# Newtons Law of Universal Gravitation Newtons Law of

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Newton’s Law of Universal Gravitation

Newton’s Law of Universal Gravitation • Describes the attraction between two (or more) bodies due to force of gravity between them • Every object puts a gravitational force on every single other object • “Universal” means everywhere in the universe – i. e. , gravity exists, even in space

Gravitation • Every mass attracts every other mass by a force (this force is gravity!) • Objects want to be pulled toward each other, therefore gravity is an attractive force • This force points along an imaginary line connecting the two masses. Earth feels a gravity pull from the sun Sun feels a gravity pull from the Earth

Pair and Share – Part I • Turn to the person next to you, and spend the next 2 minutes discussing the following questions: 1. What does “universal” mean? 2. Is there gravity in space? 3. In which direction does the gravitational force between two bodies point? 4. Does gravity create a “push” or a “pull” between two bodies?

Pair and Share – Part I - Answers Spend 1 minute with your partner discussing these answers Were you correct? If not, what misconceptions guided you astray? 1. What does “universal” mean? Exists everywhere in the universe; is a law that is applicable everywhere 2. Is there gravity in space? Yes! There is gravity everywhere! 3. In which direction does the gravitational force between two bodies point? Along an invisible line connecting the two bodies. 4. Does gravity create a “push” or a “pull” between two objects? Pull

Pair and Share – Part II • Turn to the person next to you, and spend the next 2 minutes answering the following questions: 1. Does an apple hanging on a tree feel a pull of gravity from the earth? Why? 2. Does the earth feel a pull of gravity from the apple? Why? 3. Is there a gravitational force between you and your partner right now? Why or why not?

Pair and Share – Part II - Answers Spend 1 minute with your partner discussing these answers. Were you correct? If not, what misconceptions led you astray? 1. Does an apple hanging on a tree feel a pull of gravity from the earth? Why? Yes – all objects exert a gravitational force on each other. The apple wants to be pulled toward the earth due to gravity. 2. Does the earth feel a pull of gravity from the apple? Why? Yes – see #1. The earth wants to be pulled toward the apple due to gravity! 3. Is there a gravitational force between you and your partner right now? Why or why not? Yes! Any two objects in the universe feel a gravitational force between themselves.

Gravitational “Constant” • When Newton came up with the Law of Universal Gravitation, he discovered a new “constant” which he called the “Universal Gravitational Constant” • This constant has a value of: G = 6. 67 x 10 -11 (units are Nm 2/kg 2) • (Memorize this!)

Gravitation Equation • • • FG = Force of Gravity (N) G = “Universal Gravitation Constant” = 6. 67 x 10 -11 Nm 2/kg 2 m 1 = mass of the first object (kg) m 2 = mass of the second object (kg) r = distance between the objects (m)

Sample Problem #1 • Ex: You and your boyfriend / girlfriend each have a mass of 60 kg, and the two of you are sitting 20 cm apart. Calculate the gravitational attraction force between you. Givens: m 1 = 60 kg m 2 = 60 kg G = 6. 67 x 10 -11 Nm 2/kg 2 r = 0. 2 m • Notice how small the Force is! What could we do to increase it?

Sample Problem #2 • Ex: If you have a mass of 55 kg, calculate the force of gravity you feel from the moon when standing on the moon’s surface. The mass of the moon is 7. 4 x 1022 kg, and the radius of the moon is 1. 74 x 106 m. Givens: m 1 = 55 kg m 2 = 7. 4 x 1022 kg G = 6. 67 x 10 -11 Nm 2/kg 2 r = 1. 74 x 106 • This would be your weight on the moon! Cool, huh?

Pair and Share – Part III Spend 2 minutes with your partner discussing these questions. 1. Does the formula for FG depend on just one mass, or on both masses? 2. How does the distance between the two objects affect FG? 3. If you are standing on the surface of Jupiter, and you calculate the FG between you and Jupiter, what does the answer (in Newtons) represent?

Pair and Share – Part III - Answers Spend 1 minute with your partner discussing these answers. 1. Does the formula for FG depend on just one mass, or on both masses? Both m 1 and m 2 2. How does the distance between the two objects affect FG? r must be squared in the denominator (this is called an “inverse-square” law) 3. If you are standing on the surface of Jupiter, and you calculate the FG between you and Jupiter, what does the answer (in Newtons) represent? Your weight on Jupiter

Acceleration due to Gravity • Starting with the Universal Gravitation Equation, we have: • Since the force of gravity (FG) is also known as WEIGHT, we can re-write this equation to be • • G = 6. 67 x 10 -11 Nm 2/kg 2 m 1 = mass of YOU (or the object on the surface of the planet) m 2 = mass of the planet (kg) r = distance between you and the center of the planet (i. e. , radius of planet!)

Acceleration due to Gravity • Now, cancel out m 1 on both sides: • And you get:

Acceleration due to Gravity • Therefore, the acceleration due to gravity on any planet is: • • g = acceleration due to gravity (m/s 2) G = 6. 67 x 10 -11 Nm 2/kg 2 m = mass of the planet (kg) r = radius of planet (m)

Sample Problem #3 • The mass of the earth is 5. 98 x 1024 kg, and the radius of the earth is 6. 38 x 106 m. Calculate the acceleration due to gravity on the surface of the earth. • THIS is why we’ve been using g = 9. 8 m/s 2 all year!