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Newton’s Law of Universal Gravitation

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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.

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G=6.67X10 -11 N m 2 /kg 2

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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.

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We can consider the sun to be a satellite of our galaxy, the Milky Way. The sun, mass 2.0X10 30 kg, revolves around the center of thee galaxy with a radius of 2.2X10 20 m. The period of one rotation is 2.6X10 8 years. 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. We can consider the sun to be a satellite of our galaxy, the Milky Way. The sun, mass 2.0X10 30 kg, revolves around the center of thee galaxy with a radius of 2.2X10 20 m. The period of one rotation is 2.6X10 8 years. 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. A STELLAR PROBLEM

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Kepler’s laws

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Kepler’s 1st law The paths of the planets around the sun are ellipses with the sun at one focus point

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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.

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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.

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Satellite problem Uranus requires 84 years to circle the sun. Find the distance from the sun to Uranus.

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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? What is the orbital radius of a geosynchronous satellite? (______________________) How far up from the surface of the earth is this satellite?

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