Lecture Slides CHAPTER 3: Laws of Motion Understanding Our Universe SECOND EDITION Stacy Palen, Laura Kay, Brad Smith, and George Blumenthal Prepared by Lisa M. Will, San Diego City College

Laws of Motion Describe planetary orbits. Understand laws of motion and gravity.

Planetary Orbits Copernicus realized the Solar System was heliocentric—centered on the Sun. Planets exhibit apparent retrograde motion due to their distances from Earth and orbits around the Sun.

Planetary Orbits: Ellipses Kepler’s 1st Law: Planetary orbits are ellipses. Each ellipse has two foci. The Sun is at one focus of a planet’s elliptical orbit. Figure 3.3 (a)

Planetary Orbits: Semimajor Axis An ellipse has a size, described by the semimajor axis. The longest length (major axis) is twice the length of the semimajor axis. Figure 3.3 (a)

Planetary Orbits: Eccentricity Each orbit has a shape as well as a size. The eccentricity describes the shape - how elongated the ellipse is and how far the foci are separated. Figure 3.3 (b) 6

Class Question Does Kepler’s 1st Law allow for a circular planetary orbit? Yes No Correct Answer: A

Planetary Orbits: Remember A circle is an ellipse with an eccentricity of zero. Most planetary orbits are very close to circular. The slight deviations from circular are why Kepler’s Laws are needed to explain orbits! Figure 3.5

Planetary Orbits: Remember (Cont.) Figure 3.4 (a) 9

Planetary Orbits: Remember (Cont.) Figure 3.4 (b) 10

Planetary Orbits: Kepler’s 2nd Law Kepler’s 2nd Law: the Law of Equal Areas. The line between the Sun and the planet “sweeps” out equal areas in equal times. 11

Planetary Orbits: What is Kepler’s 2nd Law What does Kepler’s 2nd law mean? A planet will go fastest when closest to the Sun. It will go slowest when farthest from the Sun. 12

Class Question The Earth is closest to the Sun in January and furthest from the Sun in July. When is the Earth moving the fastest In its orbit? January July Correct Answer: A

Planetary Orbits: Kepler’s 3rd Law Distant planets take longer to orbit the Sun. Distant planets travel at slower speeds. For P = orbital period in years and a = semimajor axis in AU P2 = a3 14

Class Question The semimajor axis of Earth’s orbit is 1 AU. The semimajor axis of Saturn’s orbit is 9.5 AU. What Saturn’s orbital period in Earth years? Use Kepler’s 3rd law! P2 = a3 So P = a3/2 Answer: Ps/PE = (aS/aE)3/2 = (9.5/1)1.5= 29. So 1 year on Saturn is about 29 Earth years!

Galileo Galileo Galilei was the first to use a telescope for astronomical observations, around the year 1609. He made important discoveries (you could have, too, if you were the first to look at the night sky with the newly invented telescope!) Galileo discovered Jupiter’s four largest moons, observing them to orbit Jupiter over several nights. He also observed phases of Venus. Both discoveries were controversial. => Contradicted the widely held geocentric view of the universe and were consistent with a heliocentric view

Galileo: Model of Motion He experimented with falling and moving objects and crafted a model of motion. =>An object in motion will continue moving along a straight line with a constant speed until an unbalanced force acts on it. He also came up with formulas for distance, velocity and acceleration as a function of time. For constant (uniform) acceleration, such as for falling bodies, starting from rest, the distance travelled is proportional to the time squared. (d ~ t2 ) 17

Laws of Motion Sir Isaac Newton discovered laws that explain why objects in the universe move the way they do. Newton’s Laws of Motion and Law of Gravity explain why planets orbit the Sun, following Kepler’s observationally-derived Laws.

Laws of Motion: Newton’s First Law of Motion Newton’s First Law of Motion: Galileo’s result (also called the law of Inertia) A moving object will stay in constant motion. “Constant” motion means at a constant speed and in a constant direction. An object at rest stays at rest. Figure 3.8 (a) 19

Laws of Motion: Newton’s Second Law Newton’s Second Law: Net forces cause changes in motion => acceleration. Figure 3.8 (b) 20

Laws of Motion: Example In this example, the coffee cup is at rest with respect to the car that it is in. As long as the car travels at a constant speed and direction, the coffee will be level. Figure 3.8 (a) 21

Laws of Motion: Acceleration A change in speed and/or direction is called acceleration. Acceleration measures how quickly a change in motion takes place. Acceleration = (change in velocity)/time a = (vfinal- vinitial)/time interval Figure 3.8 (b) P3 22

Laws of Motion: Acceleration – Force Vs. Mass A net force causes acceleration. Mass resists changes in motion. More mass => less acceleration for a given force. Greater forces => greater accelerations. F = ma (or a = F/m) Figure 3.9 23

Blue arrow is applied force , green arrow is acceleration Laws of Motion: Acceleration – Force Vs. Mass (Cont.) Blue arrow is applied force , green arrow is acceleration Figure 3.9 (a) 24

Laws of Motion: Acceleration – Force Vs. Mass (Cont.) Figure 3.9 (b) 25

Laws of Motion: Acceleration – Force Vs. Mass (Cont.) Figure 3.9 (c) 26

Laws of Motion: Summary Newton’s Third Law: forces occur in action-reaction pairs. The two forces are equal in strength. The two forces have opposite directions. Note that the strengths of the forces between the Earth and Moon are equal, but the accelerations are not! 27

Law of Gravity All objects on Earth have been experimentally shown to fall with the same acceleration, g = 9.8 m/s2. Experiments on the Moon have shown the same phenomenon but with a different value of the acceleration (about 1/6 of Earth’s) due to the Moon’s different mass and radius.

