: ~182,000 miles / s ~300,000 km / s 299,792,458 m / s (oemer was about 20% oﬀ the right value) In Newtonian gravity, the speed of light, denoted as c, has no special role force between Earth and Sun, say, is communicated instantaneously 7

8 1/17/13 Escape velocity Forms of energy before Einstein included: kine7c energy (associated with mo7on) thermal energy poten7al energy (with posi7on) Conserved: sum remains the same Escape velocity is smallest v that gives enough energy for a body to escape to very large distance ( inﬁnity ) without falling back under gravity Escape velocity Launch a projec7le, mass m, with velocity v, from surface of Earth (distance from center of Earth) v Kine7c energy = ½ m v2 Gravita7onal poten7al energy = GM Earth m (nega7ve: if I fall toward Earth kine7c energy increases, poten7al energy must become more nega7ve to conserve energy) 8

9 Escape velocity If Kine7c + Poten7al energy = 0 (or more), escape 1 2 mv 2 GM m Earth = mv 2 = GM Earthm 1 2 v 2 = GM Earth v 2 = 2GM Earth v = 2GM Earth For the Earth, the escape velocity is 25,000 mph or 11,200 m/s Dark Stars Imagine light was just like a projec7le launched with some speed c (the speed of light!) from a star of mass M. How compact would the star be to trap the light? v esc = 2GM set equal to c 9

10 Dark Stars v esc = 2GM set equal to c c = 2GM c 2 = 2GM = 2GM c 2 a star smaller than this would be a dark star, even light cannot escape Dark Stars John Michell (1784) 10

11 Dark Stars How big is this? For an object the mass of the Sun, the cri7cal radius is: = 3 km = 2GM c 2 very small because c is so large Dark Stars This argument depends on seeing light as par7cles that respond to gravity just like regular projec7les Experiments at the start of the 19 th century convinced physicists that light was instead a wave 11

12 Dark Stars Michell s crude concept of a black hole (and, as it turns out, correct es7mate of what we now call the Schwarzschild radius), was forgoten 12

By; Jarrick Serdar, Michael Broberg, Trevor Grey, Cameron Kearl, Claire DeCoste, and Kristian Fors

By; Jarrick Serdar, Michael Broberg, Trevor Grey, Cameron Kearl, Claire DeCoste, and Kristian Fors What is gravity? Gravity is defined as the force of attraction by which terrestrial bodies tend to fall