| Title | Author | Created | Published | Tags | | -------------------- | ---------------------------- | ---------------- | ---------------- | ---------------------- | | W3 - Circular Motion | <ul><li>Jon Marien</li></ul> | January 21, 2025 | January 21, 2025 | [[#classes\|#classes]] | # Exoplanets – Aliens? # Circular Motion, the Planets, and Gravity  Does the circular motion of the moon around the Earth ...  ... have anything in common with circular motion on Earth? # A ball is whirled on the end of a string with constant speed when the string breaks. Which path will the ball take? Path 1 Path 2 Path 3 Path 4  Path 3, in the direction of the tangent to point A. Neglecting gravity, the body would move in the direction it was moving when the force disappeared, in accordance with the first law. <span style="color:#efff5d">If the string breaks, the ball flies off in a straight-line path in the direction it was traveling at the instant the string broke.</span> If the string is no longer applying a force to the ball, Newton’s First Law tells us that the ball will continue to move in a straight line. Circular motion is called centripetal motion, with the string providing a centripetal force.  # Centripetal Acceleration * *Centripetal acceleration * is the rate of change in velocity of an object that is associated with the change in *direction* of the velocity. * Centripetal * acceleration is * always * perpendicular to * the velocity. * Centripetal * acceleration always * points toward the * center of the curve.  * *Centripetal acceleration * is the rate of change in velocity of an object that is associated with the change in *direction* of the velocity. * Centripetal acceleration is always perpendicular to the velocity. * Centripetal acceleration always points toward the center of the curve. * Centripetal acceleration changes direction not speed. * *The centripetal force* refers to any force *or combination of forces* that produces a *centripetal acceleration* . # Centripetal Forces * The *centripetal force* is the total force that produces a centripetal acceleration. * The centripetal force may be due to one or more individual forces, such as a normal force and/or a force due to friction. * The *Static force of friction* is the frictional force acting when there *is no* motion along the surfaces. * *No skidding or sliding* * The *Kinetic force of friction* is the frictional force acting when there *is* motion along the surfaces. # Flat Earth Theory # Foucault’s Pendulum # The Scientific Revolution # Planetary Motion * The ancient Greeks believed the sun, moon, stars and planets all revolved around the Earth. * This is called a *geocentric view* (Earth-centered) of the universe. * This view matched their observations of the sky, with the exception of the puzzling motion of the wandering planets. <span style="color:#efff5d">To explain the apparent retrograde motion of the planets, Ptolemy invented the idea of epicycles.</span>  *Retrograde motion* occurs in a planet’s orbit when the planet appears to move against the background of stars *Epicycles* are imaginary circles the planets supposedly travel while also traveling along their main (larger) orbits around the Earth. This would explain the occasional “backward motion” the planets seemed to follow. # Retrograde Motion # Planetary Motion With the help of Copernicus, Brahe, and Kepler we now know the best explanation of retrograde motion is simply planetary alignment against an apparently motionless backdrop of stars as planets orbit the Sun.  <span style="color:#efff5d">Copernicus developed a model of the universe in which the planets (including Earth!) orbit the sun.</span> * This is called a *heliocentric view* (sun-centered) of the universe. * Careful astronomical observations were needed to determine which view of the universe was more accurate. * <span style="color:#efff5d">Tycho Brahe</span> spent several years painstakingly collecting data on the precise positions of the planets * This was before the invention of the telescope!  <span style="color:#efff5d">Tycho Brahe’s large quadrant permitted accurate measurement of the positions of the planets and other heavenly bodies.</span> # Tycho Brahe # Kepler’s First Law of Planetary Motion Tycho’s assistant, <span style="color:#efff5d">Kepler</span> , analyzed the precise observation data. Kepler was able to show that the orbits of the planets around the sun are *ellipses* , with the sun at one focus. This is Kepler’s first law of planetary motion.  # Kepler’s Second Law of Planetary Motion Because planets move faster when nearer to the sun, the radius line for each planet sweeps out equal areas in equal times. The two blue sections each cover the same span of time and have equal area.  # Kepler’s Third Law of Planetary Motion The *period (T)* of an orbit is the time it takes for one complete cycle around the sun. The cube of the average radius (r) about the sun is proportional to the square of the period of the orbit.  # Newton’s Law of Universal Gravitation <span style="color:#efff5d">Newton</span> recognized the similarity between the motion of a projectile on Earth and the orbit of the moon. He imagined if a projectile was fired with enough velocity, it would fall towards Earth but never reach the surface. This projectile would be in orbit.  <span style="color:#efff5d">Newton</span> was able to explain Kepler’s 1st and 3rd laws by assuming the gravitational force between planets and the sun falls off as the inverse square of the distance. *Newton’s law of universal gravitation* says the gravitational force between two objects is proportional to the mass of each object, and inversely proportional to the square of the distance between the two objects. *G* is the *Universal gravitational constant G.* # Three equal masses are located as shown. What is the direction of the total force acting on m2?  To the left. To the right. The forces cancel such that the total force is zero. It is impossible to determine from the figure. There will be a net force acting on m2 toward m1. The third mass exerts a force of attraction to the right, but since it is farther away that force is less than the force exerted by m1 to the left. # The Moon and Other Satellites * Phases of the moon* result from the changes in the positions of the moon, Earth, and sun.