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### Universal Gravitation

• Newton’s law of gravitation: two particles of masses m1 and m2, separated by a distance r, attract each other with a force that is directly proportional to m1 and m2, and inversely proportional to the square of r.
• The acceleration due to gravity, g, depends on the force by which the Earth pulls an object toward its center. Because the gravitational force depends on the distance from the center of the Earth, it follows that g depends also on that distance, and thus on the height above the surface of the Earth.
• For a satellite moving in a circular orbit around the Earth, the gravitational pull by the Earth is equal to the centripetal force.
• For the system consisting of the Earth and an object of mass m at a height h above the surface of the Earth, the gravitational potential energy is –GmM/(R+h), where G is the universal gravitational constant, M is the mass of the Earth, and R is its radius.
• If an object is launched from the surface of the Earth with an upward velocity exceeding a certain threshold velocity, known as the escape velocity, then the object will escape into outer space.

### Universal Gravitation

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Newton's Law of Gravity 0:09
• Two Particles of Mass m1,m2
• Force of Attraction
• Sphere and Small Particle of Mass m
• Two Spheres
• Variation of g With Altitude 7:24
• Consider Earth as an Object
• Force Applied To Object
• At or Near Surface of Earth
• Satellites 15:39
• Earth and Satellite
• Geosynchronous Satellite
• Gravitational Potential Energy 27:32
• Object and Earth Potential Energy=mgh
• P.E=0 When Objects are Infinitely Separated
• Total Energy
• If Object is Very Far From Earth, R=Infinity
• Escape 42:33
• Shoot an Object Which Should Not Come Back Down
• Conservation of Energy
• Object at Maximum Height (K.E=0)
• Escape Velocity (Rmax = Infinity)
• Extra Example 1: Density of Earth and Moon
• Extra Example 2: Satellite Orbiting Earth