© 2005 Pearson Education Inc., publishing as Addison-Wesley Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity “If I have seen farther than others, it is because I have stood on the shoulders of giants.” Sir Isaac Newton (1642 – 1727) © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley The history of Universe is essentially a story about the interplay between matter and energy. We can understand what happens in Universe using physics laws we can test on the Earth (even though the sizes involved are on much bigger scale). In this Chapter we will discuss laws which govern motion and energy in the Universe; first we will learn how to describe motion; we will see what is mass (and what is weight); and then Newton’s laws of motion, conservation laws of momentum and energy and gravity law. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley 4.1 Describing Motion Our goals for learning: How do we describe motion? How is mass different from weight? © 2005 Pearson Education Inc., publishing as Addison-Wesley
How do we describe motion? Precise definitions to describe motion: speed: rate at which object moves example: speed of 10 m/s velocity: speed and direction example: 10 m/s, due east acceleration: any change in velocity units of speed/time (m/s2) Basic vocabulary of motion. Emphasize that turning, slowing, and speeding up are all examples of acceleration. momentum: product of mass and velocity. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Acceleration: Speeding up turning Slowing down © 2005 Pearson Education Inc., publishing as Addison-Wesley
The Acceleration of Gravity All falling objects accelerate at the same rate (not counting friction of air resistance). On Earth, acceleration of gravity is g ≈ 10 m/s2: speed increases 10 m/s with each second of falling (the unit is therefore m/s/s) You may also wish to do the rock and paper demonstration described in the Think About It on p. 88. Question: if you drop a feather and a rock at the same time, which one will fall first? Why? What will happen if you repeat this on the Moon? © 2005 Pearson Education Inc., publishing as Addison-Wesley
The Acceleration of Gravity (g) It was Galileo who showed that g is the same for all falling objects, regardless of their mass. He devised experiments (on the leaning tower of Pisa, the legend says) which proved this to be true (contrary to the experience). When you show this video clip, be sure to point out what is going on since it is not easy to see… Apollo 15 demonstration Review: what experiment about the motion done by Galileo do you remember from the last class? (hint: he proved Aristotle was wrong) © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Momentum and Force Momentum = mass velocity Only a net (overall) force can change momentum. It changes momentum by changing velocity or equally by causing acceleration. Force actually equals to the rate of momentum change, or the acceleration caused (times the mass). Question: What will happen if a bug, moving with speed of 30km/hr hits your car? What will happen if 2 tone truck, moving at a same speed hits it? Explain why. (hint: which has bigger momentum?) You may wish to discuss the examples given in the text on p. 79 © 2005 Pearson Education Inc., publishing as Addison-Wesley
Thought Question: Is there a net force? Y/N A car coming to a stop. A bus speeding up. An elevator moving up at constant speed. A bicycle going around a curve. A moon orbiting Jupiter. Use to check if students can figure out where a net force is acting. For bonus questions, ask if they can identify the forces. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Is there a net force? Y/N A car coming to a stop. Y A bus speeding up. Y An elevator moving at constant speed. N A bicycle going around a curve. Y A moon orbiting Jupiter. Y Question: If elevator is moving at a constant speed, does that mean there is no force acting on it? © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Summary: Whenever there is a change of speed or a direction of motion (whenever there is an acceleration) there is a net (overall) force acting on a body. That force actually equals to the mass of the body times the acceleration caused (which is also a momentum change). Change of momentum = m change of velocity = = m acceleration (= F) © 2005 Pearson Education Inc., publishing as Addison-Wesley
How is mass different from weight? mass – the amount of matter in an object; it never changes! weight – the gravitational force that acts upon an object; it changes depending were you are, or how do you move (weather you accelerate or not). W=m g. You are weightless in free-fall! © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Summary: Mass never changes, no matter where you are, or how are you moving. Weight is actually a gravitational force exerted on you, which you in turn exert on the floor. It depends on: Where you are (bigger planets will exert bigger gravity pool on you) And weather you are accelerating or not (acceleration equals force, so if you are accelerating that is like that something is applying additional force on you). Free-fall: if there is nothing to stop you from moving under the attraction of gravity (no floor) you would be weightless, while free-falling. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Questions: Why is your weight the same while elevator moves with a constant speed? (hint: what is the acceleration of elevator? What does it tell us about the force?) Why your weight changes if the elevator accelerates? Would your mass change if the elevator would go with a constant speed, on the Moon? Why? © 2005 Pearson Education Inc., publishing as Addison-Wesley
