Astronomy 103 Chapter 3 Notes
Astronomy 103 Chapter 3 Notes 10022
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This 4 page Class Notes was uploaded by Rebecca Barnett on Sunday September 11, 2016. The Class Notes belongs to 10022 at Old Dominion University taught by Stephen Bueltmann in Fall 2016. Since its upload, it has received 4 views. For similar materials see Introductory Astronomy of the Solar System in PHYSICS (PHY) at Old Dominion University.
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Date Created: 09/11/16
Astronomy 103 Chapter 3: Motion of Astronomical Bodies Motions in the sky o From our perspective on earth, it appears that everything in the sky moves and orbits around us o Early astronomers and philosophers therefore crafted mostly geocentric models of the universe to reflect this o These models became greatly fixed in the minds of astronomers for millennia o Politics and science can clash when cultural minds refuse to be changed o Another point unwilling to be conceded was the idea of “uniform circular motion” o Objects moved imperfect circles at uniform speeds o As astronomers viewed the motions of the planets, the models did not match the observations Retrograde motion o Complicated models were needed to explain phenomena such as retrograde motion o Ptolemy developed a system with epicycles in 150 CE that remained accepted for about 1,500 years Heliocentric Model o Copernicus was the first to create a mathematical model with the sun at the center and circular planet orbits o Could estimate relative distances of the planets from the sun and each other o Copernicus was able to use right-triangle trigonometry and observations of planets at opposition or conjunction to very accurately find their distances relative to the earth-sun distance o He was not able to discern our distance from the sun this way, so the distances are expressed in units of our distance (1AU) o Planet o Copernicus o Actual o Mercury o 0.38 o 0.39 o Venus o 0.72 o 0.72 o Earth o 1.00 o 1.00 o Mars o 1.52 o 1.52 o Jupiter o 5.22 o 5.20 o Saturn o 9.17 o 9.58 o Earth completes one orbit and catches up to the superior planet o Inferior planet completes one orbit and catches up to earth Sidereal and synodic periods o The synodic (S) and sidereal (P) periods the planets can be related to earth’s (E ) sidereal period (365.24 days) o Inferior planets: 1/P = 1/E + 1/S o Superior planets: 1/P = 1/E – 1/S o Synodic periods are measured from earth o Example for superior planets: S x 360 degrees/P = (S-E) x 360 degrees/E 1/P = 1/E – 1/S Heliocentric model o Copernicus’s model could explain the behavior of objects in the solar system o The ordering of the planets could explain how they sometimes interrupt their prograde motion with retrograde motion o Tycho Brahe spent decades collecting astronomical data after building his own observatory o Created his own geocentric model with other planets orbiting the sun, but with the sun orbiting earth o Using Tycho’s data, Johannes Kepler came up with empirical rules to describe planetary orbits in a heliocentric system o Empirical science describes how something works, not why Kepler’s first law o Planet orbits are ellipses with 2 foci each o The sun is at once focus of a planets elliptical orbit o An ellipse has a size described by the semi major axis o The longest length is twice the length of the semi major axis o Each orbit has a shape and size o The eccentricity describes how elongated the ellipse is and how far the foci are separated Kepler’s second law o Often called law of equal areas o The line between the sun and the planet “sweeps” out equal areas in equal times o Consequences: A planet will go fastest when closest to the sun It will also go slowest when furthest from the sun Applies to each planet individually Kepler’s third law o Relates to orbital period to the size of the orbit o Let A be the length of the semi major axis in AU o Let P be the period in years o (P years)^2 = (A AU)^3 o The relationship does not change if standard units are used o The equation is just more complicated o (P seconds)^2 = 3 x 10 ^-19 (A meters)^3 o Consequences: Distant planets take longer to orbit the sun Distant planets travel at slower speeds Galileo Galilei o The first scientist to observe the sky with a telescope o Found four moons in orbit around Jupiter o Saw that Venus had phases In a geocentric model, Venus’s phase changes are hard to explain Newton’s laws o Using observations and investigations from Galileo, Issac Newton discovered laws that apply to all objects o Basis of classical mechanics o Physical laws not empirical science Newton’s first law of motion o Galileo’s law of inertia o A moving object will stay in constant motion and an object at rest will stay at rest unless acted on by an unbalanced force o “constant” motion means at a constant speed and in a constant direction Newton’s second law of motion o Unbalanced forces cause changes in motion F = m x a o Examples: Speeding up with the gas pedal Slowing down with the brake o Velocity: the speed and direction of an object’s motion o Speed: driving 60 mph o Velocity: driving 60 mph east o A change in velocity is called acceleration o Acceleration measures how quickly a change in motion takes place o Turning at a constant speed means that acceleration is perpendicular to the direction of motion o Greater forces mean greater accelerations Newton’s third law of motion o For every force, there is an equal and opposite force o The two forces have the same size o The two have opposite directions Math: proportionality (again) o Proportionality and inverse proportionality are ways to understand how one quantity behaves relative to another quantity o It lets you get the gist of how the relationship works between those two quantities o Sometimes you need to know more than just the gist o You need to know the constant of proportionality which exactly relates the quantities o Velocity: v = g x t o Distance: d = ½ x g x t^2 Chapter 3 vocab: o Prograde motion: rotational or orbital motion of a moon that is in the same direction as the planet it orbits. The counterclockwise orbital motion of solar system objects as seen from above earth’s orbital plane. o Retrograde motion: rotation or orbital motion of a moon that is in the opposite direction as the planet it orbits. The clockwise orbital motion as seen from above earth’s orbital plane. Apparent retrograde motion is a motion of the planets with respect to fixed stars in which the planets appear to move westward for a period of time before resuming their normal eastward motion. o Superior planets: a solar system planet that orbits the sun at a greater distance than earth’s orbit. o Inferior planets: a solar system planet that orbits the sun at a closer distance than earth’s orbit. o Empirical science: scientific investigation that is based primarily on observations and experimental data. It is descriptive rather than based on theoretical inference. o Ellipse: a conic section produced by the intersection of a plane with a cone when the plane is passed through the cone at an angle to the axis other than 0 degrees or 90 degrees. The shape that results when you attach the two ends of a piece of string to a piece of paper, stretch the string tight with the tip of a pencil and then draw around those two points while keeping the string taut o Focus: one of two points that define an ellipse. A point in the focal plane of a telescope. o Eccentricity: the ratio of the distance between the two foci of an ellipse to the length of its major axis which measures how noncircular the ellipse is. o Semi major axis: half of the longer axis of an ellipse. o Inertia: the tendency for objects to retain their state of motion o Inertial from of reference: a frame of reference that is moving in a straight line at constant speed (that is not accelerating). In general relativity, a frame of reference that is falling freely in a gravitational field