Astro 113-02 Winter 2025 Slides PDF

Astro 113-02 Winter 2025 Slide 2  Topics Distance Scales Conversion of Units Coordinates Newton’s Laws Astronomy Astronomy is the study of everything in the Universe looking out from the Earth. Everything in the Universe can be understood in terms of the laws of...

Astro 113-02 Winter 2025 Slide 2  Topics Distance Scales Conversion of Units Coordinates Newton’s Laws Astronomy Astronomy is the study of everything in the Universe looking out from the Earth. Everything in the Universe can be understood in terms of the laws of Physics. Cosmology: The study of the Universe as a whole, its origin, evolution and structure, with the focus on large-scale phenomena like the big bang, dark energy and cosmic acceleration. Astronomy: The study of celestial objects such as stars, planets and galaxies, and their behavior. With the focus on smaller scale phenomena and observation. Note: Cosmology is more theoretical; astronomy is observational and object specific. Astronomy The laws of Physics are what we need to understand what goes on in stars. Fundamental forces and their role in the structure and evolution of stars. The Gravitational force. The Electromagnetic force. The Strong force. The Weak force. Therefore in this course we will introduce the concepts of physics as we need them. Astronomy In this course, we'll cover topics that are well-supported by evidence, but we'll also discuss some ideas that are more speculative. We'll clearly identify those as conjecture when we do! Terminology: Conjecture : a guess, untested. Theory : more comprehensive and self-consistent framework for describing nature. Model : A framework that has been validated through observational and experimental testing.. Laws of Physics : Well-established theories that have successfully passed every test so far. Distance Scales Comparison: Size of an atom: 1 nm: 0.000 000 000 1 m Average Height of an Adult: 1.65 m Diameter of the Earth: 12,756km: 12714000 m Distance to the moon: 384,400 km Distance to the Sun:149.6 million km: 149 600 000 000 m Distance to the nearest star (Proxima Centauri):4.24 light-years: Which is : 40.13 × 1015 m Distance to the nearest Galaxy: 2.5 million light-years Which is 23.6 × 1021 m Distance Scales Scientific Notation Powers-of-Ten Notation 101 = 10 10x10x10 = 103 = 1,000 (thousand) 106 = 1,000,000 (million) 109 = 1,000,000,000 (billion) Note: 100 =1 Distance Scales Scientific Notation Powers-of-Ten Notation 1 1 100 = 102 = 10−2 = 0.01 100 = 1 10-1 = 0.1 (one tenth) 10-3 = 0.001 (one thousandth) 10-6 = 0.000 001 (one millionth) 10-9 = 0.000 000 001 (one billionth) Distance Scales Example: Wavelength Picture from http://labman.phys.utk.edu/ Distance Scales Example: (meters) Picture is from the book “Universe” by Roger A. Freedman Some of the standard metric unit prefixes and their respective powers of 10: Prefix Power of 10 Prefix Power of 10 tera (T) 1012 centi (c) 10–2 giga (G) 109 milli (m) 10–3 mega (M) 106 micro () 10–6 kilo (k) 103 nano (n) 10–9 A Physical Quantity And Units Fundamental quantities Quantities Units: Mass SI (Systeme International) Kg (kilogram) Time Second Length Meter Charge Spin Standards of Length, Mass, and Time All physical quantities can be expressed in terms of the base dimensions of length, L, mass, M, time, T, electric current, temperature, amount of substance, and luminous intensity. In mechanics, the base dimensions are length, L, mass, M, and time, T; and the corresponding fundamental SI units of meter, kilogram, and second have well- defined, precise values. Distance Scales In Astronomy there are 3 other commonly used units The Astronomical Unit (AU) = Average distance between the Earth and the Sun. 1 AU = 1.496 x 108 km=92.96 million miles Example: The average distance between the sun and Jupiter: 5.2AU Distance Scale The Light Year (ly) = the distance light travels in one year. Light travels at a speed of 3.00 x 108 m/s. (more exact number for the speed of light: 299 792 458 m/s) Therefore the distance light travels in one year can be calculated:. Speed of light: 3.00 × 108 𝑚𝑠 1 ly  (3.00 108 m/s)(1 y)  365.25 d  24 h/d  60 min/h  60 s/min   (3.00 108 m/s)(1 y)   1y   9.46 1015 m 1 ly = 9.46 x 1012 km = 63,240 AU  Distance Scales The Parsec (pc) (We will define it precisely later in the course.) 1 pc=3.26 ly 1pc = 3.09 × 1013 𝑘𝑚 It is common to use the prefixes, kilo (k) and mega (M) for large distances. 1 km=103 𝑚 3 You are here 1kly= 10 ly 1Mpc=106 pc Example: Distance from the sun to the center of the Milky Way=28kly Image credit: NASA/JPL-Caltech Conversion of Units Write the conversion factor as a fraction so that the unwanted units are cancelled when the fraction is multiplied by the quantity in question. Examples: 1. Convert 2.5km to m: 2. 