1. Universal Law of Gravitation
EQ: What is Newton’s law of universal gravitation and how does the mass and distance between objects affect the gravitational force?

2. Because of Newton’s 3rd law every body in the universe exerts a force of attraction on every other body.
This is Newton’s Universal Law of Gravitation
The force between two objects, due to their masses, is called the gravitational force (Fg)- the gravitational force is affected by mass and distance.

3. Universal Gravitational Constant- 6.67 x10-11
Masses of the 2 objects (kg)
Distance between
the objects from their center (m)
Gravitational force (N)

4. Example 1:What is the gravitational force between the Earth and the Moon?
mEarth = M = 6.0 x 1024 kg mMoon = m = 7.4 x 1022 kg r = 3.8 x 108 m G = 6.67 x 10-11
Fg = 2.1 x 1020

5. Example 2: What is the gravitational force between the Earth and Venus?
mEarth = M = 6.0 x 1024 kg mVenus = m = 5.0 x 1024 kg r = 3.8 x 1010 m G = 6.67 x 10-11
Answer:
F = 1.386x1018 N

6. The sun has a mass of 2. 0 x 1030 kg and a radius of 7. 0 x 105 km
The sun has a mass of 2.0 x 1030 kg and a radius of 7.0 x 105 km. What mass must be located at the sun’s surface for a gravitational force of 470 N to exist between the mass and the sun?

7. The gravitational attraction between the Earth and Mars is 8
The gravitational attraction between the Earth and Mars is 8.7 x 1016 N. The distance between the two planets is 5.5 x 1010m. Earth has a mass of 6.0 x 1024 kg. What’s the mass of Mars?

8. Answer behind Exit Ticket:
Distance also plays a role in the force of gravity.
-Explain how the force changes with respect to distance.
-Explain how the acceleration between 2 objects changes with respect to distance. (Hint: think about Newton’s 2nd Law of motion and the relationship between force, mass, and acceleration 𝑎= 𝐹 𝑚 )

9. Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is standing at sea level, a distance of 6.38 x 106 m from earth's center.
Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is in an airplane at feet above earth's surface. This would place the student a distance of 6.39 x 106 m from earth's center.

11. There is also a way to determine the gravitational field around one object:
This is now
the gravitational
Field Strength(GFS)

12. Example 3: What is the Gravitational Field Strength in Earth?
Radius of the Earth – 6.37 x 106 m

13. Example 4: What is the Gravitational field strength on the moon?
Radius of the Moon – 1.7 x 106 m

14. Is Gravity Diluted?
The distance d is in the denominator of this relationship, it can be said that the force of gravity is inversely related to the distance. This mathematical relationship is sometimes referred to as an inverse square law since one quantity depends inversely upon the square of the other quantity

15. Check your understanding
Suppose that two objects attract each other with a gravitational force of 16 units. If the distance between the two objects is doubled, what is the new force of attraction between the two objects?
Answer: F = 4 units
If the distance is increased by a factor of 2, then force will be decreased by a factor of 4 (22). The new force is then 1/4 of the original 16 units.
F = (16 N) / 4 = 4 units

16. Check your understanding
Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of both objects was doubled, and if the distance between the objects remained the same, then what would be the new force of attraction between the two objects?
Answer: F = 64 units
If each mass is increased by a factor of 2, then force will be increased by a factor of 4 (2*2). The new force is then 4 times the original 16 units.
F = (16 units ) • 4 = 64 units

17. Both the ULG and the GFS follow the Inverse square law:
ULG-If the distance between two objects is doubled the gravitational attraction is (1/4) of the original. OR
GFS-If we travel beyond the Earth by a distance that is double it’s radius than we will only feel a quarter of Earth’s gravitational pull (9.81 m/s2/4 = 2.45 m/s2).

18. re = 6.4 x 106 m 1x 2x 3x 4x ¼ re= 2.24 m/s2 1/9 re = 1.09 m/s2