Astronomy Ch.4 PDF

Astronomy Chapter 4: Making Sense of the Universe: Understanding Motion, Energy, and Gravity 4.1 Describing Motion: Examples from Daily Life Speed and Velocity Speed - How fast or slow something moves SI standard is meters per second (m/s) Average Speed...

Astronomy Chapter 4: Making Sense of the Universe: Understanding Motion, Energy, and Gravity 4.1 Describing Motion: Examples from Daily Life Speed and Velocity Speed - How fast or slow something moves SI standard is meters per second (m/s) Average Speed = Total Distance / Total Time Rearrange this equation to solve for distance and time (record on notes) Calculating Distance, Time, and Speed Use the equation that solves for the quantity you want Add your known quantities to the formula and calculate Universal Speed Limit Nothing can travel faster than light Speed of light in a vacuum (c) is about 300 million m/s (300,000,000 m/s) Average Speed Total Distance Traveled / Total Time of Journey If I travel 100 km in 2 hours, my average speed is 50 km/hr. Instantaneous Speed Speed at any given instant in time Speed on your speedometer Velocity Vector - has size and direction Denoted with an arrow. Length of the arrow tells its size, Arrow points in the direction of the vector Velocity is like speed but also gives a direction Graphs of Motion Time on x-axis Position / Distance on y-axis Slope of the graph gives the speed. Steeper line gives a faster speed. Acceleration Another vector. Change in velocity over time Magnitude can change (speed up or slow down) Or can change direction Calculating Acceleration from Velocity and Time A = acceleration ΔV = change in velocity or speed ΔT = change in time Solve this equation for Velocity and time Velocity vs. Time Graphs Slope of Velocity vs. Time graph is acceleration Area under the graph gives the distance traveled Area of Triangle = ½ Base * height Area of a Rectangle = Base * Height Force Force - a push or a pull Measured in Newtons (1 N = 1 kg m /s2) English Imperial Units (Pound - lb) Force Causes Motion The greater the force, the greater the change in motion A minimum force is required to overcome other forces like friction. Force is a Vector Has size and direction Contact and Field Forces Contact force - two objects actually touch and interact Field Force - objects interact at a distance by a force field (gravity, electricity, magnetism) Freefall Acceleration You can calculate the Acceleration due to gravity from a falling object by the equation A = acceleration due to gravity, d = distance dropped, t = time of fall. A = 2 d / t2 Gravity At the surface of the Earth, the pull of gravity on a Mass, m is given by Fgravity = m g = weight Where g = 9.8 m/s2 ‘g’ depends on the size (R) and mass (M) of the planet Each planet has a unique ‘g’ value Gravity and Weight Mass is a measure of how much matter an object contains Weight is the pull of a planet’s gravity on that mass given by (F = mg) If you go to another planet, the value for g will be different and thus you will have a different weight, but you mass will be the same. Since g also depends on radius, the further from Earth’s surface, the lower your weight. Apparent Weight In freefall, your weight is mass x acceleration from gravity Weight = mg If your are accelerating, you will feel a change in your weight depending on the direction of your acceleration. What objects can give you a vertical acceleration? Terminology Force - a push or pull Momentum - (mass times velocity) is constant unless acted upon by a force Angular momentum - Spinning motion, stays constant. Speed depends on how mass is distributed. Centripetal Force Center pointing Force Keeps object on a string in a circular path 4.2 Newton’s Laws of Motion Isaac Newton English, (1643 - 1727) Born on Christmas Day same year Galileo died. 1661 attends Trinity College in Cambridge 1665 begins work on calculus (Developed simultaneously by Leibniz) Prisms 1666, Showed prisms bend different colored light by different amounts. White light is made of many colors. Chromatic Aberration With a lens, each color of light will focus in a slightly different place giving a smeared image. 1668, Builds Reflecting Telescope (Newtonian) Uses curved mirror instead of a lens, no chromatic aberration Newton’s Laws of Motion Developed formal system for the motion of objects in space (Kinematics) 1. An object at rest stays at rest, an object in motion stays in motion unless acted upon by an unbalanced force. 2. The acceleration of an object is directly proportional to the net force applied to the object. 3. For every action, there is an equal and opposite reaction. Newton’s Laws of Motion Developed formal system for the motion of objects in space (Kinematics) 1. An object at rest stays at rest, an object in motion stays in motion unless acted upon by an unbalanced  force. 2. The acceleration of an object is directly proportional to the net force applied to the object. 3. For every action, there is an equal and opposite reaction. Newton’s Cannon What if a giant cannon could shoot a cannon ball fast enough, then it could orbit the Earth. What makes the cannon ball fall to the Earth? 4.3 Conservation Laws in Astronomy Conservation of Momentum Momentum is conserved if no net force acts upon an object In a collision, the momentum before the collision is equal to the momentum afterward Conservation of Angular Momentum If an object is spinning, then it will tend to stay spinning unless a net torque (twisting force) is applied Angular Momentum (L) depends upon the mass the is spinning, and how that mass is arranged. Bringing the mass closer to the center of rotation will cause a decrease in inertia, the system will respond by an increase in the rate of spin to maintain a constant momentum. Conservation of Energy Objects gain or lose energy by interacting with others. Energy gets converted from one form to another Kinetic Energy - energy of motion Potential energy - energy due to position (gravity or electromagnetic) Radiative Energy - light Thermal Energy Net kinetic energy of the particles in a material All particles are in constant motion. As heat is added to the system, the particles vibrate faster. Temperature is a measure of the average kinetic energy of the particles in a material. Matter and Energy Einstein showed that matter is a form of stored energy. We can convert matter into energy E = mc2 E = energy M = mass C = speed of light = 3.0 x 108 m/s 4.4 The Universal Law of Gravitation Postulated the existence of a force that would work over vast distances. 1680, used motion of a comet to prove the centripetal force holding planets in elliptical orbits is proportional to the radius of orbit square F = k / R2 Universal Law of Gravitation Depends on the masses of the two objects and the distance between them. Never goes to zero Weightlessness Weight never goes to zero, except at infinite distance from a Mass. Still feel pull of gravity from Earth in space. Really in a state of freefall and just seem weightless. Revision to Kepler’s Law Should include the mass of each object. P2 = a3 / (Msun + Mplanet) Msun = Mass of the Sun Mplanet = Mass of the Planet Mplanet