Thought Question On the Moon: My weight is the same, my mass is less. My weight is less, my mass is the same. My weight is more, my mass is the same. My weight is more, my mass is less. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley On the Moon… My weight is the same, my mass is less. My weight is less, my mass is the same. My weight is more, my mass is the same. My weight is more, my mass is less. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Why are astronauts weightless in space? (make a guess…) © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Why are astronauts weightless in space? (make a guess…) Question: is it true that there is no gravity in the space? © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Why are astronauts weightless in space? (make a guess…) Question: is it true that there is no gravity in the space? weightlessness is due to a constant state of free-fall: Let’s imagine you could fall through the Earth. Question: If you would run on the tower and then jump of off it, what would your path be? Now imagine your speed when jumping off the tower is so huge, you actually miss the Earth… You may wish to start by discussing the common misconception of no gravity in space, as presented in the box in the book on p. 82. Then can use this interactive figure to explain how, with enough speed, you can be “falling around” Earth and thus in a constant state of free-fall. Can extend idea to any other orbital trajectory, which simply means falling in response to gravity. Note: the rocket orientations in Fig 4.4 are arbitrary since, once in orbit with rocket no longer firing, the orientation will be determined by whatever net rotation the rocket had initially. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley What have we learned? How do we describe motion? Speed = distance/time Speed + direction => velocity (v) Change in velocity => acceleration (a) Momentum = mass velocity Force causes a change in momentum, which means acceleration. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley What have we learned? How is mass different from weight? Mass = quantity of matter Weight = force acting on mass Objects are weightless when in free-fall © 2005 Pearson Education Inc., publishing as Addison-Wesley
4.2 Newton’s Laws of Motion Our goals for learning: How did Newton change our view of the universe? What are Newton’s three laws of motion? © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley How did Newton change our view of the Universe? Realized the same physical laws that operate on Earth also operate in the heavens one universe Question: how does this compare with Aristotle’s understanding of nature (remember Aristotle’s teaching were “near gospel truth” at that time)? Discovered laws of motion and gravity Much more: experiments with light; first reflecting telescope, calculus… Sir Isaac Newton (1642-1727) © 2005 Pearson Education Inc., publishing as Addison-Wesley
What are Newton’s three laws of motion? Published in 1687, under the title “Philosophiae Naturalis Principia Mathematica” Newton’s first law of motion: An object moves at constant velocity unless a net force acts to change its speed or direction. Question: who was the first to discover the basics of this law in his careful experiments? (hint: it helped him as an argument against Earth-centered system) You may wish to discuss the examples in the book on p. 83-84. © 2005 Pearson Education Inc., publishing as Addison-Wesley
Newton’s second law of motion: What happens when the force is present… Force = mass acceleration Again, you may wish to discuss the same examples given in the text, which are on p. 84. Question: if you throw away a ball made of plastic and the rock of about the same size, which one would fly further? Why? (hint: what is the force in this example? What is the acceleration?) © 2005 Pearson Education Inc., publishing as Addison-Wesley
Newton’s third law of motion: For every force, there is always an equal reaction force in opposite direction. A rocket is propelled upward by a force equal and opposite to the force with which gas is expelled out its back. Again, you may wish to discuss the same examples given in the text, which are on p. 84. You may also wish to go over the common misconception about rocket launches in the box on p. 84-5. Example: measuring weight on a balance. Question: when we are pulled down by Earth’s gravity, are we also pulling up the Earth? Why doesn’t the Earth move? © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Thought Question: A compact car and a Mack truck have a head-on collision. Are the following true or false? The force of the car on the truck is equal and opposite to the force of the truck on the car. The momentum transferred from the truck to the car is equal and opposite to the momentum transferred from the car to the truck. The change of velocity of the car is the same as the change of velocity of the truck. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Thought Question: A compact car and a Mack truck have a head-on collision. Are the following true or false? The force of the car on the truck is equal and opposite to the force of the truck on the car. T The momentum transferred from the truck to the car is equal and opposite to the momentum transferred from the car to the truck. T The change of velocity of the car is the same as the change of velocity of the truck. F © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley What have we learned? How did Newton change our view of the universe? He discovered laws of motion & gravitation. He realized these same laws of physics were identical in the universe and on Earth. What are Newton’s Three Laws of Motion? Object moves at constant velocity if no net force is acting. Force = mass acceleration For every force there is an equal and opposite reaction force. © 2005 Pearson Education Inc., publishing as Addison-Wesley
