Universal Gravitation The Big Idea: Everything pulls on everything else.

Discussion Here are some questions and answers which lead towards Newton’s Law of Universal Gravitation: 1. What causes the weight that each student feels? 2. What affects the size of the Earth’s pull on you? Why would you weigh a different amount on the Moon? 3. If the Earth is pulling down on you, then what else must be occurring, by Newton’s 3rd Law? 4. What happens to the strength of the pull of the Earth as you go further away from it?

Newton’s Law of Universal Gravitation Newton discovered that gravity is universal. Everything pulls on everything else in a way that involves only mass and distance.

Universal Gravitation Newton’s law of universal gravitation states that every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object. Newton deduced that the force decreases as the square of the distance between the centers of mass of the objects increases.

Universal Gravitation The force of gravity between objects depends on the distance between their centers of mass.

Universal Gravitation Your weight is less at the top of a mountain because you are farther from the center of Earth.

Universal Gravitation The Universal Gravitational Constant, G The law of universal gravitation can be expressed as an exact equation when a proportionality constant is introduced. The universal gravitational constant, G, in the equation for universal gravitation describes the strength of gravity.

Universal Gravitation The Universal Gravitational Constant, G The force of gravity between two objects is found by multiplying their masses, dividing by the square of the distance between their centers, and then multiplying this result by G. >The magnitude of G is given by the magnitude of the force between two masses of 1 kilogram each, 1 meter apart: 0.0000000000667 newton. In scientific notation: G = 6.67 × 10−11 N·m2/kg2 >The units of G are such as to make the force of gravity come out in newtons. Contributor: J. Flores Source: Prentice Hall; Conceptual Physics

Universal Gravitation The Mass of the Earth >Once the value of G was known, the mass of Earth was easily calculated. >The force that Earth exerts on a mass of 1 kilogram at its surface is 10 newtons. >The distance between the 1-kilogram mass and the center of mass of Earth is Earth’s radius, 6.4 × 106 meters. Contributor: J. Flores Source: Prentice Hall; Conceptual Physics So the mass of Earth m1 = 6 × 1024 kilograms.

Problem Find the gravitational attraction, which exists between a 60 kg boy and a 50 kg girl at a distance of 3 m. Now find the gravitational attraction between the 60 kg boy and the Earth using the Law of Universal Gravitation. Is the result surprising?

Field lines represent the gravitational field about Earth. Universal Gravitation Gravitational Fields Field lines represent the gravitational field about Earth. Contributor: J. Flores Source: Prentice Hall; Conceptual Physics

Gravitational Fields Inside a Planet Universal Gravitation Gravitational Fields Inside a Planet As you fall into a hole bored through Earth, your acceleration diminishes. The pull of the mass above you partly cancels the pull below. Contributor: J. Flores Source: Prentice Hall; Conceptual Physics

Gravitational Fields Inside a Planet Universal Gravitation Gravitational Fields Inside a Planet Starting at the North Pole end, you’d fall and gain speed all the way down to the center, and then overshoot and lose speed all the way to the South Pole. You’d gain speed moving toward the center, and lose speed moving away from the center. Without air drag, the trip would take nearly 45 minutes. Contributor: J. Flores Source: Prentice Hall; Conceptual Physics

Gravitational Fields Inside a Planet Universal Gravitation Gravitational Fields Inside a Planet At the beginning of the fall, your acceleration would be g, but it would decrease as you continue toward the center of Earth. As you are pulled “downward” toward Earth’s center, you are also being pulled “upward” by the part of Earth that is “above” you. When you get to the center of Earth, the net force on you is zero. There is no acceleration as you whiz with maximum speed past the center of Earth. Contributor: J. Flores Source: Prentice Hall; Conceptual Physics

Gravitational Fields Inside a Planet Universal Gravitation Gravitational Fields Inside a Planet In a cavity at the center of Earth, your weight would be zero, because you would be pulled equally by gravity in all directions. Contributor: J. Flores Source: Prentice Hall; Conceptual Physics

Universal Gravitation and Orbits