Newton’s Law of Universal Gravitation. gravityDescribes the attraction between two (or more) bodies due to force of gravity between them objectEvery object.

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Universal Gravitation

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Presentation transcript:

Newton’s Law of Universal Gravitation

gravityDescribes the attraction between two (or more) bodies due to force of gravity between them objectEvery object puts a gravitational force on every single other object everywhere“Universal” means everywhere in the universe – i.e., gravity exists, even in space

Gravitation attractsEvery mass attracts every other mass by a force (this force is gravity!) pulledObjects 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

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 (units are Nm 2 /kg 2 ) You can store this value in calculator: 6.67x STO -> ALPHA -> G -> ENTER

Gravitation Equation F G = Force of Gravity (N) G = “Universal Gravitation Constant” = 6.67 x Nm 2 /kg 2 m 1 = mass of the first object (kg) m 2 = mass of the second object (kg) r = distance between the centers of the objects (m)

Sample Problem #1 cmEx: You and your boyfriend / girlfriend each have a mass of 60kg, and the two of you are sitting 20 cm apart. Calculate the gravitational attraction force between you.

Sample Problem #1 cmEx: You and your boyfriend / girlfriend each have a mass of 60kg, and the two of you are sitting 20 cm apart. Calculate the gravitational attraction force between you. m 1 = 60 kg m 2 = 60 kg G = 6.67 x Nm 2 /kg 2 r = 0.2 m Givens:

Sample Problem #1 cmEx: You and your boyfriend / girlfriend each have a mass of 60kg, and the two of you are sitting 20 cm apart. Calculate the gravitational attraction force between you. m 1 = 60 kg m 2 = 60 kg G = 6.67 x Nm 2 /kg 2 r = 0.2 m Givens: 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 kg, and the radius of the moon is 1.74 x 10 6 m.

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 kg, and the radius of the moon is 1.74 x 10 6 m. m 1 = 55 kg m 2 = 7.4 x kg G = 6.67 x Nm 2 /kg 2 r = 1.74 x 10 6 Givens:

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 kg, and the radius of the moon is 1.74 x 10 6 m. m 1 = 55 kg m 2 = 7.4 x kg G = 6.67 x Nm 2 /kg 2 r = 1.74 x 10 6 Givens: This would be your weight on the moon! Cool, huh?

Acceleration due to Gravity Starting with the Universal Gravitation Equation, we have:

Acceleration due to Gravity WEIGHTSince the force of gravity (F G ) is also known as WEIGHT, we can re-write this equation to be G = 6.67 x 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 m1 on both sides:

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 Nm 2 /kg 2 m = mass of the planet (kg) r = radius of planet (m) NOT on the formula chart!!! This equation is NOT on the formula chart!!!

Sample Problem #3 The mass of the earth is 5.98 x kg, and the radius of the earth is 6.38 x 10 6 m. Calculate the acceleration due to gravity on the surface of the earth.

Sample Problem #3 The mass of the earth is 5.98 x kg, and the radius of the earth is 6.38 x 10 6 m. Calculate the acceleration due to gravity on the surface of the earth.

Sample Problem #3 The mass of the earth is 5.98 x kg, and the radius of the earth is 6.38 x 10 6 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!