Law of Gravity: Weight Weight is the product of your mass and the acceleration due to gravity: Because different worlds have different gravitational accelerations, you would weigh a different amount elsewhere! 29

Class Question The acceleration due to gravity on the Moon is 1/6 g. The acceleration due to gravity on Mars is 1/3 g. On which of these worlds would you weigh more? Mars Moon Correct Answer: A

Law of Gravity: Definition Gravity is an attractive, mutual force between any two objects with mass. It depends on the objects’ masses. It depends on the distance between them.

Law of Gravity: Mass Vs. Force The greater the mass, the greater the gravitational force they experience. The force of gravity includes the product of both masses.

Law of Gravity: Distance Vs. Force The greater the distance between the objects, the weaker the gravitational force. The gravitational force is dependent on the inverse square of the distance between the two objects.

Law of Gravity: Inverse Square Law Putting the pieces together: G is the universal gravitational constant. The m terms are the two masses. The r is the separation distance. This form is known as an inverse square law.

Class Question Object A and Object B initially have the same mass. If Object A’s mass increased, what would happen to the gravitational force between the two masses? The force would decrease. The force would increase. Correct Answer: B

Class Question Object A and Object B have the same mass. If the distance between the two objects increased, what would happen to the gravitational force between the two masses? The force would decrease. The force would increase. Correct Answer: A

Law of Gravity: Orbits and Satellite Orbits are one body falling around another. The less massive object is considered a satellite of the more massive object. Figure 3.13

Law of Gravity: Orbits and Satellite (Cont.) Figure 3.13 (a) 38

Law of Gravity: Orbits and Satellite (Cont.) Figure 3.13 (b) 39

Law of Gravity: Orbits and Satellite (Cont.) Figure 3.13 (c) 40

Law of Gravity: Orbits and Satellite (Cont.) Figure 3.13 (d) 41

Law of Gravity: Centripetal Force Gravity provides the centripetal force that holds a satellite in its orbit. If moving too fast or too slow, orbit will not be circular. Figure 3.15 42

Law of Gravity: Centripetal Force (Cont.) Figure 3.15 (a) 43

Law of Gravity: Centripetal Force (Cont.) Figure 3.15 (b) 44

Law of Gravity: Astronauts Astronauts float freely in the space station because they and the station are both falling at the same rate around Earth. Gravity is acting on the astronauts!

Law of Gravity: Relation to Planetary Orbits How does this relate to planetary orbits? Gravity changes both the direction and the speed of the planet. Explains Kepler’s Second Law. Figure 3.16 46

Law of Gravity: Relation to Planetary Orbits (Cont.) Figure 3.16 (a) 47

Law of Gravity: Relation to Planetary Orbits (Cont.) Figure 3.16 (b) 48

Law of Gravity: Bound or Unbound Orbit An object’s speed at its closest approach will determine the shape of the orbit and if the orbit will be bound or unbound. For example, an comet with an unbound orbit will orbit the Sun once and never return. 49

Newton and Kepler Newton derived Kepler’s Laws from his law of gravity. Physical laws explain Kepler’s results! Newton’s laws were tested by Kepler’s observations. Their agreement showed that Newton’s law of gravitation was correct.

Chapter Summary Kepler’s Laws describe planetary orbits. Planetary orbits are ellipses. Planets sweep out equal areas in their orbits in equal times. The larger the orbit of a planet, the longer the orbital period of the planet. Newton’s Laws of Motion and Gravitation explain why Kepler’s Laws work.

Astronomy in Action Velocity, Force and Acceleration Click the image to launch the Astronomy in Action Video (Requires an active Internet connection)

AstroTour Elliptical Orbits Click the image to launch the AstroTour Animation (Requires an active Internet connection)

AstroTour Newton’s Laws and Universal Gravitation Click the image to launch the AstroTour Animation (Requires an active Internet connection)

AstroTour Velocity, Acceleration, Inertia Click the image to launch the Nebraska Applet (Requires an active Internet connection)

Nebraska Applet Ptolemaic Orbit of Mars Click the image to launch the Nebraska Applet (Requires an active Internet connection)

Nebraska Applet Ptolemaic Phases of Venus Click the image to launch the Nebraska Applet (Requires an active Internet connection)

Nebraska Applet Retrograde Motion Click the image to launch the Nebraska Applet (Requires an active Internet connection)

Nebraska Applet Eccentricity Demonstrator Click the image to launch the Nebraska Applet (Requires an active Internet connection)

Nebraska Applet Planetary Configurations Simulator Click the image to launch the Nebraska Applet (Requires an active Internet connection)

Nebraska Applet Planetary Orbit Simulator Click the image to launch the Nebraska Applet (Requires an active Internet connection)

Nebraska Applet Synodic Period Calculator Click the image to launch the Nebraska Applet (Requires an active Internet connection)

Nebraska Applet Kepler’s Third Law Click the image to launch the Nebraska Applet (Requires an active Internet connection)

Nebraska Applet Phases of Venus Click the image to launch the Nebraska Applet (Requires an active Internet connection)

Nebraska Applet Newton’s Law of Gravity Calculator Click the image to launch the Nebraska Applet (Requires an active Internet connection)

Nebraska Applet Gravity Algebra Click the image to launch the Nebraska Applet (Requires an active Internet connection)

Nebraska Applet Planetary Orbit Simulator Click the image to launch the Nebraska Applet (Requires an active Internet connection)

Nebraska Applet Earth Orbit Plot Click the image to launch the Nebraska Applet (Requires an active Internet connection)

This concludes the Lecture slides for Understanding Our Universe SECOND EDITION Stacy Palen, Laura Kay, Brad Smith, and George Blumenthal Prepared by Lisa M. Will, San Diego City College This concludes the Lecture slides for CHAPTER 3: Laws of Motion wwnpag.es/uou2