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Newton’s Law of Universal Gravitation Any two objects exert a gravitational force of attraction on each other. The magnitude of the force is proportional to the product of the gravitational masses of the objects, and inversely proportional to the square of the distance between them. Gm1m2 Fg 2 r G=6.67X10-11 N m2/kg2 BASIC PROBLEM Find the gravitational force between a baseball (m=0.3kg) and a billiard ball (m=0.4kg) if the distance between their centers is 0.3m. The gravitational force between two electrons 1.00m apart is 5.42X10-71N. Calculate the mass of an electron. What is the electrical force between these two electrons? A STELLAR PROBLEM We can consider the sun to be a satellite of our galaxy, the Milky Way. The sun, mass 2.0X1030kg, revolves around the center of the galaxy with a radius of 2.2X1020 m. The period of one rotation is 8.2X1016. a. Find the approximate mass of the galaxy. b. Assume the average star in the galaxy has the mass of the sun, find the number of stars in the galaxy. Acceleration due to gravity Find the acceleration due to gravity on Earth’s surface. Find the acceleration due to gravity on the surface of the asteroid in Armageddon. r = 2.35x105 m, m = 4.28x1020 kg. International Space Station The International Space Station has an orbital height of 370 km, what is its speed as orbits the earth? Earth mass – 5.97x1024kg Earth radius – 6.38x106m In minutes, how long does it take the ISS to rotate once around the Earth? Kepler’s laws Kepler’s laws Kepler’s 1st law The paths of the planets around the sun are ellipses with the sun at one focus point Kepler’s 2nd law An imaginary line drawn from a planet to the sun sweeps out equal areas in equal amounts of time as the planet travels along its elliptical path. Kepler’s 2nd law An imaginary line drawn from a planet to the sun sweeps out equal areas in equal amounts of time as the planet travels along its elliptical path. A1 A2 Kepler’s 2nd law If A1 = A2, then t1 = t2 t1 A1 A2 t2 Kepler’s 3rd law The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of the planets average distances from the sun. 2 A 2 B T T 3 A 3 B r r Problem- A Geosynchronous satellite What is the orbital radius of a geosynchronous satellite? (______________________) How far up from the surface of the earth is this satellite? Satellite problem Uranus requires 84 years to circle the sun. Find the distance from the sun to Uranus. Kepler’s Third Law Problems 1. Comet Halley returns every 74 years. Find the average distance from Halley to the sun. 2. Find the orbital radius of a Geosynchronous satellite. How far from the surface of the earth is the satellite located? 3. Mars has a period around the sun of 686 days. What is its average distance from the sun? 4. An asteroid revolves around the sun with an average orbital radius twice that of Earth’s. Predict the period of the asteroid in Earth years. 5. What is the period of a satellite that orbits the Earth at 6.7X106 m measured from the Earth’s center?