4.3 Conservation Laws in Astronomy: Our goals for learning: What keeps a planet rotating and orbiting the Sun? Where do objects get their energy? © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Newton used force to describe interactions. We will se now a different approach. There are three important conservation laws: Conservation of momentum Conservation of angular momentum Conservation of energy These laws are embodied in Newton’s laws, but offer a different and sometimes more powerful way to consider motion. The conservation laws actually show why Newton’s laws are true, by reflecting deeper aspects of nature – conservation of certain quantities. Example: According to Newton’s second law can we actually change momentum? (hint: how do you change momentum of an object) You might wish to give the example of how momentum conservation derives directly from Newton’s laws… © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley What keeps a planet rotating and orbiting the Sun? Conservation of Angular Momentum As long as Earth doesn’t transfer angular momentum to other objects, its rotation and orbit cannot change. Question: we have seen this law during the last class already? Do you remember who discovered it? Remember, then it was only an empirical law, here it is explained based on laws of nature. You may wish to go over this figure in some detail to be sure the idea is clear. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Angular momentum conservation also explains why objects rotate faster as they shrink in radius: Discuss astronomical analogs: disks of galaxies, disks in which planets form, accretion disks… Also explains why everything in the universe is rotating… © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Conservation of Energy Where do objects get their energy? What is energy? Energy makes matter move. Basic Types of Energy Kinetic (motion): all objects which move have this energy. E=mv2/2. Radiative (light): all radiation carries this type of energy, that is why sun-light warms up our planet. Stored or potential: energy which can be converted to other two types, I.e., rock on a hill has gravitational potential energy, because if it slips it will start to fall, converting its energy to kinetic energy of his new motion. Begin by defining energy… © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Energy is conserved, but it can: Transfer from one object to another Change in form Energy can change type but cannot be destroyed. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Scientific unit of energy is Joule, (1 calorie = 4,184 J). There is the same unit for all three forms of energy. Can use these comparisons to introduce the unit of joules. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Subcategories of energy important in Astronomy: Subcategory: thermal energy - the collective kinetic energy of many particles It is easier to talk about thermal energy than kinetic energy of each of the billions of molecules in a glass of water, for example. Thermal energy is related to temperature but it is NOT the same. Temperature is parameter which measures the average kinetic energy of the many particles in a substance. Students sometimes get confused when we’ve said there are 3 basic types of energy (kinetic, potential, radiative) and then start talking about subtypes, so be sure they understand that we are now dealing with subcategories. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Temperature Scales Kelvin (K) is the unit used in scientific computations. Use this figure to review temperature scales. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Thermal energy is a measure of the total kinetic energy of all the particles in a substance. It therefore depends both on temperature AND density Example: We’ve found this example of the oven and boiling water to be effective in explaining the difference between temperature and thermal energy. You may then wish to discuss other examples, such as the Think About It on p. 88. You might also want to note that the temperature in low-Earth orbit is actually quite high, but astronauts get cold because of the low density. © 2005 Pearson Education Inc., publishing as Addison-Wesley
