13.1 Newton’s Law of Universal Gravitation 13.2 Gravitation Near Earth’s Surface 13.3 Gravitational Potential Energy and Total Energy 13.4 Satellite Orbits and Energy 13.5 Kepler’s Laws of Planetary Motion 13.6 Tidal Forces 13.7 Einstein’s Theory of Gravity

Learning Objectives By the end of this section, you will be able to: Newton’s law of universal gravitation accurately predicts much of what we see within our solar system. Indeed, only Newton’s laws have been needed to accurately send every…

Learning Objectives By the end of this section, you will be able to: The origin of Earth’s ocean tides has been a subject of continuous investigation for over 2000 years. But the work of Newton is considered to be the…

Learning Objectives By the end of this section, you will be able to: Using the precise data collected by Tycho Brahe, Johannes Kepler carefully analyzed the positions in the sky of all the known planets and the Moon, plotting their…

Learning Objectives By the end of this section, you will be able to: The Moon orbits Earth. In turn, Earth and the other planets orbit the Sun. The space directly above our atmosphere is filled with artificial satellites in orbit.…

Learning Objectives By the end of this section, you will be able to: We studied gravitational potential energy in Potential Energy and Conservation of Energy, where the value of g remained constant. We now develop an expression that works over distances such that g is…

Learning Objectives By the end of this section, you will be able to: In this section, we observe how Newton’s law of gravitation applies at the surface of a planet and how it connects with what we learned earlier about…

Learning Objectives By the end of this section, you will be able to: We first review the history of the study of gravitation, with emphasis on those phenomena that for thousands of years have inspired philosophers and scientists to search…

Figure 13.1 Our visible Universe contains billions of galaxies, whose very existence is due to the force of gravity. Gravity is ultimately responsible for the energy output of all stars—initiating thermonuclear reactions in stars, allowing the Sun to heat Earth, and making…