1. Universal Gravitation
Ch 12 Notes
Universal Gravitation
Newton’s idea was that gravity was a universal force acting between any two objects.

2. Law of Universal Gravitation
Ch 12 Notes
Law of Universal Gravitation
In symbols, Newton’s Law of Universal Gravitation is:
Fgrav = G
Where G is a constant of proportionality.
G = 6.67 x N m2/kg2 Mm
r 2

3. Orbits

4. The Gravitational Field
Ch 12 Notes
The Gravitational Field
During the 19th century, the notion of the “field” entered physics (via Michael Faraday).
Objects with mass create an invisible disturbance in the space around them that is felt by other massive objects - this is a gravitational field.

5. The Gravitational Field
Ch 12 Notes
The Gravitational Field
All objects with mass create a gravitational field.

6. Gravitational Field Strength
Ch 12 Notes
Gravitational Field Strength
To measure the strength of the gravitational field at any point, measure the gravitational force, F, exerted on any “test mass”, m.
Gravitational Field Strength, g = F/m

7. Gravitational Field Strength
We can calculate the gravitational field produced by any mass by using the equation g = GM/r2 where r is the distance from the source mass, G is the universal gravitational constant, and M is the mass of the source mass.

8. Problem 1
Use the gravitational force law to find an approximate value for the mass of the Earth.

10. Ch 12 Notes
Problem 2
If an object weighs 270 N at the Earth’s surface, what will it weigh at an altitude equal to twice the radius of the Earth?
30 N

12. Ch 12 Notes
Problem 3
Determine the magnitude of the free fall acceleration at an altitude of 500 km. By what percentage is the weight of the body reduced at this altitude?
8.43 m/s^2

14. Ch 12 Notes
Problem 4
Two ocean liners, each with a mass of 40,000,000 kilograms are moving on parallel courses, 100 m apart. What is the magnitude of the acceleration of one of the liners towards the other due to their mutual gravitational attraction? Model the ships as particles
2.67 x 10^-7

16. Ch 12 Notes
Problem 5
On the way to the Moon the Apollo astronauts reached a point where the moon’s gravitational pull became stronger than the Earth’s.
Determine the distance of this point from the center of the Earth.
What is the acceleration due to the Earth’s gravity at this point?
a)3.46 x 10^8 m b) 3.34 x 10^-3 m/s^2 toward the center

18. Problem 6
Three uniform spheres of mass 2 kg, 4 kg, and 6 kg are placed at the corners of a right triangle as shown. Calculate the net gravitational force on the 4 kg sphere, assuming the spheres are isolated from the rest of the Universe.

19. Ch 12 Notes
Problem 6
(-100i j) pN