Universe: Stars And Galaxies
Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 4, Problem 31Q
To determine

Newton’s three laws and tell everyday example of each law.

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Choose one of the Newton's laws and explain it. What is the importance of this law? Give an example in your daily life about this law.
What is Kepler's first law of planetary motion? The period of a planet's orbit is proportional to its distance from the sun. Planets have circular orbits. Planets have elliptical orbits. The eccentricity of a planet's orbit is proportional to its distance from the sun.
Kepler's Third Law and Newton's Law of Universal Gravitation (a) Use Newton's Universal Law of Gravitation and what you know about centripetal acceleration/force to derive Kepler's Third Law for a planet in a circular orbit about the sun: T² = Kr³ K = constant = 4²/GM where T is the orbital period of the planet (the time for one complete orbit), r is the radius of the planet's orbit, M is the mass of the sun, and G is the universal gravitational constant. (b) Determine the metric system units of K and show that they make the units of T² – Kr³ work out correctly. (c) The earth orbits the sun once per year (365 days) and its average orbital radius is 1.50 x 10¹¹ m. Use this information and Kepler's Third Law to estimate the mass of the sun in kilograms. [answer: about 2 x 10³⁰ kg] (d) The radius of the sun is about 7 x 108 m. Use this radius and the mass of the sun estimated in part (c) to estimate the acceleration of an object near the surface of the sun. [answer: about 300 m/s²] F₂ =G…
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