1. Chapter 7-2 Newton’s Law of Universal Gravitation St. Augustine Preparatory School January 14, 2015

2. Gravitational Force Gravitational force is the mutual force of attraction between particles of matter. Every particle has an attraction to every other particle, meaning that every object in our daily lives has an attraction to every other object – These attractions are very, very weak however. This is why we don’t notice these attractions.

3. Free Fall Orbiting objects are considered to be in free fall. Newton's Cannonball - Wikipedia (w/animations) Newton's Cannonball - Wikipedia (w/animations) Sir Isaac Newton hypothesized that if a cannonball was fired from the top of a very tall mountain at the right speed, it would continue to fall towards Earth at the same rate that Earth curves away from it. The cannonball would then orbit Earth, just like the moon.

4. Newton’s Law of Universal Gravitation The gravitational force between two objects depends on the masses and the distance that each objects center of gravity is separated by. F g is the force of gravity (N) G is the gravitation constant (6.673 x 10 -11 Nm 2 /kg 2 ) m 1 is the first mass m 2 is the second mass r 2 is the distance between the center of the two objects, squared.

5. Example Question Find the distance between the surface of a 0.300kg billiard ball and a 0.400kg billiard ball if the magnitude of the gravitational force between them is 8.92 x 10 -11 N. Assume both balls have a radius of 0.05 m.

6. Solution 0.05m The radius calculated is the distance between the center of both billiard balls. We only need the distance between the surfaces. To find this, we can do the following: d = 0.3m – 0.05m – 0.05m d = 0.2m The surfaces of the two balls are 0.2m apart.

7. An apple and the Earth If you throw an apple upwards, would it pull the Earth towards itself? Would the Earth pull the apple towards itself? Which one is exposed to the greater force?

8. An apple and Earth Try the math: – Mass of the Earth: 5.97 x 10 24 kg – Radius of Earth: 6.38 x 10 6 m – Mass of an apple: 0.102 kg – Radius of an apple: 0.04m – Height an apple is thrown: 4 m (randomly picked)

9. An apple and Earth Remember that F = ma, so for the apple: a = F/m = 0.998N / 0.102kg = 9.78 m/s 2 And for the Earth: a = F/m = 0.998N / 6.38 x 10 6 kg = 1.54 x 10 -7 m/s 2 As you can see, the acceleration the Earth gains is hardly noticeable, as where for the apple it is.

10. Solution Yes, the apple does pull the Earth towards itself, just as the Earth will pull the apple towards itself. The apple and the Earth actually experience the exact same force!

11. Practice Questions 1.Mars has a mass of about 6.4x10 23 kg, and it’s moon Phobos has a mass of about 9.6x10 15 kg. If the magnitude of the gravitational force between the two bodies is 4.6x10 15 N, how far apart are Mars and Phobos? 2.Two massive objects are placed with their centers 2550m apart. If the first object has a mass of 1.5x10 22 kg and the other object has a mass of 2.6x10 24 kg, at what acceleration will each of the objects move towards each other at? (you will need to calculate two separate accelerations).