Subcategory: gravitational potential energy On Earth, depends on: object’s mass (m) strength of gravity (g) distance object could potentially fall (height, h) We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy. Question: where does the ball travel faster, when it is higher or closer to the ground? © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Question: In space, does a gas cloud has more gravitational energy when it is spread over a large area or when it closer to the center of gravity? (hint: farther the particles are from the center, is their gravitational potential energy bigger or smaller?) © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley A contracting cloud converts gravitational potential energy to thermal energy. We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy. © 2005 Pearson Education Inc., publishing as Addison-Wesley
Subcategory: energy contained in mass itself – “mass-energy” Mass itself is a form of potential energy E = mc2 A small amount of mass can release a great deal of energy Concentrated energy can spontaneously turn into particles (for example, in particle accelerators or in the early Universe) 1 mega tone H bomb converts only about 100 grams (3 ounces) of mass into energy. Enough to destroy a major city. © 2005 Pearson Education Inc., publishing as Addison-Wesley
Conservation of Energy Energy can be neither created nor destroyed. It can change form or be exchanged between objects. The total energy content of the Universe was determined in the Big Bang and remains the same today. You might wish to go through the example tracing the energy of a baseball back through time, as described on p. 90 of the text. Question: where do objects get their energy? © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Question: why do we say that the history of Universe is based on the interplay between mater and energy? © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley What have we learned? What keeps a planet rotating and orbiting the Sun? The law of conservation of angular momentum Where do objects get their energy? Conservation of energy: energy cannot be created or destroyed; it can only be transformed from one type to another. Energy comes in 3 basic types: kinetic, potential, radiative. Some subtypes important in astronomy: thermal energy, grav. Potential energy, mass-energy (E = mc2). © 2005 Pearson Education Inc., publishing as Addison-Wesley
4.4 The Force of Gravity the most important force in astronomy Our goals for learning: What determines the strength of gravity? How does Newton’s law of gravity extend Kepler’s laws? How do gravity and energy together allow us to understand orbits? How does gravity cause tides? © 2005 Pearson Education Inc., publishing as Addison-Wesley
What determines the strength of gravity? The Universal Law of Gravitation (Newton) Every mass attracts every other mass. Attraction is directly proportional to the product of their masses. Attraction is inversely proportional to the square of the distance between their centers.. G- gravitational constant. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Question: how does the gravitational force between two objects change if the distance between them triples? If the mass of one object doubles? © 2005 Pearson Education Inc., publishing as Addison-Wesley
How does Newton’s law of gravity extend Kepler’s laws? Newton published Principia in 1687. By that time Kepler’s laws have been well tested (for 70 years) and there was no doubt they were correct. But they were empirical laws (based on observation and it was not clear why they are true. Newton used mathematical expression of his law of gravity and derived all three of Kepler laws, showing they are consequence of more fundamental laws. In doing so, he also found that Kepler’s laws are only part of a story of how objects move under the influence of gravity. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Newton found that: Kepler’s first two laws apply to all orbiting objects, not just planets (for example, satellites around Earth, two stars in a binary system…) Ellipses are not the only stable orbital paths. Orbits can be: bound (ellipses) Unbound (objects close only once) Parabola hyperbola © 2005 Pearson Education Inc., publishing as Addison-Wesley
Newton also generalized Kepler’s Third Law: Question: What is Kepler’s third law stating? Emphasize that this law allows us to measure the masses of distant objects — an incredibly powerful tool. © 2005 Pearson Education Inc., publishing as Addison-Wesley
Newton’s version of Kepler’s Third Law p = orbital period a=average orbital distance (between centers) (M1 + M2) = sum of object masses So, if you measure the period and average distance of a smaller object orbiting the larger one, you can calculate the mass of larger object! Optional: use this slide if you wish to introduce the equation for Newton’s version of Kepler’s third law. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Examples: Calculate mass of Sun from Earth’s orbital period (1 year) and average distance (1 AU). Calculate mass of Earth from orbital period and distance of a satellite. Calculate mass of Jupiter from orbital period and distance of one of its moons. Question: whether the space shuttle and the astronaut outside of it have the same orbital period around the Earth? Why, what determines their periods? Does the astronaut needs to be attached to the shuttle? © 2005 Pearson Education Inc., publishing as Addison-Wesley
How can orbital paths change? Question: Can orbits change spontaneously? © 2005 Pearson Education Inc., publishing as Addison-Wesley
