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• Who discovered gravity? • How in the world can we determine the mass of Earth? I mean, you can’t put it on a scale or balance! • Is gravity a strong force? Objectives 1. Historical perspective 2. Determining Newton’s Law of Universal Gravitation 3. Defining the Universal Gravitational Force equation involving two objects 4. Confirming acceleration due to gravity is 9.8 m/s2. Earth’s Radius • There is a water well that is directly under the sun at noon on the Summer Solstice in Syene, Egypt. • There is a tower of a known distance from the water well in Alexandria, Egypt. • In 235 B.C. the angle of the shadow of the tower was measured on the Summer Solstice. It was approx. 1/50th of 360 degrees (7.1 degrees). Thus the distance from the tower to the water well is 1/50th of the circumference of Earth. Law of Universal Gravitation The Law of Universal Gravitation Newton (1642-1727) proposed that the force which makes an apple fall from a tree towards the earth is the same force which keeps the moon orbiting Earth and Earth orbiting the Sun. In fact, he claimed that this same force called gravity governs the Universe. (1686) In his terms… any two bodies exert a force upon each other. Say WHAT!?! Newton’s Law of Gravitation m1m2 Fg 2 r m1m2 Fg const _ of _ proportionality 2 r Gm1m2 Fg 2 r Unit analysis… G = 6.67 X 10^¯11 N•m²/Kg² • G is the Universal Gravitational Constant. It was needed to complete the calculations of Universal Gravitation. But it’s SO SMALL! How can we measure something so small? • In 1798 Henry Cavendish developed an experiment which did indeed measure something so small. Earth’s Mass • Once G is known, the mass of any object can be determined. • Solve for mearth. • Fg (?) = G(√) m₁(√) mearth(?) rearth (√) • Fg = m₁ g • Now solve for g!!!! • Mearth = 5.98 * 10 ²⁴ Kg. • HOLY SMOKES!!!! • Compare this mass to everyday objects. Applications • • • • Tides Black holes Planet/ Star formation Satellite motion (GPS, weather, spying!) Homework • Pg 242 Practice C • Due tomorrow