Chapter 4 Making Sense of the Universe: 4.1 Describing Motion Understanding Motion, Energy, and Gravity • Our goals for learning: • How do we describe motion? • How is mass different from weight? How do we describe motion? The Acceleration of Gravity Precise definitions to describe motion: • All falling objects • Speed : Rate at which object moves accelerate at the speed = distance units of m ⎛ ⎞ ⎜ s ⎟ same rate (not time ⎝ ⎠ counting friction of example: speed of 10 m/s air resistance). • On Earth, g ≈ 10 • Velocity : Speed and direction example: 10 m/s, due east m/s 2 : speed increases 10 m/s • Acceleration : Any change in velocity with each second of units of speed/time (m/s 2 ) falling. Momentum and Force The Acceleration of Gravity ( g ) • Momentum = mass × velocity • Galileo showed that g is the same for all • A net force changes momentum, which falling objects, generally means an acceleration (change in regardless of their velocity) mass. • Rotational momentum of a spinning or orbiting object is known as angular momentum Apollo 15 demonstration 1
Why are astronauts weightless How is mass different from weight? in space? • Mass – the amount of matter in an object • Weight – the force that acts upon an object • There is gravity in space • Weightlessness is due to a constant state of free-fall You are weightless in free-fall! What have we learned? What have we learned? • How do we describe motion? • How is mass different from weight? – Speed = distance / time – Mass = quantity of matter – Speed & direction => velocity – Weight = force acting on mass – Change in velocity => acceleration – Objects are weightless in free-fall – Momentum = mass x velocity – Force causes change in momentum, producing acceleration How did Newton change our 4.2 Newton’s Laws of Motion view of the universe? • Realized the same physical laws Our goals for learning: that operate on Earth also operate in the heavens • How did Newton change our view of the ⇒ one universe universe? • Discovered laws of motion and gravity • What are Newton’s three laws of motion? • Much more: Experiments with light; first reflecting telescope, calculus… Sir Isaac Newton (1642-1727) 2
What are Newton’s three laws of motion? Newton’s second law of motion Force = mass × acceleration Newton’s first law of motion: An object moves at constant velocity unless a net force acts to change its speed or direction. What have we learned? Newton’s third law of motion: • How did Newton change our view of the universe? For every force, there is always an equal and opposite – He discovered laws of motion & gravitation reaction force. – He realized these same laws of physics were identical in the universe and on Earth • What are Newton’s Three Laws of Motion? – 1. Object moves at constant velocity if no net force is acting. – 2. Force = mass × acceleration – 3. For every force there is an equal and opposite reaction force Conservation of Momentum 4.3 Conservation Laws in Astronomy: Our goals for learning: • The total momentum • Why do objects move at constant velocity if of interacting objects no force acts on them? cannot change unless an external force is • What keeps a planet rotating and orbiting acting on them the Sun? • Interacting objects • Where do objects get their energy? exchange momentum through equal and opposite forces 3
Conservation of Angular What keeps a planet rotating and Momentum orbiting the Sun? angular momentum = mass x velocity x radius • The angular momentum of an object cannot change unless an external twisting force (torque) is acting on it • Earth experiences no twisting force as it orbits the Sun, so its rotation and orbit will continue indefinitely Angular momentum conservation also explains why objects rotate faster as they shrink in radius: Where do objects get their energy? • Energy makes matter move. • Energy is conserved, but it can: – Transfer from one object to another – Change in form Thermal Energy: Basic Types of Energy the collective kinetic energy of many particles (for example, in a rock, in air, in water) • Kinetic (motion) Thermal energy is related to temperature but it is NOT • Radiative (light) the same. • Stored or potential Temperature is the average kinetic energy of the many particles in a substance. Energy can change type but cannot be destroyed. 4
Temperature Scales 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: Gravitational Potential Energy Gravitational Potential Energy • On Earth, depends on: • In space, an object or gas cloud has more gravitational energy when it is spread out than when it contracts. – object’s mass (m) ⇒ A contracting cloud converts gravitational potential – strength of gravity ( g ) energy to thermal energy. – distance object could potentially fall Mass-Energy Conservation of Energy • Mass itself is a form of potential energy • Energy can be neither created nor destroyed. E = mc 2 2 E = mc • It can change form or be exchanged between objects. • A small amount of mass can release a great deal of energy • The total energy content of the Universe was • Concentrated energy can determined in the Big Bang and remains the spontaneously turn into particles same today. (for example, in particle accelerators) 5
What have we learned? 4.4 The Universal Law of Gravitation • Why do objects move at constant velocity if no force acts on them? – Conservation of momentum Our goals for learning: • What keeps a planet rotating and orbiting the Sun? • What determines the strength of gravity? – Conservation of angular momentum • Where do objects get their energy? • How does Newton’s law of gravity extend – Conservation of energy: energy cannot be created or Kepler’s laws? destroyed but only transformed from one type to another. – Energy comes in three basic types: kinetic, potential, radiative. What determines the strength of gravity? How does Newton’s law of gravity extend Kepler’s laws? The Universal Law of Gravitation: 1. Every mass attracts every other mass. • Kepler’s first two laws apply to all orbiting 2. Attraction is directly proportional to the product of objects, not just planets their masses. • Ellipses are not the only 3. Attraction is inversely proportional to the square of orbital paths. Orbits can the distance between their centers. be: – Bound (ellipses) – Unbound • Parabola • Hyperbola Center of Mass Newton and Kepler’s Third Law His laws of gravity and motion showed that the • Because of momentum relationship between the orbital period and conservation, orbiting average orbital distance of a system tells us the objects orbit around total mass of the system. their center of mass Examples: • Earth’s orbital period (1 year) and average distance (1 AU) tell us the Sun’s mass. • Orbital period and distance of a satellite from Earth tell us Earth’s mass. • Orbital period and distance of a moon of Jupiter tell us Jupiter’s mass. 6
Newton’s Version of Kepler’s Third Law What have we learned? • What determines the strength of gravity? M 1 + M 2 = 4 π 2 a 3 4 π 2 p 2 = G ( M 1 + M 2 ) a 3 OR – Directly proportional to the product of the p 2 G masses (M x m) – Inversely proportional to the square of the separation • How does Newton’s law of gravity allow us to p = orbital period extend Kepler’s laws? a= average orbital distance (between centers) – Applies to other objects, not just planets. (M 1 + M 2 ) = sum of object masses – Includes unbound orbit shapes: parabola, hyperbola – Can be used to measure mass of orbiting systems. How do gravity and energy together 4.5 Orbits, Tides, and the allow us to understand orbits? Acceleration of Gravity More gravitational energy; • Total orbital energy Less kinetic energy (gravitational + Our goals for learning: kinetic) stays constant if there is • How do gravity and energy together allow no external force us to understand orbits? • Orbits cannot change • How does gravity cause tides? spontaneously. Less gravitational energy; • Why do all objects fall at the same rate? More kinetic energy Total orbital energy stays constant Changing an Orbit Escape Velocity ⇒ So what can make an • If an object gains enough orbital energy, it may object gain or lose orbital escape (change from a energy? bound to unbound orbit) • Friction or atmospheric • Escape velocity from drag Earth ≈ 11 km/s from sea • A gravitational level (about 40,000 km/hr) encounter. 7
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