1 Newton s Laws of Motion

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1 Exam 1 Ast 4 - Chapter 2 - Newton s Laws Exam 1 is scheduled for the week of Feb 19th Bring Pencil Scantron 882-E (available in the Bookstore) A scientific calculator (you will not be allowed to use you cell phone) 1 Newton s Laws of Motion of Motion Any moving object will continue moving with the same speed and in the same direction unless acted upon by an unbalanced force. Any object in a state of rest will continue in that state of rest unless acted upon by an unbalanced force The mere existence of motion does nor require any outside forces No force is required to maintain motion is a straight line with constant speed Velocity is an object s speed and direction of Motion Any object continues in a state of constant velocity unless acted upon by an unbalanced force Newton s Second Law Newton s Second Law of Motion The acceleration of an object is proportional to the net force acting on the object and inversely proportional to the objects mass F a = m or F = m a

2 Newton s Second Law Acceleration is the rate of change of velocity acceleration can change the speed of an object acceleration can change the direction of motion of an object or both Nature of Forces Force is a description of the process by which two objects interact. Thus, forces come in pairs Newton s Third Law Newton s Third Law of Motion If any object A exerts a force upon another object B, then B also exerts a force of the same strength but in the opposite direction upon A; To every action there is an equal and opposite reaction 2 Law of Universal Gravitation Law of universal gravitation The second law of motion requires a force for circular motion A force must be acting on the planets as they orbit the Sun This force must decrease as the planet moves further away from the Sun Jupiter s moons, our Moon, and the behavior of falling objects near Earth s surface can be explained the same way Law of universal gravitation Every pair of objects in the universe exerts a mutual force on each other that Proportional to the product of the two masses Inversely proportional to the square of the distance between them F g m 1 m 2 d 2 2

3 Law of universal gravitation F g = Gm 1m 2 r 2 G is known as the gravitational constant. Its value in SI units is N m 2 /kg 2. Newton applied his theory to explain Ocean tides The perturbation by Jupiter and Saturn of each others orbits Origin of precession 3 Kepler revisited Revision to Kepler s Laws The gravitational force pulls each planet towards the Sun. Based on Newton s third law the Sun experiences a force due to the planet Revision to Kepler s Laws Kepler s First Law The orbit of a planet around the Sun is an ellipse, with the center of mass of the planet-sun system at one focus 3

4 Revision to Kepler s Laws Kepler s Third Law P 2 (in years) = a 3 (in A.U.) M total (in solar units) M total is the combined mass of the two objects 4 Example calculation Example: Mass of the Earth-Moon System Calculating the mass of the Earth-Moon System Distance from the Earth to the Moon: km Length of sidereal month: 27.3 days ( ) 1 yr P Moon = 27.3 days = yrs 365 days ( ) a moon = A.U. km = A.U. km Example: Mass of the Earth-Moon System Kepler s third law M (Earth + Moon) = a3 Moon P 2 Moon M (Earth + Moon) = ( ) 3 ( ) 2 M M (Earth + Moon) = M Because the Earth s mass is so much larger than Moon s mass, M Earth M (Earth + Moon) 5 Concept Review Chapters 1 & 2 Elements of the scientific method R.A. and Declination coordinate system The motions of the Earth and their associated time periods Rotational (23 h 56 m ) Orbital ( days) Precessional ( 26,000 yrs) 4

5 The seasons Moon phases Retrograde motion Ptolemy s geocentric model Copernican model Prediction of the phases of Venus Galileo s observations of The moon Jupiter s moons Phases of Venus Sunspots Kepler s 3 laws Properties of orbits Newton s 3 laws of motion Newton s law of gravitation 5