1 mi= 1609 m : convert 5 mi to m 3. 1 in. =0.0254m=2.54cm Convert 20 in. to cm 4. Convert v=21m/s to mi/s 5. Convert a=20 m/s^2 to km/min^2 Conversion of Units 1 AU = 1.496 x 108 km Example: Mars is 1.524 AU from the Sun. Find the distance in km: 1.496×108 𝑘𝑚 1.524 AU = 1.524 AU × = 2.28 × 108 𝑘𝑚 1𝐴𝑈 Coordinate Systems A coordinate system used to specify locations in space consists of: A fixed reference point, the origin A set of specified axes or directions Instructions on labelling a point in space relative to the origin and axes  Review of Trigonometry r 2  x2  y 2 opposite sin   hypotenuse adjacent cos   hypotenuse opposite sin  tan    adjacent cos  Coordinate Systems Two useful two- dimensional coordinate systems are Cartesian (rectangular) and Plane Polar Coordinates How to relate “r” in polar coordinate to (x,y) in Cartesian: x= rcos 𝜃 y=rsin 𝜃 How to relate the angel to (x,y) −1 𝑦 𝑡𝑎𝑛 =𝜃 𝑥 Important: Degree vs radians Force A force is a push or a pull. Forces can be categorized as: contact forces the interacting objects are in physical contact; field forces an object creates an invisible ‘influence’ or field around it; other objects experience a force when they interact with the field. Force is a Vector Quantity To completely describe a force, or to completely determine its effect, must consider the direction of the force as well as its magnitude. As you know, quantities that possess direction as well as magnitude can be represented by vectors. They are vector quantities. The direction of a vector is always a physical direction in space. Newton’s First Law An object moves with a velocity that is constant in magnitude and direction unless a non-zero NET force acts on it. An object’s velocity does not change if and only if the NET force acting on the object is zero. Note that the law is not written in terms of a single force, but rather the NET force. Net Force The VECTOR SUM of ALL the external forces exerted on an object (the NET FORCE) determines the motion of the object.      Fnet  F  F1  F2 ...  Fn Note: Unit of Force: Newton (N) Inertia Inertia is the tendency of an object to continue its motion in the absence of a force. Inertia also refers to the tendency of an object to resist changes in its motion. Newton’s Second Law Newton’s second law explains what happens to an object that does have a net force acting on it: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Newton’s Second Law   a F m    F  ma F x  max ,  Fy  ma y ,  Fz  maz When there is no net force on an object, its acceleration is zero, which means its velocity is constant. The Gravitational Force Newton’s Law of Universal Gravitation describes the gravitational forces of attraction that any two objects exert on one another: m: Mass r: Distance Gm1m2 G: Gravitational Constant F r2 where r is distance b/w centres 11 G  6.67 10 N  m /kg 2 2  Weight Consider an object of mass m near the Earth’s surface (so that r ≈ RE). An object in free-fall near the Earth’s surface has an acceleration of magnitude g. From Newton II law we know that this acceleration must be caused by a net force – the gravitational force of the Earth on the object. The magnitude of the gravitational force on an object is called its weight, w. Weight The magnitude of the gravitational force on an object is called its weight, w. F  m a Fgrav  magrav w  mg Weight Substituting from Newton’s Law of Universal Gravitation…   F  ma M Em G 2  mg RE ME G 2 g RE  Relationship between mass and weight: w = mg g depends on location (larger at the poles due to Earth being a flattened sphere) g depends on geologic formations beneath the surface g depends on altitude effective value of g is influenced by the rotation of the Earth and of course if you are on the Moon or a different planet, g is entirely different Newton’s Third Law Forces always occur in pairs. Every force is part of an interaction between two objects and each of those objects exerts a force on the other. The two forces are an action/reaction pair of forces. Note that the action and reaction forces act on different objects. Newton’s Third Law The action and reaction forces always have the same magnitude and are in opposite directions. “For every action, there is an equal and opposite reaction.” If the force exerted by object 1 on object 2 is F12 and the force exerted by object 2 on object 1 is F21, then   F12   F21  Important Notes When an object is in equilibrium the net force acting on it is zero. A vector can only have zero magnitude if all of its components are zero:  F  0 implies Fx  0 and Fy  0 and Fz  0 Even when the net force on an object is not zero, choosing one of the coordinate axes to be in the direction of the acceleration means that the component of the net force in that direction will be the only component that is nonzero.