Kepler and the Laws of Motion of the Planets.docx.pdf

Kepler and the Laws of Motion of the Planets Renee Karikari Intro to Astronomy October 4, 2023 Kepler and the Laws of Motion of the Planets Introduction

Johannes Kepler was a German astronomer who made significant contributions to our understanding of the motion of planets in our solar system during the late 16th and early 17th centuries. Kepler's work laid the foundation for our modern understanding of planetary motion and was instrumental in the development of Isaac Newton's laws of motion and universal gravitation. Kepler's Laws of Planetary Motion: Kepler's First Law (Law of Ellipses): Kepler's first law states that the orbits of planets around the Sun are elliptical (oval) in shape, with the Sun at one of the two foci of the ellipse. This law replaced the previous belief that planetary orbits were perfectly circular. Kepler's Second Law (Law of Equal Areas): Kepler's second law, also known as the Law of Equal Areas, states that a line segment joining a planet and the Sun sweeps out equal areas in equal intervals of time. This means that a planet moves faster in its orbit when it is closer to the Sun (perihelion) and slower when it is farther from the Sun (aphelion). Kepler's Third Law (Law of Harmonies): Kepler's third law relates the orbital periods (the time it takes a planet to complete one orbit around the Sun) and the average distances from the Sun for different planets. Mathematically, it can be expressed as: T^2 = k * R^3, where T is the orbital period, R is the average distance from the Sun (semi-major axis), and k is a constant that depends on the mas

Kepler's laws provided a precise description of how planets move in their orbits, but they did not explain why planets followed these laws. It was Isaac Newton who later developed the laws of motion and universal gravitation, which provided the underlying physics to explain Kepler's laws. Isaac Newton's Contributions: Newton's laws of motion, particularly his laws of inertia and the relationship between force and acceleration, explained why objects, including planets, move the way they do. Newton's law of universal gravitation provided a gravitational force equation that explained the attractive force between all objects with mass, including planets and the Sun. Using these principles, Newton showed that Kepler's laws could be derived from his own laws of motion and gravitation, thus unifying celestial and terrestrial mechanics. Hypothesis We can derive Kepler's third law by starting with Newton's laws of motion and the universal law of gravitation. We can therefore demonstrate that the force of gravity is the cause of Kepler's laws. Consider a circular orbit of a small mass m around a large mass M. Gravity supplies the centripetal force to mass m Objective The first is to observe the period of revolution of the planets. The second is to measure the distance to each planet from the point of view of the Sun. The third and final objective is to use Kepler’s 3 rd law, and prove or disprove the existence of a constant resultant. Procedure

TABLE 1 Planet Start Date(MM/DD/YR) End Date(MM/DD/YR) Orbital Period , p(days) Orbital Period , P (years) p/365.25 Mercury 11/23/2009 11/23/2012 (60,190 Earth days 165 Earth years Venus 11/23/2008 11/23/2012 2087 0.62 year, Earth 11/23/2009 11/23/2012 365.25636 365.25636 solar days Mars 11/23/2010 11/23/2012 2000 3.53 Jupiter 11/23/2011 11/23/2014 12000 12 Earth years Saturn 11/23/2015 11/23/2017 40,000 29.4475 yr Uranus 11/23/2014 11/23/2016 840000 84 years. Neptune 11/11/2016 11/23/2016 45746234 4 165 Earth years

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help