AST 1002 Who were Aristotle Eratosthenes Ptolemy Galileo Kepler and Newton and What were their main contributions to science Aristotle A Greek philosopher that laid the groundwork for future generations Asserted that the universe is comprehensible and it is governed by natural laws Eratosthenes Greek mathematician and astronomer who is best known for making an accurate estimate of the circumference of the Earth by measuring the angle of the Sun s rays at two different locations at the same time Ptolemy his theory that each planet is assumed to move in a small circle called an epicycle the center of which moves in a larger circle called a deferent whose center is offset from Earth He assembled his calculations in the Almagest in which the positions and paths of the Sun the Moon and the planets were described with unprecedented accuracy The commonsense explanation of the Earth centered cosmology began to go awry After Newton s time scientists knew that orbital motion required a force to be acting on the body However nothing in Ptolemy s epicycle theory produced such a force Galileo Helped prove the heliocentric cosmology by 1 He observed that Jupiter had moons that revolved around it This meant that not all objects revolved around earth which was supposed to be the center of the universe in the geocentric model to explain gravity among other things 2 He observed that Venus had phases just like the moon This was possible only if Venus was revolving around the sun In the geocentric model we would always see Venus as a mostly crescent phase Kepler Before Kepler s time it was thought that planets and other bodies moved in circles Kepler spent many years trying to find the course of the planets and he found that planets orbital path is ellipse The elliptical path was very close to where the planets actually orbited and he came up with 3 laws that give equations for the observations that Tycho his predecessor made Newton He began with three physical assumptions now called Newton s laws of motion which led to equations that have since been tested and shown to be correct in many everyday situations He also found a formula for the force of gravity or gravitation the attraction between all objects due to their masses Putting the assumptions into mathematical form and combining them with the equation for gravity Newton was able to derive Kepler s three laws and use them to predict the orbits of bodies such as comets and other objects in the solar system Newton also was able to use these same equations to predict the motions of bodies on and near Earth such as the path of a projectile or the speed of a falling object Constellation the celestial equator the ecliptic the celestial poles right ascension and declination Constellation Any of the 88 contiguous regions that cover the entire celestial sphere including all the objects in each region also a configuration of stars often named after an object a person or an animal The sun moves though 13 constellations every year called the zodiacs Celestial Equator A great circle on the celestial sphere 90 from the celestial poles The ecliptic crosses the celestial equator at two points known as equinoxes If we expand Earth s equator onto the celestial sphere we obtain the celestial equator which divides the sky into northern and southern hemispheres We can also project the north and south poles into outer space along Earth s axis of rotation Doing so gives us the north celestial pole and the south celestial pole The ecliptic The annual path of the Sun on the celestial sphere the plane of Earth s orbit around the Sun per day The Sun appears to move along the ecliptic at a rate of slightly less than 1 The ecliptic and the celestial equator are different circles tilted 23 5 with respect to each other on the celestial sphere This occurs because Earth s rotation axis is tilted 23 5 away from a line perpendicular to the ecliptic their intersections are opposites and each are called an equinox Celestial Poles The point on the celestial sphere directly above either of the earth s geographic poles around which the stars and planets appear to rotate during the course of the night The north celestial pole is currently within one degree of the star Polaris Right Ascension The celestial coordinate analogous to longitude on Earth and measured around the celestial equator from the vernal equinox The boundaries of the constellations run along lines of constant right ascension or declination Declination The coordinate on the celestial sphere exactly analogous to latitude on Earth measured north and south of the celestial equator The synchronous motion of the Moon the tides Gravitational interactions between Earth and the Moon produce tides in the oceans of Earth and set the Moon into synchronous rotation The Moon is moving away from Earth and consequently Earth s rotation rate is decreasing The earth and the moon rotate at the same rate once very 27 3 earth days meaning we only see one side of the moon always The gravitational Forces of the moon deform the oceans and is the greatest where facing the moon and the center and the opposite side of the earth that is facing the moon As it rotates the locations of the tides change Neap tides The least change from high to low tide during a day it occurs during the first and third quarter phases of the Moon Spring tide The greatest daily difference between high tide and low tide occurring when the Moon is new or full Kepler s three laws elliptical orbits law of equal areas third law Kepler s First Law The orbit of each planet around the Sun is an ellipse with the Sun at one focus Kepler s Second Law A line joining a planet and the Sun sweeps out equal areas in equal intervals of time Basically the planet sweeps out equal areas in equal time intervals A consequence of Kepler s second law is that each planet s speed decreases as it moves from perihelion closest to the sun to aphelion farthest from the sun and vice versa Kepler s Third Law The Square of a planet s sidereal period around the Sun is directly proportional to the cube of the length of its orbit s semi major axis The Sidereal period is the orbital period of one object around another measured in earth years with respect to the stars P The semi major axis is the average distance from the sun measured in AU a P 2 a 3 This equation says that a planet closer to the Sun has a shorter year than does a planet farther from the Sun Using this equation with Kepler s second law