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Astronomy 114 Lecture 6: Newton’s Laws of Motion and Gravity Martin D. Weinberg [email protected] UMass/Astronomy Department A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—1/17 Announcements Problem Set #2 posted today, due next Friday Grade/homework posting release form A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—2/17 Announcements Problem Set #2 posted today, due next Friday Grade/homework posting release form Newton’s Laws Physical laws, Fundamental forces Explain Kepler’s Laws and Galileo’s observations in one theory A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—2/17 Newton (1642-1727) Recognized importance of Galileo’s contribution A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—3/17 Newton (1642-1727) Recognized importance of Galileo’s contribution Laws of Motion A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—3/17 Newton (1642-1727) Recognized importance of Galileo’s contribution Laws of Motion Law of Gravitation A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—3/17 Newton (1642-1727) Recognized importance of Galileo’s contribution Laws of Motion Law of Gravitation Explained all of planetary motion A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—3/17 Newton (1642-1727) Recognized importance of Galileo’s contribution Laws of Motion Law of Gravitation Explained all of planetary motion Explains much of all motion in the Universe A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—3/17 Principia Mathematica, 1687 Unified observations of Kepler and Galileo Invented Calculus to solve the problem Beginning physics! A114: Lecture 6—09 Feb 2007 Read: Ch. 4 of modern Astronomy 114—4/17 Newton’s 3 Laws of Motion (1/5) 1. Law of Inertia: A body remains at rest, or moves in a straight line at a constant speed, unless acted on by an outside force A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—5/17 Newton’s 3 Laws of Motion (1/5) 1. Law of Inertia: A body remains at rest, or moves in a straight line at a constant speed, unless acted on by an outside force 2. Second Law: Acceleration of an object is proportional to the force acting on that object F=ma m is mass a is acceleration A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—5/17 Newton’s 3 Laws of Motion (1/5) 1. Law of Inertia: A body remains at rest, or moves in a straight line at a constant speed, unless acted on by an outside force 2. Second Law: Acceleration of an object is proportional to the force acting on that object F=ma m is mass a is acceleration 3. Third Law: When one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—5/17 Newton’s 3 Laws of Motion (2/5) First Law: Law of Inertia The motion of an object has speed and direction An object’s resistance to changes in motion is known as inertia Contradicted the still popular theories of Aristotle that objects will eventually come to rest A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—6/17 Newton’s 3 Laws of Motion (3/5) Second Law of Motion F= ma F describes the force acting m is the mass of the object a is its acceleration, the change in its motion. Like motion, force has both a value or strength, and a direction in which it acts. Acceleration refers to any change (“speeding up”, “slowing down”, or change of direction) Implies First Law of Motion A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—7/17 Newton’s 3 Laws of Motion (4/5) Second Law of Motion: examples The larger the force the larger the acceleration For equal force, a larger mass must have a smaller acceleration Larger mass has greater inertia. Can use this to measure mass of an object Unit of force (metric) is called a Newton (N): 1 Newton is equal to 1 kg · m/s2 Inertial mass A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—8/17 Newton’s 3 Laws of Motion (5/5) Third Law: equal and opposite force Example: smack an object Object moves as a result Your hand also feels a force and bounces back (and hurts) A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—9/17 Newton’s 3 Laws of Motion (5/5) Third Law: equal and opposite force Example: smack an object Object moves as a result Your hand also feels a force and bounces back (and hurts) Example: small object hits a large object If the forces are equal, why does the smaller object bounce back faster? A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—9/17 Newton’s 3 Laws of Motion (5/5) Third Law: equal and opposite force Example: smack an object Object moves as a result Your hand also feels a force and bounces back (and hurts) Example: small object hits a large object If the forces are equal, why does the smaller object bounce back faster? msmall asmall = F = mlarge alarge mlarge alarge asmall = m small A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—9/17 Fundamental Forces (1/2) Physicists have identified four natural forces Gravity Holds the Sun and planets together in the solar system Holds stars together in galaxies Things fall “down” on Earth A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—10/17 Fundamental Forces (1/2) Physicists have identified four natural forces Gravity Holds the Sun and planets together in the solar system Holds stars together in galaxies Things fall “down” on Earth Electromagnetism: a force between objects with electric charge Holds atoms together Responsible for chemical reactions Friction of book on table Magnets A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—10/17 Fundamental Forces (2/2) Strong force Holds nuclei of atoms together Generation of energy in stars, supernovae Power, bombs A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—11/17 Fundamental Forces (2/2) Strong force Holds nuclei of atoms together Generation of energy in stars, supernovae Power, bombs Weak force Radioactive decay Also energy in stars, supernovae A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—11/17 Newton’s Law of Gravity (1/6) Newton described the force of gravity mathematically Every body in the Universe attracts every other body with a force proportional to the product of their masses and inversely proportional to the square of the distance between them: Fgravity Gm1 m2 = r2 G is the same here as it is in a distant galaxy. It is a physical constant of the Universe. A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—12/17 Newton’s Law of Gravity (2/6) Gravity is an attractive force, and in accordance with Newton’s Third Law, the two masses feel equal and opposite forces Gravity is relatively weak because of the small value of the gravitation constant G; in metric units: G = 6.7 × 10−11 N · m2 /kg2 Large masses are required to provide an appreciable force, e.g. the mass of the Earth is 6.0 × 1024 kg A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—13/17 Newton’s Law of Gravity (3/6) On the surface of a planet: Fgravity Fgravity Gm2 = m1 × 2 r = m1 × aEarth’s surface Acceleration caused by the Earth on any object placed on its surface is the same: its value is 9.8 m/sec/sec. Acceleration on the surface determines weight of object A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—14/17 Newton’s Law of Gravity (3/6) On the surface of a planet: Fgravity Fgravity Gm2 = m1 × 2 r = m1 × aEarth’s surface Acceleration caused by the Earth on any object placed on its surface is the same: its value is 9.8 m/sec/sec. Acceleration on the surface determines weight of object On another planet 2 mplanet rEarth aplanet = × 2 aEarth mEarth rplanet A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—14/17 Newton’s Law of Gravity (3/6) On the surface of a planet: Fgravity Fgravity Gm2 = m1 × 2 r = m1 × aEarth’s surface Acceleration caused by the Earth on any object placed on its surface is the same: its value is 9.8 m/sec/sec. Acceleration on the surface determines weight of object On Mars 2 0.11 mMars rEarth aMars 1 = = × 2 × aEarth mEarth 1 0.53 rMars A114: Lecture 6—09 Feb 2007 Read: Ch. 4 2 = 0.39 Astronomy 114—14/17 Newton’s Law of Gravity (4/6) Velocity Planet Acceleration Combined with Laws of Motion: explains orbits Kepler’s Three Laws Resulting trajectory A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—15/17 Newton’s Law of Gravity (5/6) Newton discovered that orbiting bodies may follow any one of a family of curves called conic sections The ellipse is only one possibility A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—16/17 Newton’s Law of Gravity (6/6) Planets obey the same laws as objects on Earth A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—17/17 Newton’s Law of Gravity (6/6) Planets obey the same laws as objects on Earth Kepler’s laws: explained by force of gravity Planets orbit around the center of mass of the Solar System Since most of the mass is the Sun, Sun is very close to center of mass Third law depends on the sum of the two masses: P2 = A114: Lecture 6—09 Feb 2007 " 4π 2 G(m1 + m2 ) Read: Ch. 4 # a3 Astronomy 114—17/17 Newton’s Law of Gravity (6/6) Planets obey the same laws as objects on Earth Kepler’s laws: explained by force of gravity Planets orbit around the center of mass of the Solar System Since most of the mass is the Sun, Sun is very close to center of mass Third law depends on the sum of the two masses: P2 = " 4π 2 G(m1 + m2 ) # a3 New types of unbound orbits — hyperbolas and parabolas — in addition to ellipses A114: Lecture 6—09 Feb 2007 Read: Ch. 4 Astronomy 114—17/17