1. Newton’s Law of Universal Gravitation

2. Newton’s Law of Universal Gravitation
Newton's law of universal gravitation states that any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

4. Newton’s Law of Universal Gravitation
In other words:

5. Newton’s Law of Universal Gravitation
Practice: Object A and Object B are floating in space. Object A has a mass of 10,000 kg and Object B has a mass of 5,000 kg. From the center of mass of both objects the distance between them is 10 m. Draw a picture and calculate the gravitational force each object has on the other.

6. Newton’s Law of Universal Gravitation
Practice: Object A and Object B are floating in space. Object A has a mass of 10,000 kg and Object B has a mass of 10,000 kg. From the center of mass of both objects the distance between them is 10 m. Draw a picture and calculate the gravitational force each object has on the other.

7. Newton’s Law of Universal Gravitation
Practice: Object A and Object B are floating in space. Object A has a mass of 10,000 kg and Object B has a mass of 10,000 kg. From the center of mass of both objects the distance between them is 100 m. Draw a picture and calculate the gravitational force each object has on the other.

8. What do you notice?

9. What do you notice?

10. Newton’s Law of Universal Gravitation

11. Newton’s Law of Universal Gravitation
Practice: The gravitation force of two objects in space is 10,000 N. If the mass of Object A doubles what would be the new gravitational force?

12. Newton’s Law of Universal Gravitation
Practice: The gravitation force of two objects in space is 10,000 N. If the mass of Object A and Object B double what would be the new gravitational force?

13. Newton’s Law of Universal Gravitation
Practice: The gravitation force of two objects in space is 10,000 N. If the distance between the two objects doubles what would be the new gravitational force?

14. Newton’s Law of Universal Gravitation
Practice: The gravitation force of two objects in space is 10,000 N. If the distance between the two objects triples what would be the new gravitational force?

15. Newton’s Law of Universal Gravitation
Finding the acceleration of one of the objects. For mass 1 𝐹=𝐺 𝑚 1 𝑚 2 𝑑 2 𝑑𝑖𝑣𝑖𝑑𝑒 𝑏𝑦 𝑚 1 𝑠𝑜 𝑡ℎ𝑎𝑡 𝑎 1 = 𝐹 𝑚 1 =𝐺 𝑚 2 𝑑 2 For mass 2 𝐹=𝐺 𝑚 1 𝑚 2 𝑑 2 𝑑𝑖𝑣𝑖𝑑𝑒 𝑏𝑦 𝑚 1 𝑠𝑜 𝑡ℎ𝑎𝑡 𝑎 2 = 𝐹 𝑚 2 =𝐺 𝑚 1 𝑑 2

16. Newton’s Law of Universal Gravitation
Practice Problem: The gravitation force of two objects in space is 1 N. If the mass of Object A is 100,000 kg and the mass of Object B is 200,000 kg what would be the acceleration of Object A if the objects are 1.15 m apart?

17. Newton’s Law of Universal Gravitation
Practice Problem: The gravitation force of two objects in space is 1 N. If the mass of Object A is 100,000 kg and the mass of Object B is 200,000 kg what would be the acceleration of Object B if the objects are 1.15 m apart?

18. Newton’s Law of Universal Gravitation
Finding the mass of one of the objects. Finding mass 1 𝐹=𝐺 𝑚 1 𝑚 2 𝑑 2 𝑑𝑖𝑣𝑖𝑑𝑒 𝑏𝑦 𝐺 𝑚 2 𝑑 2 𝑠𝑜 𝑡ℎ𝑎𝑡 𝑚 1 = 𝐹 𝑚 1 =𝐺 𝑚 2 𝑑 2 For mass 2 𝐹=𝐺 𝑚 1 𝑚 2 𝑑 2 𝑑𝑖𝑣𝑖𝑑𝑒 𝑏𝑦 𝐺 𝑚 2 𝑑 2 𝑠𝑜 𝑡ℎ𝑎𝑡 𝑚 2 = 𝐹 𝑚 2 =𝐺 𝑚 1 𝑑 2

19. Newton’s Law of Universal Gravitation
Practice Problem: The gravitation force of two objects in space is 2 N. If the mass of Object A is 100,000 kg and the objects are 1.15 m apart what is the mass of Object B?

20. Newton’s Law of Universal Gravitation
Practice Problem: The gravitation force of two objects in space is 1 N. If the mass of Object B is 50,000 kg and the objects are 10 m apart what is the mass of Object B?