 The Law of Universal Gravitation Isaac Newton’s Big Idea MoonApple Earth.

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The Law of Universal Gravitation Isaac Newton’s Big Idea MoonApple Earth

Newton’s Big Idea The centripetal force that holds the moon in orbit is the same force that pulls an apple toward the ground Orbiting objects are in free-fall! –They never hit the ground because they are moving sideways fast enough –Recall that an object in free-fall experiences only one force: gravity

Gravitational Force Gravitational force is the mutual force of attraction between objects with mass –Gravity acts between any two objects with mass –The closer the objects, the greater the force –Gravity holds the Moon in orbit around Earth –Gravity holds the planets in orbit around the Sun –The gravity we feel on Earth comes from the enourmous size of the Earth’s mass

Gravitational Force (cont.) Newton’s Law of Universal Gravitation: F g = G  where F g is the gravitational force m 1 is the mass of object 1 m 2 is the mass of object 2 r is the dist. between the objects G is the constant of universal gravitation (= 6.673  10 -11 N·m 2 /kg 2 ) m1m2m1m2 r2r2

Details of NLUG Gravitational force: 1.Is attractive 2.Points toward the center of the other object 3.Comes in force-pairs that are equal in magnitude, opposite in direction 4.Distance, r, is center-to-center Earth Moon FgFg FgFg r

Example What is the force of the Earth on the Moon? F g = Gm 1 m 2 /r 2 = (6.673  10 -11 Nm 2 /kg 2 )(5.97  10 24 kg)(7.35  10 22 kg) (3.84  10 8 m) 2 = 1.99  10 20 N What is the force of the Moon on the Earth?

Gravity on Earth Let’s apply NLUG to objects near the surface of Earth –We already know that F g = mg where m is the mass of an object at the Earth’s surface –Let M = mass of Earth, R = radius of Earth –Objects on Earth are approx. a distance R from the center Earth R mass = M m

–Combine F g = mg with NLUG: mg = F g = GmM/R 2 –We get the formula for the acceleration due to gravity, “little g”, in terms of G, M, and R g = GM/R 2 This formula can be generalized for any planet P g P = GM P /R P 2 Gravity on Earth (cont.)

Examples On Earth we have g = (6.673  10 -11 Nm 2 /kg 2 )(5.97  10 24 kg) (6.38  10 6 m) 2 = 9.79 m/s 2 On Mars we have g = (6.673  10 -11 Nm 2 /kg 2 )(6.42  10 23 kg) (3.40  10 6 m) 2 = 3.71 m/s 2

What was Newton’s Big Idea? 1.The force that holds the moon in orbit is a different kind of force than the force that makes an apple fall. 2.Both the Moon and a falling apple are in free-fall in the Earth’s gravitational field. 3.What goes up, must come down. 4.Gravity doesn’t affect the Moon; it only affects falling objects like apples.

The Moon doesn’t crash into the Earth because the Moon 1.does not experience the pull of gravity. 2.moves in a perfectly circular orbit. 3.is moving sideways fast enough to stay in orbit. 4.experiences other forces from the sun and planets.

The Earth and Moon put gravitational forces on each other. What can we say about the size of those forces? 1.Force on Earth < Force on Moon 2.Force on Earth > Force on Moon 3.Force on Earth = Force on Moon 4.It varies: sometimes the force on the Moon is bigger than the force on the Earth, or vice versa

The direction of the gravitation force between two objects is such that 1.the two objects attract each other exactly along the line connecting their centers. 2.the two objects repel each other. 3.the two objects sometimes attract each other and sometimes repel each other. 4.the two objects attract each other but at an angle of up to 90 .

What is the role of distance on gravity? 1.The closer two objects are, the smaller the force of gravity. 2.The closer two objects are, the greater the force of gravity. 3.Gravity doesn’t change with distance. 4.The force of gravity decreases as objects get closer together.

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