How can orbital paths change? Question: Can orbits change spontaneously? Let’s define an energy of an object in its orbit: total orbital energy = kinetic energy + gravitational potential energy Total orbital energy stays constant along an orbit. Question: Does kinetic energy change along orbit? How about potential energy? The concept of orbital energy is important to understanding orbits. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley So what can make an object gain or lose orbital energy? A gravitational encounter with a third object: for example, if a comet passes by Jupiter (large planet), comet’s orbit around the Sun can change dramatically. Question: where did the energy lost by a comet go (when it went from unbound to the bound orbit)? Also used by spacecraft to boost orbits. Each of the two Voyagers that visited the outer planets in 1980s was deliberately sent close by Jupiter on a path that caused it to gain orbital energy at Jupiter’s expense. Examples worth mentioning: satellites in low-Earth orbit crashing to Earth due to energy loss to friction with atmosphere captured moons like Phobos/Deimos or many moons of Jupiter: not easy to capture, and must have happened when an extended atmosphere or gas cloud allowed enough friction for the asteroid to lose significant energy. Gravitational encounters have affected comets like Halley’s; also used by spacecraft to boost orbits… © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Friction or atmospheric drag: Examples: satellites in low-Earth orbit can crash to Earth due to energy loss to friction with atmosphere captured moons like Phobos/Deimos or many moons of Jupiter: they are big and not easy to capture. Capture by Jupiter must have happened when an extended atmosphere or gas cloud allowed enough friction for the asteroid (now moon) to lose significant amount of its energy. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley And other way around: If an object gains enough orbital energy, it may escape (change from a bound to unbound orbit) Adding some energy to a spacecraft can make a spacecraft move to a higher orbit, or ultimately escape to an unbound orbit. Example: Hubble telescope. Can use this to discuss how adding velocity can make a spacecraft move to a higher orbit or ultimately to escape on an unbound orbit. escape velocity from Earth ≈ 11 km/s from sea level (about 40,000 km/hr). © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Use this tool from the Orbits and Kepler’s laws tutorial to discuss escape velocity. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Escape and orbital velocities don’t depend on the mass of the cannonball © 2005 Pearson Education Inc., publishing as Addison-Wesley
How does gravity cause tides? The stretching (tidal) force arises from the difference between the force of gravity on the side of the Earth closer and farther from the Moon. Use this figure to explain the origin of the tidal bulges. Gravitational pull decreases with (distance)2, the Moon’s pull on Earth is strongest on the side facing the Moon, weakest on the opposite side. The Earth gets stretched along the Earth-Moon line. The oceans rise relative to land at these points. Questions: How many tides there are during a day? © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley The Sun also affects the tides. Tides vary with the phase of the Moon: © 2005 Pearson Education Inc., publishing as Addison-Wesley
Special Topic: Why does the Moon always show the same face to Earth? Optional special topic. You might wish to perform the demonstration shown in the figure… Moon rotates in the same amount of time that it orbits… But why? © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Tidal friction… Optional special topic. You might wish to perform the demonstration shown in the figure… Tidal friction gradually slows Earth rotation (and makes Moon get farther from Earth). Question: Explain this effect using a conservation law? (hint: which quantity describes rotation?) Moon once orbited faster; tidal friction caused it to “lock” in synchronous rotation. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley What have we learned? What determines the strength of gravity? Directly proportional to the product of the masses (M x m) Inversely proportional to the square of the separation d How does Newton’s law of gravity allow us to extend Kepler’s laws? Applies to other objects, not just planets. Includes unbound orbit shapes: parabola, hyperbola We can now measure the mass of other systems. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley What have we learned? How do gravity and energy together allow us to understand orbits? Gravity determines orbits Orbiting object cannot change orbit without energy transfer Enough energy -> escape velocity -> object leaves. How does gravity cause tides? Gravity stretches Earth along Earth-Moon line because the near side is pulled harder than the far side. © 2005 Pearson Education Inc., publishing as Addison-Wesley
© 2005 Pearson Education Inc., publishing as Addison-Wesley Review: To describe motion we use: speed, velocity, acceleration, momentum. Mass is measure of amount of matter in a body. It is different from weight! Newton’s laws are: If there is no net force the objects move with constant velocity F=ma Whenever there is a net force acting on an object, that object is acting with an equal force in the opposite direction on surrounding. Conservation laws: angular momentum (mvr) and energy are conserved! Gravitational law: F=GmM/d2 © 2005 Pearson Education Inc., publishing as Addison-Wesley