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**Isaac Newton’s 3rd Law and the Universal Law of Gravitation**

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**= a push or pull acting on an object.**

Force = a push or pull acting on an object. Examples: gravity = pull electrostatic attraction = pull electrostatic repulsion = push

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**Newton’s Second Law of Motion:**

The acceleration of an object is directly proportional to the force acting on it, and inversely proportional to its mass. In mathematical form: Or alternatively:

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**Example of Newton’s Second Law:**

A package of cookies has mass m = kilograms, And experiences gravitational acceleration g = 9.8 meters/second2 How large is the force acting on the cookies?

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**Newton’s Third Law of Motion:**

For every action, there is an equal and opposite reaction. Whenever A exerts a force on B, B exerts a force on A that’s equal in size and opposite in direction. All forces come in pairs.

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**Example of Newton’s Third Law:**

Cookies push on hand: F = 1 pound, downward. Hand pushes on cookies: F = 1 pound, upward. Remove hand! Earth pulls on cookies: F = 1 pound, downward. Cookies pull on earth: F = 1 pound, upward.

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**THIRD Law states: force on Earth = force on cookies**

SECOND Law states: acceleration = force divided by mass Mass of Earth = 1025 x mass of cookies Therefore, acceleration of cookies = x acceleration of Earth. (Cookies reach a high speed while the Earth hardly budges.)

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**But…why do the cookies and the Earth exert a force on each other?**

Newton’s Law of Gravity states that gravity is an attractive force acting between ALL pairs of massive objects. Gravity depends on: (1) MASSES of the two objects, (2) DISTANCES between the objects.

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**Newton’s question: can GRAVITY be the force keeping the Moon in its orbit?**

Newton’s approximation: Moon is on a circular orbit. Even if its orbit were perfectly circular, the Moon would still be accelerated.

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**The Moon’s orbital speed:**

radius of orbit: r = 3.8 x 108 m circumference of orbit: 2pr = ???? m orbital period: T = 27.3 days = ???? sec orbital speed: v = (2pr)/T = ??? m/sec = ? km/sec!

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**The Moon’s orbital speed:**

radius of orbit: r = 3.8 x 108 m circumference of orbit: 2pr = 2.4 x 109 m orbital period: T = 27.3 days = 2.4 x 106 sec orbital speed: v = (2pr)/T = 103 m/sec = 1 km/sec!

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**Acceleration required to keep Moon on a circular orbit**

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**Ratio of Accelerations to Distances**

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**Bottom Line Triumph for Newton!!**

If gravity goes as one over the square of the distance, Then it provides the right acceleration to keep the Moon on its orbit (“to keep it falling”). Triumph for Newton!!

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Figure 5-2 The force on a 0.1-kilogram mass at various distances from Earth. Notice that the force decreases as the square of the distance. Fig. 5-2, p.81

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Figure 5-3 The sum of all the forces on the apple exerted by all portions of Earth acts as if all the mass were located at Earth’s center. Fig. 5-3, p.82

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**Figure 5-1 If the sphere’s radius is doubled, the sphere’s surface increases by a factor of 4.**

Fig. 5-1, p.80

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**Earth's surface 6.38 x 106 m 9.8 1000 km above surface 7.38 x 106 m**

Location Distance from Earth's center (m) Value of g m/s2 Earth's surface 6.38 x 106 m 9.8 1000 km above surface 7.38 x 106 m 7.33 2000 km above surface 8.38 x 106 m 5.68 3000 km above surface 9.38 x 106 m 4.53 4000 km above surface 1.04 x 107 m 3.70 5000 km above surface 1.14 x 107 m 3.08 6000 km above surface 1.24 x 107 m 2.60 7000 km above surface 1.34 x 107 m 2.23 8000 km above surface 1.44 x 107 m 1.93 9000 km above surface 1.54 x 107 m 1.69 10000 km above surface 1.64 x 107 m 1.49 50000 km above surface 5.64 x 107 m 0.13

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p. 83: The attraction between these spheroidal friends depends on the distance between their centers. p.83

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**(4) Newton’s Law of Gravity:**

The gravitational force between two objects F = gravitational force M = mass of one object m = mass of the second object r = distance between centers of objects G = “universal constant of gravitation”

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**Example: What is gravitational force between Earth and cookies?**

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**Example: What is gravitational force between Earth and cookies?**

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Table p.85

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**p. 85: The lunar rover would collapse under its own weight if used on Earth. (NASA)**

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**p. 89 (bottom): Star clusters provide evidence of gravity at work between stars. (NASA)**

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**p. 90: The Andromeda Galaxy is similar to our own Milky Way Galaxy**

p.90: The Andromeda Galaxy is similar to our own Milky Way Galaxy. (California Institute of Technology/Palomar Observatory) p.90

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Q5- 3: (NASA) Fig. Q5-3, p.92

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Fig. Q5-19, p.93

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Q5-25: (NASA) Fig. Q5-25, p.93

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**Isaac Newton (1643-1727): English**

Discovered: three laws of motion, one law of universal gravitation.

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