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Universal Gravitation Newton’s Law of Universal Gravitation states that gravity is universal and that all objects attract each other with some force of gravitational attraction You and the person next to you are attracted to each other with some small force…maybe around 2 x 10-7 Newtons The formula for Universal Gravitation is: F = Gm1m2/d2 G is the gravitational constant (it always equals 6.67 x 10-11) ○ m1 is the mass of one object ○ m2 is the mass of the other object ○ d is the distance between the two objects ○ How changing the mass effects the gravitational force In general, the larger the mass the larger the force ! How changing the distance effects the gravitational force Example Determine the force of gravitational attraction between Earth, which has a mass of 5.98 x 1024 kg, and a 70 kg physics student who is standing at sea level, a distance of 6.38 x 106 m from Earth’s center. F = Gm1m2/d2 F = (6.67 x 10-11)(5.98 x 1024)(70) (6.38 x 106)2 F = 2.79 x 1016 4.07 x 1013 F = 685 N Kepler’s Laws of Planetary Orbit In the 1600’s Kepler came up with the Laws of Planetary Motion that are still used today These laws go against what the church at the time believed (in a Earth centered solar system) 1st Law: Law of Ellipses The path of the planets around the sun are elliptical in shape with the center of the sun being located at one focus 2nd Law: Law of Equal Areas This law states that an imaginary line from the sun to a planet sweeps out equal areas in equal time intervals 3rd Law: Law of Periods This law states that the square of the orbital period (how long it takes the planet to orbit the sun) is proportional to the cube of its distance from the Sun 2 P 3 R Basically, this means the farther away a planet is from the Sun, the longer it takes to orbit the Sun and the relationships are proportional!