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Gravity. Ch 11. Kepler’s Laws. LAW 1: All planets move in elliptical orbits with the Sun at one focus. LAW 2: A line joining any planet to the Sun sweeps out equal areas in equal times.

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## Gravity

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**Gravity**Ch 11**Kepler’s Laws**LAW 1: All planets move in elliptical orbits with the Sun at one focus.**LAW 2: A line joining any planet to the Sun sweeps out**equal areas in equal times.**LAW 3: The square of the period of any planet is**proportional to the cube of the semimajor axis of its orbit. C has the same value for all planets b/c force exerted by Sun on a planet varies inversely with the square of the distance from the Sun to the planet. Ellipse: Locus of points for which r1+r2=constant Semimajor axis: distance a Semiminor axis: distance b**Jupiter’s mean orbital radius is 5.2AU. What is the**period of Jupiter’s orbit around the Sun?1 AU is the mean distance from Earth to Sun.**Newton’s Law of Gravity**• Newton proved that an attractive force that varies inversely with the square of the distance between the Sun and a planet would result in an elliptical orbit, as observed by Kepler. • Bold assumption: This attractive force acts between any two objects. • Newton showed that laws of physics apply equally well to both terrestrial and nonterrestrial objects**Show that the gravitational force that attracts a 65kg man**to a 50kg woman when they are .50m apart is 8.7X10-7N.**This demonstrates that the gravitational force exerted by an**object of ordinary size on another such object is so small as to be unnoticeable. Calculate the force of attraction between two mosquitos that are .50m apart weighing 1X10-7N each. That’s the weight of about 9 mosquitos!!! A 50kg woman weighs about 490N – Half a billion times greater than the force between the man and woman.**What would be the free fall acceleration of an object at the**altitude of the space shuttle’s orbit, about 400km about the Earth’s surface?**You are trying to view the International Space Shuttle,**which travels in a roughly circular orbit around the Earth. If its altitude is 385km about the Earth’s surface, how long do you have to wait between sightings? Earth’s mass: 5.98X1024kgEarth’s radius: 6375km

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